Daily Papers

The upper 6 GHz (U6G) band with XL-MIMO is a key enabler for sixth-generation wireless systems, yet intelligent radiomap prediction for such systems remains challenging. Existing datasets support only small-scale arrays (up to 8x8) with predominantly isotropic antennas, far from the 1024-element directional arrays envisioned for 6G. Moreover, current methods encode array configurations as scalar parameters, forcing neural networks to extrapolate array-specific radiation patterns, which fails when predicting radiomaps for configurations absent from training data. To jointly address data scarcity and generalization limitations, this paper advances XL-MIMO radiomap prediction from three aspects. To overcome data limitations, we construct the first XL-MIMO radiomap dataset containing 78400 radiomaps across 800 urban scenes, five frequency bands (1.8-6.7 GHz), and nine array configurations up to 32x32 uniform planar arrays with directional elements. To enable systematic evaluation, we establish a comprehensive benchmark framework covering practical scenarios from coverage estimation without field measurements to generalization across unseen configurations and environments. To enable generalization to arbitrary beam configurations without retraining, we propose the beam map, a physics-informed spatial feature that analytically computes array-specific coverage patterns. By decoupling deterministic array radiation from data learned multipath propagation, beam maps shift generalization from neural network extrapolation to physics-based computation. Integrating beam maps into existing architectures reduces mean absolute error by up to 60.0% when generalizing to unseen configurations and up to 50.5% when transferring to unseen environments. The complete dataset and code are publicly available at https://lxj321.github.io/MulticonfigRadiomapDataset/.

We propose BERMo, an architectural modification to BERT, which makes predictions based on a hierarchy of surface, syntactic and semantic language features. We use linear combination scheme proposed in Embeddings from Language Models (ELMo) to combine the scaled internal representations from different network depths. Our approach has two-fold benefits: (1) improved gradient flow for the downstream task as every layer has a direct connection to the gradients of the loss function and (2) increased representative power as the model no longer needs to copy the features learned in the shallower layer which are necessary for the downstream task. Further, our model has a negligible parameter overhead as there is a single scalar parameter associated with each layer in the network. Experiments on the probing task from SentEval dataset show that our model performs up to 4.65% better in accuracy than the baseline with an average improvement of 2.67% on the semantic tasks. When subject to compression techniques, we find that our model enables stable pruning for compressing small datasets like SST-2, where the BERT model commonly diverges. We observe that our approach converges 1.67times and 1.15times faster than the baseline on MNLI and QQP tasks from GLUE dataset. Moreover, our results show that our approach can obtain better parameter efficiency for penalty based pruning approaches on QQP task.

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

The paper shows that the application of the fixed-effect multiple linear regression model to an overparameterized dataset is equivalent to fitting the data with a hyper-curve parameterized by a single scalar parameter. This equivalence allows for a predictor-focused approach, where each predictor is described by a function of the chosen parameter. It is proven that a linear model will produce exact predictions even in the presence of nonlinear dependencies that violate the model assumptions. Parameterization in terms of the dependent variable and the monomial basis in the predictor function space are applied here to both synthetic and experimental data. The hyper-curve approach is especially suited for the regularization of problems with noise in predictor variables and can be used to remove noisy and "improper" predictors from the model.

Molecular docking is critical to structure-based virtual screening, yet the throughput of such workflows is limited by the expensive optimization of scoring functions involved in most docking algorithms. We explore how machine learning can accelerate this process by learning a scoring function with a functional form that allows for more rapid optimization. Specifically, we define the scoring function to be the cross-correlation of multi-channel ligand and protein scalar fields parameterized by equivariant graph neural networks, enabling rapid optimization over rigid-body degrees of freedom with fast Fourier transforms. The runtime of our approach can be amortized at several levels of abstraction, and is particularly favorable for virtual screening settings with a common binding pocket. We benchmark our scoring functions on two simplified docking-related tasks: decoy pose scoring and rigid conformer docking. Our method attains similar but faster performance on crystal structures compared to the widely-used Vina and Gnina scoring functions, and is more robust on computationally predicted structures. Code is available at https://github.com/bjing2016/scalar-fields.

This note clarifies the relationship between the recent TurboQuant work and the earlier DRIVE (NeurIPS 2021) and EDEN (ICML 2022) schemes. DRIVE is a 1-bit quantizer that EDEN extended to any b>0 bits per coordinate; we refer to them collectively as EDEN. First, TurboQuant_{mse} is a special case of EDEN obtained by fixing EDEN's scalar scale parameter to S=1. EDEN supports both biased and unbiased quantization, each optimized by a different S (chosen via methods described in the EDEN works). The fixed choice S=1 used by TurboQuant is generally suboptimal, although the optimal S for biased EDEN converges to 1 as the dimension grows; accordingly TurboQuant_{mse} approaches EDEN's behavior for large d. Second, TurboQuant_{prod} combines a biased (b-1)-bit EDEN step with an unbiased 1-bit QJL quantization of the residual. It is suboptimal in three ways: (1) its (b-1)-bit step uses the suboptimal S=1; (2) its 1-bit unbiased residual quantization has worse MSE than (unbiased) 1-bit EDEN; (3) chaining a biased (b-1)-bit step with a 1-bit unbiased residual step is inferior to unbiasedly quantizing the input directly with b-bit EDEN. Third, some of the analysis in the TurboQuant work mirrors that of the EDEN works: both exploit the connection between random rotations and the shifted Beta distribution, use the Lloyd-Max algorithm, and note that Randomized Hadamard Transforms can replace uniform random rotations. Experiments support these claims: biased EDEN (with optimized S) is more accurate than TurboQuant_{mse}, and unbiased EDEN is markedly more accurate than TurboQuant_{prod}, often by more than a bit (e.g., 2-bit EDEN beats 3-bit TurboQuant_{prod}). We also repeat all accuracy experiments from the TurboQuant paper, showing that EDEN outperforms it in every setup we have tried.

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the kinetic model serve as an efficient alternative, but typically require closure assumptions to model unrepresented higher-order moments. In this study, we present a learning framework based on neural networks that exploit rotational symmetries in the closure terms to learn accurate closure models directly from kinetic simulations. The data-driven closures demonstrate excellent a-priori predictions comparable to the state-of-the-art Bingham closure. We provide a systematic comparison between different neural network architectures and demonstrate that nonlocal effects can be safely ignored to model the closure terms. We develop an active learning strategy that enables accurate prediction of the closure terms across the entire parameter space using a single neural network without the need for retraining. We also propose a data-efficient training procedure based on time-stepping constraints and a differentiable pseudo-spectral solver, which enables the learning of stable closures suitable for a-posteriori inference. The coarse-grained simulations equipped with data-driven closure models faithfully reproduce the mean velocity statistics, scalar order parameters, and velocity power spectra observed in simulations of the kinetic theory. Our differentiable framework also facilitates the estimation of parameters in coarse-grained descriptions conditioned on data.

Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function f which is only accessible via point evaluations. It is typically used in settings where f is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network architectures. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.

Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap online diagnostics, mean pairwise attention-head cosine similarity and entropy standard deviation, that track training dynamics from attention activations alone and complement loss-landscape diagnostics at lower compute cost. Across eleven experimental conditions and three model scales (0.82M to 85M parameters), the weight-decay axis separates memorization, developmental grokking, and collapse. A near-transition logistic fit localizes the memorization-to-developmental boundary at λ_c=0.0158 (95% CI [0.0109, 0.0200], N=210); a power-law fit gives an empirical exponent ν=0.757 (CI [0.725, 0.799]). Reference exponents ν=1/2 and 3D Ising νapprox 0.63 lie outside this empirical CI under our four-bin grid, so we report ν as empirical and defer universality-class identification to denser finite-size-scaling work. A horizon-matched multi-task replication (n=280, four modular operations) preserves the weight-decay control pattern; a paired attention-head re-initialization experiment at λ=0.05 changes Phase-2 amplitude (Cohen's d=-1.190, n=10, p_t=4.5 times 10^{-3}), while matched weight-norm clipping does not. Three cross-architecture probes (4L MLP, 4L LSTM, and 4L Mamba; each n=70) replicate the weight-decay-controlled transition with architecture-specific λ_c values. Main diagnostic claims are scoped to modular arithmetic in small transformer attention models; the non-attention experiments are scope probes, and architecture-wide, language-model, and universality-class claims are out of scope.

Some time ago, Seiberg and Witten solved for moduli spaces of vacua parameterized by scalar vacuum expectation values in N=2 gauge theories. More recently, new vacua associated to soft theorems and asymptotic symmetries have been found. This paper takes some first steps towards a complete picture of the infrared geometry of N=2 gauge theory incorporating both of these infrared structures.

This paper introduces EnergyFlow, a framework that unifies generative action modeling with inverse reinforcement learning by parameterizing a scalar energy function whose gradient is the denoising field. We establish that under maximum-entropy optimality, the score function learned via denoising score matching recovers the gradient of the expert's soft Q-function, enabling reward extraction without adversarial training. Formally, we prove that constraining the learned field to be conservative reduces hypothesis complexity and tightens out-of-distribution generalization bounds. We further characterize the identifiability of recovered rewards and bound how score estimation errors propagate to action preferences. Empirically, EnergyFlow achieves state-of-the-art imitation performance on various manipulation tasks while providing an effective reward signal for downstream reinforcement learning that outperforms both adversarial IRL methods and likelihood-based alternatives. These results show that the structural constraints required for valid reward extraction simultaneously serve as beneficial inductive biases for policy generalization. The code is available at https://github.com/sotaagi/EnergyFlow.

Recent results from Type Ia supernovae (SNe Ia) and baryon acoustic oscillations (BAO), in combination with cosmic microwave background (CMB) measurements, have focused renewed attention on dark energy models with a time-varying equation-of-state parameter, w(z). In this paper, we describe the simplest, physically motivated models of evolving dark energy that are consistent with the recent data, a broad subclass of the so-called thawing scalar field models that we dub w_ϕCDM. We provide a quasi-universal, quasi-one-parameter functional fit to the scalar-field w_ϕ(z) that captures the behavior of these models more informatively than the standard w_0w_a phenomenological parametrization; their behavior is completely described by the current value of the equation-of-state parameter, w_0=w(z=0). Combining current data from BAO (DESI Data Release 2), the CMB (Planck and ACT), large-scale structure (DES Year-3 3times2pt), SNe Ia (DES-SN5YR), and strong lensing (TDCOSMO + SLACS), for w_ϕCDM we obtain w_0=-0.904_{-0.033}^{+0.034}, 2.9σ discrepant from the Λ cold dark matter (ΛCDM) model. The Bayesian evidence ratio substantially favors this w_ϕCDM model over ΛCDM. The data combination that yields the strongest discrepancy with ΛCDM is BAO+SNe Ia, for which w_0=-0.837^{+0.044}_{-0.045}, 3.6σ discrepant from ΛCDM and with a Bayesian evidence ratio strongly in favor. We find that the so-called S_8 tension between the CMB and large-scale structure is slightly reduced in these models, while the Hubble tension is slightly increased. We forecast constraints on these models from near-future surveys (DESI-extension and the Vera C. Rubin Observatory LSST), showing that the current best-fit w_ϕCDM model will be distinguishable from ΛCDM at over 9σ.

Pre-trained large language models (LLMs) require fine-tuning to improve their responsiveness to natural language instructions. Federated learning (FL) offers a way to perform fine-tuning using the abundant data on end devices without compromising data privacy. Most existing federated fine-tuning methods for LLMs rely on parameter-efficient fine-tuning techniques, which may not reach the performance heights possible with full-parameter tuning. However, the communication overhead associated with full-parameter tuning is prohibitively high for both servers and clients. This work introduces FedKSeed, a novel approach that employs zeroth-order optimization (ZOO) with a set of random seeds. It enables federated full-parameter tuning of billion-sized LLMs directly on devices. Our method significantly reduces transmission requirements between the server and clients to just a few scalar gradients and random seeds, amounting to only a few thousand bytes. Building on this, we develop a strategy to assess the significance of ZOO perturbations for FL, allowing for probability-differentiated seed sampling. This prioritizes perturbations that have a greater impact on model accuracy. Experiments across six scenarios with different LLMs, datasets and data partitions demonstrate that our approach outperforms existing federated LLM fine-tuning methods in terms of both communication efficiency and new task generalization.

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in General Relativity, the conformalon mode, directly at the level of \(2\to2\) scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons \((TTT)\) and Abelian gauge currents \((TJJ)\), through single-graviton exchange derived from the quadratic expansion of the Einstein--Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behaviour arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in de Donder gauge. The resulting anomaly-mediated \(4\)-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated \(2\to2\) graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

Weight quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into two sets of methods: simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier at low bit-widths but are notoriously hard to implement and to scale, and have gained relatively less traction. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized scalar quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making the relaxation tight and the optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus fully compatible with existing scalar inference kernels. We further show that GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply.

We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter LambdaCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base LambdaCDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Omega_c h^2 = 0.120pm 0.001, baryon density Omega_b h^2 = 0.0224pm 0.0001, scalar spectral index n_s = 0.965pm 0.004, and optical depth tau = 0.054pm 0.007 (in this abstract we quote 68,% confidence regions on measured parameters and 95,% on upper limits). The angular acoustic scale is measured to 0.03,% precision, with 100theta_*=1.0411pm 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-LambdaCDM cosmology, the inferred late-Universe parameters are: Hubble constant H_0 = (67.4pm 0.5)km/s/Mpc; matter density parameter Omega_m = 0.315pm 0.007; and matter fluctuation amplitude sigma_8 = 0.811pm 0.006. We find no compelling evidence for extensions to the base-LambdaCDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be N_{rm eff} = 2.99pm 0.17, and the neutrino mass is tightly constrained to sum m_nu< 0.12eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -LambdaCDM at over 2,sigma, which pulls some parameters that affect the lensing amplitude away from the base-LambdaCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

The tokenization of speech with neural audio codec models is a vital part of modern AI pipelines for the generation or understanding of speech, alone or in a multimodal context. Traditionally such tokenization models have concentrated on low parameter-count architectures using only components with strong inductive biases. In this work we show that by scaling a transformer architecture with large parameter count to this problem, and applying a flexible Finite Scalar Quantization (FSQ) based bottleneck, it is possible to reach state-of-the-art speech quality at extremely low bit-rates of 400 or 700 bits-per-second. The trained models strongly out-perform existing baselines in both objective and subjective tests.

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS_{5}) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into scalar-type and vector-type components according to their tensorial behavior on the three-sphere. Two degrees of freedom of the field are described by scalar-type components, which are coupled due to the mass term, while the remaining two degrees of freedom are described by a vector-type component, which decouples completely. Motivated by the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz in the limit of zero spin, we use a field transformation to decouple the scalar-type components at the expense of introducing a complex separation parameter β. This parameter can be determined analytically, and its values correspond to two distinct polarizations of the scalar-type sector: "electromagnetic" and "non-electromagnetic", denoted by β_{+} and β_{-}, respectively. In the scalar-type sector, the radial differential equation for each polarization is a Fuchsian differential equation with five singularities, whereas in the vector-type sector, the radial equation has four singularities. By means of the isomonodromy method, we reformulate the boundary value problem in terms of the initial conditions of the Painlevé VI τ function and, using a series expansion of the τ function, we compute the scalar-type and vector-type quasinormal modes (QNMs) in the small horizon limit. Our results are in overall very good agreement with those obtained via the numerical integration method. This shows that the isomonodromy method is a reliable method to compute quasinormal modes in the small horizon limit with high accuracy.

We develop a differential-geometric framework for variational quantum circuits in which noisy single- and multi-qubit parameter spaces are modeled by weighted projective lines (WPLs). Starting from the pure-state Bloch sphere CP1, we show that realistic hardware noise induces anisotropic contractions of the Bloch ball that can be represented by a pair of physically interpretable parameters (lambda_perp, lambda_parallel). These parameters determine a unique WPL metric g_WPL(a_over_b, b) whose scalar curvature is R = 2 / b^2, yielding a compact and channel-resolved geometric surrogate for the intrinsic information structure of noisy quantum circuits. We develop a tomography-to-geometry pipeline that extracts (lambda_perp, lambda_parallel) from hardware data and maps them to the WPL parameters (a_over_b, b, R). Experiments on IBM Quantum backends show that the resulting WPL geometries accurately capture anisotropic curvature deformation across calibration periods. Finally, we demonstrate that WPL-informed quantum natural gradients (WPL-QNG) provide stable optimization dynamics for noisy variational quantum eigensolvers and enable curvature-aware mitigation of barren plateaus.

We study the scalar curvature of the Fisher information metric on the microscopic coupling-parameter manifold of lattice spin models at criticality. For a d-dimensional lattice with periodic boundary conditions and n = L^d sites, the Fisher manifold has m = d cdot n dimensions (one per bond), and we find |R(J_c)| sim n^{d_R} with d_R = (dν+ 2η)/(dν+ η), where ν and η are the correlation-length and anomalous-dimension critical exponents. For 2D Ising (ν= 1, η= 1/4), this predicts d_R = 10/9, confirmed by exact transfer-matrix computations (L = 6--9: d_R = 1.1115 pm 0.0002) and multi-seed MCMC through L = 24. For 3D Ising (ν= 0.630, η= 0.0363), the prediction d_R = 1.019 is consistent with MCMC on L^3 tori up to L = 10 (power-law fit: d_R = 1.040). For 2D Potts q = 3 (predicted 33/29 approx 1.138), FFT-MCMC through L = 40 shows d_eff oscillating non-monotonically around sim 1.20, consistent with O(1/(ln L)^2) logarithmic corrections. For q = 4 (predicted 22/19), effective exponents oscillate with strong logarithmic corrections. The Ricci decomposition identity R_3 = -R_1/2, R_4 = -R_2/2 holds to 5--6 digits for all models. This exponent is distinct from Ruppeiner thermodynamic curvature and reflects the collective geometry of the growing Fisher manifold. We provide falsification criteria and predictions for additional universality classes.

The growing scale of Large Language Models (LLMs) has necessitated the development of parameter-efficient fine-tuning techniques. Low-Rank Adaptation (LoRA) has emerged as a promising approach, reducing the number of trainable parameters by applying low-rank updates to pretrained weights. While standard LoRA learns both update factors directly, several recent variants first initialize those matrices via an SVD of the pretrained weights -- an operation that can be expensive on large models and yields singular vectors that are not always easy to interpret. In this work, we extract an orthonormal basis from the pretrained weight matrix using QR decomposition with column pivoting, and then express the LoRA update as a linear combination of these basis vectors -- training only the scalar coefficients, which imposes clear structure on adaptation and drastically reduces parameter count. Experiments across GLUE tasks show that QR-LoRA matches or exceeds the performance of full fine-tuning, standard LoRA, and SVD-LoRA (LoRA with update matrices initialized via singular value decomposition) with as few as 601 parameters -- a reduction of over 1000x compared to full fine-tuning and 77x fewer than typical LoRA setups.

Sparse Attention Vectors (SAVs) have emerged as an excellent training-free alternative to supervised finetuning or low-rank adaptation to improve the performance of Vision Language Models (VLMs). At their heart, SAVs select a few accurate attention heads for a task of interest and use them as classifiers, rather than relying on the model's prediction. In a similar spirit, we find that directly probing the raw activations of the VLM, in the form of scalar values, is sufficient to yield accurate classifiers on diverse visually grounded downstream tasks. Shifting focus from attention vectors to scalar activations dramatically increases the search space for accurate parameters, allowing us to find more discriminative neurons immediately from the first generated token. We call such activations Super Neurons (SNs). In this probing setting, we discover that enough SNs appear in the shallower layers of the large language model to allow for extreme early exiting from the first layer of the model at the first generated token. Compared to the original network, SNs robustly improve the classification performance while achieving a speedup of up to 5.10x.

In this paper we study quasinormal modes and absorption cross sections for the (1+3)-dimensional Bardeen black hole surrounded by perfect fluid dark matter. Studies of the massless scalar field is already done in Sun:2023slzl. Hence, in this paper we will focus on the massive scalar field perturbations and massless Dirac field perturbations. To compute the quasinormal modes we use the semi-analytical 3rd-order WKB method, which has been shown to be one of the best approaches when the effective potential is adequate and when n < ell and n < lambda. We have also utilized the P\"oschl-Teller method to compare the valus obtained using the WKB approach. We have computed quasinormal frequencies by varying various parameters of the theory such as the mass of the scalar field mu, dark matter parameter alpha and the magnetic charge g. We have summarized our solutions in tables and figures for clarity. As for the absorption cross section, we used third order WKB approach to compute reflection, transmission coefficients and partial absorption cross sections. Graphs are presented to demonstrate the behavior of the above quantities when the dark matter parameter and mass of the massive scalar field are varied.

Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby boosting expressivity and accuracy but at the same time resulting in a multiplicative increase in parameters and memory. We propose MetaCluster, a framework that makes KANs highly compressible without sacrificing accuracy. Specifically, a lightweight meta-learner, trained jointly with the KAN, is used to map low-dimensional embedding to coefficient vectors, shaping them to lie on a low-dimensional manifold that is amenable to clustering. We then run K-means in coefficient space and replace per-edge vectors with shared centroids. Afterwards, the meta-learner can be discarded, and a brief fine-tuning of the centroid codebook recovers any residual accuracy loss. The resulting model stores only a small codebook and per-edge indices, exploiting the vector nature of KAN parameters to amortize storage across multiple coefficients. On MNIST, CIFAR-10, and CIFAR-100, across standard KANs and ConvKANs using multiple basis functions, MetaCluster achieves a reduction of up to 80times in parameter storage, with no loss in accuracy. Code will be released upon publication.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

Uncertainty learning and quantification of models are crucial tasks to enhance the trustworthiness of the models. Importantly, the recent surge of generative language models (GLMs) emphasizes the need for reliable uncertainty quantification due to the concerns on generating hallucinated facts. In this paper, we propose to learn neural prediction set models that comes with the probably approximately correct (PAC) guarantee for quantifying the uncertainty of GLMs. Unlike existing prediction set models, which are parameterized by a scalar value, we propose to parameterize prediction sets via neural networks, which achieves more precise uncertainty quantification but still satisfies the PAC guarantee. We demonstrate the efficacy of our method on four types of language datasets and six types of models by showing that our method improves the quantified uncertainty by 63% on average, compared to a standard baseline method.

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar {\alpha}, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/{\alpha}) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/{\alpha}^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

We investigate thermodynamics of static and spherically symmetric black holes (BHs) in the Horndeski theories. Because of the presence of the higher-derivative interactions and the nonminimal derivative couplings of the scalar field, the standard Wald entropy formula may not be directly applicable. Hence, following the original formulation by Iyer and Wald, we obtain the differentials of the BH entropy and the total mass of the system in the Horndeski theories, which lead to the first-law of thermodynamics via the conservation of the Hamiltonian. Our formulation covers the case of the static and spherically symmetric BH solutions with the static scalar field and those with the linearly time-dependent scalar field in the shift-symmetric Horndeski theories. We then apply our results to explicit BH solutions in the Horndeski theories. In the case of the conventional scalar-tensor theories and the Einstein-scalar-Gauss-Bonnet theories, we recover the BH entropy obtained by the Wald entropy formula. In the shift-symmetric theories, in the case of the BH solutions with the static scalar field we show that the BH entropy follows the ordinary area law even in the presence of the nontrivial profile of the scalar field. On the other hand, in the case of the BH solutions where the scalar field linearly depends on time, i.e., the stealth Schwarzschild and Schwarzschild-(anti-) de Sitter solutions, the BH entropy also depends on the profile of the scalar field. By use of the entropy, we find that there exists some range of the parameters in which Schwarzschild-(AdS) BH with non-trivial scalar field is thermodynamically stable than Schwarzschild-(AdS) BH without scalar field in general relativity.

We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single scalar before computing a parameter update. Sven treats each data point's residual as a separate condition to be satisfied simultaneously, using the Moore-Penrose pseudoinverse of the loss Jacobian to find the minimum-norm parameter update that best satisfies all conditions at once. In practice, this pseudoinverse is approximated via a truncated singular value decomposition, retaining only the k most significant directions and incurring a computational overhead of only a factor of k relative to stochastic gradient descent. This is in comparison to traditional natural gradient methods, which scale as the square of the number of parameters. We show that Sven can be understood as a natural gradient method generalized to the over-parametrized regime, recovering natural gradient descent in the under-parametrized limit. On regression tasks, Sven significantly outperforms standard first-order methods including Adam, converging faster and to a lower final loss, while remaining competitive with LBFGS at a fraction of the wall-time cost. We discuss the primary challenge to scaling, namely memory overhead, and propose mitigation strategies. Beyond standard machine learning benchmarks, we anticipate that Sven will find natural application in scientific computing settings where custom loss functions decompose into several conditions.

The efficacy of deep residual networks is fundamentally predicated on the identity shortcut connection. While this mechanism effectively mitigates the vanishing gradient problem, it imposes a strictly additive inductive bias on feature transformations, thereby limiting the network's capacity to model complex state transitions. In this paper, we introduce Deep Delta Learning (DDL), a novel architecture that generalizes the standard residual connection by modulating the identity shortcut with a learnable, data-dependent geometric transformation. This transformation, termed the Delta Operator, constitutes a rank-1 perturbation of the identity matrix, parameterized by a reflection direction vector k(X) and a gating scalar β(X). We provide a spectral analysis of this operator, demonstrating that the gate β(X) enables dynamic interpolation between identity mapping, orthogonal projection, and geometric reflection. Furthermore, we restructure the residual update as a synchronous rank-1 injection, where the gate acts as a dynamic step size governing both the erasure of old information and the writing of new features. This unification empowers the network to explicitly control the spectrum of its layer-wise transition operator, enabling the modeling of complex, non-monotonic dynamics while preserving the stable training characteristics of gated residual architectures.

Long-context inference is increasingly constrained by the KV cache: resident memory grows with context length, and decoding becomes limited by repeated High Bandwidth Memory (HBM) streaming rather than arithmetic. Existing methods such as eviction, windowing, quantization, and offloading reduce footprint, but often leave the critical-path bottleneck only partially addressed, especially when compressed states must still be reconstructed into dense vectors during decoding. We present Spherical KV, a long-context inference method that treats KV allocation as a rate-distortion problem grounded in attention geometry for efficient decoding. The method is built on two ideas: (i) represent directional information cheaply in the decode hot loop, and (ii) allocate retention and precision according to estimated future utility. Its first component, Angle-Domain Attention (ADA), stores keys in a spherical parameterization consisting of a scalar radius and compact angle codes, and computes attention logits directly from these codes without reconstructing dense keys. This preserves a paged, block-local, fusion-friendly decode path and directly targets HBM traffic in realistic serving settings. Its second component, Rate-Distortion Retention (RDR), jointly chooses keep/drop decisions and precision tiers per token and head under a fixed budget, producing tier-homogeneous pages with lightweight metadata and coalesced reads. Together, ADA and RDR provide a deployment-oriented mechanism for reducing KV residency while preserving decode efficiency.

When a language model is fed a wrong answer, what happens inside the network? Current understanding treats truthfulness as a static property of individual-layer representations-a direction to be probed, a feature to be extracted. Less is known about the dynamics: how internal representations diverge across the full depth of the network when the model processes correct versus incorrect continuations. We introduce forced-completion probing, a method that presents identical queries with known correct and incorrect single-token continuations and tracks five geometric measurements across every layer of four decoder-only models(1.5B-13B parameters). We report three findings. First, correct and incorrect paths diverge through rotation, not rescaling: displacement vectors maintain near-identical magnitudes while their angular separation increases, meaning factual selection is encoded in direction on an approximate hypersphere. Second, the model does not passively fail on incorrect input-it actively suppresses the correct answer, driving internal probability away from the right token. Third, both phenomena are entirely absent below a parameter threshold and emerge at 1.6B, suggesting a phase transition in factual processing capability. These results show that factual constraint processing has a specific geometric character-rotational, not scalar; active, not passive-that is invisible to methods based on single-layer probes or magnitude comparisons.

In this article, we consider a newly proposed parameterization of the viscosity coefficient zeta, specifically zeta=zeta_0 {Omega^s_m} H , where zeta_0 = zeta_0{{Omega^s_{m_0}}} within the coincident f(Q) gravity formalism. We consider a non-linear function f(Q)= -Q +alpha Q^n, where alpha and n are arbitrary model parameters, which is a power-law correction to the STEGR scenario. We find an autonomous system by invoking the dimensionless density parameters as the governing phase-space variables. We discuss the physical significance of the model corresponding to the parameter choices n=-1 and n=2 along with the exponent choices s=0, 0.5, and 1.05. We find that model I shows the stable de-Sitter type or stable phantom type (depending on the choice of exponent s) behavior with no transition epoch, whereas model II shows the evolutionary phase from the radiation epoch to the accelerated de-Sitter epoch via passing through the matter-dominated epoch. Hence, we conclude that model I provides a good description of the late-time cosmology but fails to describe the transition epoch, whereas model II modifies the description in the context of the early universe and provides a good description of the matter and radiation era along with the transition phase.

In the 3-3-1 model with right-handed neutrinos, three triplets of scalars engender the correct sequence of symmetry breaking, SU(3)_C times SU(3)_L times U(1)_X rightarrow SU(3)_C times SU(2)_L times U(1)_Y rightarrow SU(3)_C times U(1)_{EM}, generating mass for all fermions, except neutrinos. Tiny neutrino masses may be achieved by adding one sextet of scalars to the original scalar content. As consequence, it emerges a very complex scalar sector, involving terms that violate lepton number explicitly, too. The main obstacle to the development of the phenomenology of such scenario is the knowledge of its spectrum of scalars since, now, there are 15 massive scalar particles on it. The proposal of this work is to do an exhaustive analysis of such scalar sector with lepton number being explicitly violated at low, electroweak and high energy scales by means of trilinear terms in the potential. The first case can be addressed analytically and, as a nice result, we have observed that the scalar content of such case is split into two categories: One belonging to the 331 energy scale and the other belonging to the EWSB energy scale, with the last recovering the well known THDM+triplet. For the other cases, the scalar sector can be addressed only numerically. Hence, we proposed a very general approach for the numerical study of the potential, avoiding simplifications that can make us reach conclusions without foundation. We show that, in the case of lepton number being explicitly violated at electroweak scale, it is possible to recover the same physics of the THDM+triplet, as the previous case. Among all the possibilities, we call the attention to one special case which generates the 3HDM+triplet scenario. For the last case, when lepton number is violated at high energy scale, the sextet become very massive and decouples from the original scalar content of the 3-3-1 model.

We propose a simple interpretation of the gammagamma excesses reported by both CMS and ATLAS groups at 95 GeV together with the LEP excess in the Zbb channel around the same mass in terms of a neutral scalar field in the minimal left-right symmetric model (LRSM). We point out that the scalar field which implements the seesaw mechanism for neutrino masses has all the right properties to explain these observations, without introducing any extra scalar fields. The key point is that this scalar particle is hardly constrained because it couples only to heavy right-handed particles. As a result, the diphoton decay mode receives contributions from both mixing with the Standard Model (SM) Higgs and the heavy charged bosons in the LRSM, depending on the SU(2)_Rtimes U(1)_{B-L} symmetry breaking scale v_R. The complete allowed parameter space for explaining the 95 GeV excesses in this model can be probed with the high-precision measurements of the SM Higgs mixing with other scalars at the high-luminosity LHC and future Higgs factories.

Recent measurements from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) have placed the strictest constraints on the primordial scalar perturbation spectrum, reporting a spectral index of n_ssim0.967-0.98 at 95% confidence level. This result indicates a stronger scale invariance of the scalar perturbation than earlier estimates, posing challenges for numerous inflation models. In this work, we propose a novel inflationary scenario based on Weyl scale-invariant gravity, where the quadratic curvature establishes the scale invariance of the scalar spectrum, while the higher-order extensions imprint the observed slight deviation. Specifically, the exponential curvature extensions are introduced to suppress the mass divergence of the inflaton. We find such scenario naturally yields leading-order predictions of n_ssimeq1-3/(2N)sim0.97-0.975 or n_ssimeq1-5/(3N)sim0.967-0.972 for various models, in excellent agreement with the ACT/SPT constraints. This result builds a concrete bridge between theoretical and observational scale invariance, implying an enduring cosmic echo of the primordial symmetry.

We reassess the realistic discovery reach of Solar-System experiments for dark energy (DE) and dark matter (DM), making explicit the bridge from cosmology-level linear responses to local, screened residuals. In scalar-tensor frameworks with a universal conformal coupling A(phi) and chameleon/Vainshtein screening, we map cosmological responses {mu(z,k),Sigma(z,k)} inferred by DESI and Euclid to thin-shell or Vainshtein residuals in deep Solar potentials Phi_N. We emphasize a two-branch strategy. In a detection-first branch, a verified local anomaly -- an Einstein equivalence principle (EEP) violation, a Shapiro-delay signal with |gamma-1|simfewtimes 10^{-6}, an AU-scale Yukawa tail, or a ultralight DM (ULDM) line in clocks/atom interferometers in space (AIS) -- triggers a joint refit of cosmology and Solar-System data under a common microphysical parameterization {V(phi),A(phi)}. In a guardrail branch, Solar-System tests enforce constraints (EEP; PPN parameters gamma,beta; and dot G/G) and close unscreened or weakly screened corners indicated by cosmology. We forecast, per conjunction, |gamma-1|lesssim (2-5)times 10^{-6} (Ka-/X-band or optical Shapiro), eta_{EEP}sim (1--10)times 10^{-17} (drag-free AIS), |dot G/G|sim(3-5)times10^{-15},yr^{-1} (sub-mm-class LLR), a uniform ~2x tightening of AU-scale Yukawa/DM-density bounds, and (3-10)times improved ULDM-coupling reach from clocks. For a conformal benchmark, mu_{ lin,0}=0.10 implies chisimeq mu_{lin,0/2} and a Sun thin shell Delta R/Rlesssim (1/3chi)|gamma-1|/2=2.4times 10^{-3} at |gamma-1|=5times 10^{-6}; Vainshtein screening at 1 AU yields |gamma-1|lesssim 10^{-11}, naturally below near-term reach. We recommend a cost-effective guardrail+discovery portfolio with explicit triggers for escalation to dedicated missions.

The Stokes V parameter characterizes asymmetry of amplitudes between right- and left-handed waves, and non-vanishing value of the V parameter yields a circularly polarized signal. Cosmologically, V parameter may be a direct probe for parity violation in the universe. In this paper, we theoretically investigate a measurement of this parameter, particularly focusing on the gravitational-wave backgrounds observed via ground-based interferometers. In contrast to the traditional analysis that only considers the total amplitude (or equivalently Omega_{GW}), the signal analysis including a circular-polarized mode has a rich structure due to the multi-dimensionality of target parameters. We show that, by using the network of next-generation detectors, separation between polarized and unpolarized modes can be performed with small statistical loss induced by their correlation.

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale (E_{QG}) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for chi^2 as a function of E_{QG} below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that E_{QG} geq 2.55 times 10^{16} GeV and E_{QG} geq 1.85 times 10^7 GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (sintheta). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle sintheta<0.05. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, the freeze-in parameter space is also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

We explore the consequences of multi-trace deformations in applications of gauge-gravity duality to condensed matter physics. We find that they introduce a powerful new "knob" that can implement spontaneous symmetry breaking, and can be used to construct a new type of holographic superconductor. This knob can be tuned to drive the critical temperature to zero, leading to a new quantum critical point. We calculate nontrivial critical exponents, and show that fluctuations of the order parameter are `locally' quantum critical in the disordered phase. Most notably the dynamical critical exponent is determined by the dimension of an operator at the critical point. We argue that the results are robust against quantum corrections and discuss various generalizations.

We discuss relevant scalar deformations of a holographic theory with a compact boundary. An example of such a theory would be the global AdS_4 with its spatially compact boundary S^2. To introduce a relevant deformation, we choose to turn on a time-independent and spatially homogeneous non-normalizable scalar operator with m^2 = -2. The finite size of a compact boundary cuts down the RG flow at a finite length scale leading to an incomplete RG flow to IR. We discuss a version of {\it incomplete} C-theorem and an {\it incomplete} attractor like mechanism. We discuss the implication of our results for entanglement entropy and geometric quantities like scalar curvature, volume and mass scale of fundamental excitation of the how these quantities increase or decrease (often monotonically) with the strength of the deformation. Thermal physics of a holographic theory defined on a compact boundary is more interesting than its non-compact counterpart. It is well known that with a compact boundary, there is a possibility of a first order Hawking-Page transition dual to a de-confinement phase transition. From a gravity perspective, a relevant deformation dumps negative energy inside the bulk, increasing the effective cosmological constant (Lambda) of the AdS. Dumping more negative energy in the bulk would make the HP transition harder and the corresponding HP transition temperature would increase. However, we have found the size of the BH at the transition temperature decreases.

We construct the charged Hayward-anti-de Sitter (AdS) black hole (BH) with a cloud of strings (CS) and perfect fluid dark matter (PFDM), and analyze its extended thermodynamic phase structure. The Hayward parameter g replaces the central singularity with a de Sitter (dS) core, while the CS parameter a and the PFDM parameter β encode astrophysically motivated matter content. Treating the cosmological constant as pressure, we derive the thermodynamic quantities, verify the Smarr relation, and establish P--V criticality with a van der Waals (vdW)-like small-large BH phase transition and mean-field critical exponents. The Gibbs free energy (GFE) exhibits the characteristic swallowtail below the critical pressure. The Joule-Thomson (JT) expansion yields T_i^{rm min}/T_c approx 0.247, roughly half the Reissner--Nordström-AdS value. The parameters g and Q contract the cooling region, β expands it, and a reshapes it non-monotonically. A holographic heat engine with a rectangular cycle gives efficiencies η= 0.362--0.396 and Carnot benchmarking ratios η/η_C = 0.625--0.791 across six configurations. The CS parameter improves the engine efficiency by reducing the enthalpy at fixed thermodynamic volume, while the PFDM parameter degrades it by adding gravitational enthalpy without contributing to the mechanical work.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent y_t = 1.58693 (9) and the magnetic renormalization exponent y_h = 2.48178 (5). The corrections to scaling are governed by the irrelevant exponent y_1 = -0.821 (5).

We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We establish that the second-order increments of the solution can be approximated by those of the corresponding linearized wave equation, modulated by the diffusion coefficient. These findings extend the previous results of Huang et al. HOO2024, which addressed the case of space-time white noise. As applications, we analyze the quadratic variation of the solution and construct a consistent estimator for the diffusion parameter.

Many machine learning models based on neural networks exhibit scaling laws: their performance scales as power laws with respect to the sizes of the model and training data set. We use large-N field theory methods to solve a model recently proposed by Maloney, Roberts and Sully which provides a simplified setting to study neural scaling laws. Our solution extends the result in this latter paper to general nonzero values of the ridge parameter, which are essential to regularize the behavior of the model. In addition to obtaining new and more precise scaling laws, we also uncover a duality transformation at the diagrams level which explains the symmetry between model and training data set sizes. The same duality underlies recent efforts to design neural networks to simulate quantum field theories.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

The μ-parameterization (μP) provides a principled foundation for large language model (LLM) training by prescribing width-independent learning dynamics, which in turn enables predictable scaling behavior and robust hyperparameter transfer across model sizes. A central requirement of μP is the satisfaction of certain spectral conditions on weight matrices, which ensure consistent feature learning and optimization behavior as model width grows. While these conditions are well understood in theory, guaranteeing their validity in practical training for matrix-based optimizers such as Muon is still under studied. Existing works that study Muon under μP exhibit important limitations: they either do not ensure that the spectral conditions hold throughout the entire training horizon, or require repeated spectral normalization (or Newton-Schulz iterations) applied to both weights and updates, leading to significant computational overhead and reduced practicality. In this work, we show how to reliably guarantee the spectral conditions required by μP for Muon during the entire training process. Our key insight is that for moderately large models, maintaining spectral control at the level of optimizer updates alone is sufficient to preserve μP-compatible scaling, eliminating the need for explicit spectral normalization of the weights. Based on this principle, we develop a variant of Muon, namely Muon++, that satisfies spectral condition throughout the training process. Our results bridge the gap between the theoretical promises of μP and the practical deployment of matrix-based optimizers in long-horizon training. We also take the first step towards an adaptive spectral condition by incorporating data-dependent effects, making it better suited for long-horizon LLM training.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

We allow the Higgs field Phi to interact with a dilaton field chi of the background spacetime via the coupling chi^2,Phi^daggerPhi. Upon spontaneous gauge symmetry breaking, the Higgs VEV becomes proportional to chi. While traditionally this linkage is employed to make the Planck mass and particle masses dependent on chi, we present an textit alternative mechanism: the Higgs VEV will be used to construct Planck's constant hbar and speed of light c. Specifically, each open set vicinity of a given point x^* on the spacetime manifold is equipped with a replica of the Glashow-Weinberg-Salam action operating with its own effective values of hbar_* and c_* per hbar_*proptochi^{-1/2}(x^*) and c_*proptochi^{1/2}(x^*), causing these ``fundamental constants'' to vary alongside the dynamical field chi. Moreover, in each open set around x^*, the prevailing value chi(x^*) determines the length and time scales for physical processes occurring in this region as lproptochi^{-1}(x^*) and tauproptochi^{-3/2}(x^*). This leads to an textit anisotropic relation tau^{-1}propto l^{-3/2} between the rate of clocks and the length of rods, resulting in a distinct set of novel physical phenomena. For late-time cosmology, the variation of c along the trajectory of light waves from distant supernovae towards the Earth-based observer necessitates modifications to the Lema\^itre redshift relation and the Hubble law. These modifications are capable of: (1) Accounting for the Pantheon Catalog of SNeIa through a declining speed of light in an expanding Einstein--de Sitter universe, thus avoiding the need for dark energy; (2) Revitalizing Blanchard-Douspis-Rowan-Robinson-Sarkar's CMB power spectrum analysis that bypassed dark energy [A&A 412, 35 (2003)]; and (3) Resolving the H_0 tension without requiring a dynamical dark energy component.

Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the field of previously known variable star RS Car) and compare results to that obtained using the TP fits. For this system, the statistically optimal number of parameters is 44, but the fit is still worse than that of the NAV fit. Application to the system GSC 3692-00624 argues that the NAV fit is better than the TP one even for the case of EW-type stars with much wider eclipses. Model parameters are listed.

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization (muP) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading muP transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as eta/lambda with an approximately invariant shape; under width scaling d, we observe that the top singular value scales approximately as eta/lambdacdot d^{0.75}. Combining this observation with the muP learning-rate rule eta_2propto d^{-1} for matrix-like parameters implies an empirical weight-decay scaling rule lambda_2propto d that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at eta_1=Theta_d(1) and lambda_1=0, this yields zero-shot transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend muP beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

We investigate in more detail the holographic model of a superconductor recently found by Hartnoll, Herzog, and Horowitz [Phys. Rev. Lett. 101, 031601], which is constructed from a condensate of a charged scalar field in AdS_4-Schwarzschild background. By analytically studying the perturbation of the gravitational system near the critical temperature T_c, we obtain the superconducting coherence length proportional to 1/1-T/T_c via AdS/CFT correspondence. By adding a small external homogeneous magnetic field to the system, we find that a stationary diamagnetic current proportional to the square of the order parameter is induced by the magnetic field. These results agree with Ginzburg-Landau theory and strongly support the idea that a superconductor can be described by a charged scalar field on a black hole via AdS/CFT duality.

We show that pairs of widely separated interferometers are advantageous for measuring the Stokes parameter V of a stochastic background of gravitational waves. This parameter characterizes asymmetry of amplitudes of right- and left-handed waves and generation of the asymmetry is closely related to parity violation in the early universe. The advantageous pairs include LIGO(Livingston)-LCGT and AIGO-Virgo that are relatively insensitive to Omega_GW (the simple intensity of the background). Using at least three detectors, information of the intensity Omega_GW and the degree of asymmetry V can be separately measured.

The observed cosmological constant may originate as the minimum value U_{min} of a scalar field potential, where the scalar field is frozen due to a large mass. If this vacuum is metastable, it may decay to a true vacuum either at present or in the future. Assuming its decay rate Gamma is comparable to the Hubble expansion rate H_0, we estimate the scale of true vacuum bubbles and analyze their evolution. We find that their initial formation scale is sub-millimeter and their tension causes rapid collapse if m gtrsim 1.7 cdot 10^{-3}, eV. For smaller masses, the bubbles expand at the speed of light. We extend our analysis to scalar-tensor theories with non-minimal coupling, finding that the nucleation scale of gravitational constant bubbles remains consistent with the sub-millimeter regime of General Relativity. The critical mass scale remains around 10^{-3},eV. A theoretical estimate at redshift z_{obs} sim 0.01 suggests an observable bubble radius of sim 50 Mpc, implying a gravitational transition triggered sim 300 Myr ago, with a present-day size approaching 100 Mpc. Additionally, we explore mass ranges (m < 10^{-3},eV) and non-minimal coupling xi ranges (10^{-8},eV^{2-n} - 10^{-1},eV^{2-n}) that lead to a variation Delta G/G_N within the 1%-7% range. We assume non-minimal coupling of the form F(phi)=1/kappa - xi phi^n, with kappa=8pi G_N and 2 leq n leq 9. Finally, we review various local physics or/and transition based proposed solutions to the Hubble tension, including ultra-late-time transitional models (z sim 0.01), screened fifth-force mechanisms, and the Lambda_{rm s}CDM model, which features a transition at z sim 2. We discuss observational hints supporting these scenarios and the theoretical challenges they face.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

In this study, we analyze the ghost dark energy model in Brans-Dicke cosmology in the framework of a flat Friedmann-Lemaitre-Robertson-Walker universe. We consider an interaction between ghost dark energy and dark matter with a sign-changeable interaction term. To discuss the cosmological implications of the model, we consider a well-motivated logarithmic form of the Brans-Dicke scalar field. By deriving the cosmological evolution equations, we obtain the cosmological parameters such as the equation of state and deceleration parameters. We analyze the behavior of the cosmological parameters by plotting their graphs against the redshift parameter (z). We observe that the equation of state parameter shows quintessence-like behaviour during present and future epochs; however, phantom-like behavior is also possible for suitable values of the model parameters. Analysis of the deceleration parameter shows a smooth recent phase transition of the universe (deceleration to acceleration). An interesting result we observe is the decelerated expansion of the universe in the far future, i.e, the universe experiences another phase transition in the future. The physical significance of the well-known cosmological plane (w_D-w_D' plane) is discussed in our model. We observe that the trajectories start in the freezing region with the same initial behavior, deviate from each other during the evolution and ends in the thawing region. Finally, we perform a detailed thermodynamic analysis and demonstrate that the generalized second law of thermodynamics is satisfied within the present interacting ghost dark energy model.

Entropic cosmology with the Rényi entropy of the apparent horizon S_R=(1/α)ln(1+αS_{BH}), where S_{BH} is the Bekenstein--Hawking entropy, is studied. By virtue of the thermodynamics-gravity correspondence a model of dark energy is investigated. The generalised Friedmann equations for the Friedmann--Lemaître--Robertson--Walker spatially flat universe with the barotropic matter fluid are obtained. We compute the dark energy density ρ_D, pressure p_D and the deceleration parameter q of the universe. At some model parameters the normalized density parameter of the matter Ω_{m0}approx 0.315 and the deceleration parameter q_0approx -0.535 for the current epoch, which are in the agreement with the Planck data, are found. Making use of the thermodynamics-gravity correspondence, we describe the late time of the universe acceleration. The entropic cosmology considered is equivalent to cosmology based on the teleparallel gravity with the definite function F(T). The Hubble parameters are in approximate agreement (within 5 percents) with the observational Hubble data for redshifts 0.07leq z leq 1.75 at the entropy parameter αapprox 0.305~GH_0^2.

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables z_i, we derive a system of partial differential equations w.r.t.\ new variables x_j, which parameterize the differentiable constraints z_i=y_i(x_j). In our algorithm, the powers of propagators can be considered as arbitrary parameters. Our algorithm can also be used for the reduction of multiple hypergeometric sums to sums of lower dimension, finding special values and reduction equations of hypergeometric functions in a singular locus of continuous variables, or finding systems of partial differential equations for master integrals with arbitrary powers of propagators. As an illustration, we produce a differential equation of fourth order in one variable for the one-loop two-point Feynman diagram with two different masses and arbitrary propagator powers.

Let (C, ω_{C}) be a Ricci-flat, simply connected, conical Kähler manifold. We establish a Liouville theorem for constant scalar curvature Kähler (cscK) metrics on C. The theorem asserts that any cscK metric ω satisfying the uniform bound 1{C} ω_{C} leq ωleq C ω_{C} for some Cgeq1 is equal to ω_{C} up to a holomorphic automorphism that commutes with the scaling action of the cone structure. Next, we develop a C^{0,α}-estimate for uniformly bounded Kähler metrics on a ball around the apex, using a Hölder-type seminorm inspired by Krylov. This estimate applies for small α> 0 under the assumption of uniformly bounded scalar curvature. As a corollary of this result, we show that such a Kähler metric ω is asymptotic to the Ricci-flat cone metric ω_{C}, with polynomial decay rate r^α and for sufficiently small α> 0.

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

We describe a novel method for the application of Convolutional Neural Networks (CNNs) to fields defined on the sphere, using the HEALPix tessellation scheme. Specifically, We have developed a pixel-based approach to implement convolutional layers on the spherical surface, similarly to what is commonly done for CNNs in Euclidian space. The algorithm is fully integrable with existing libraries for NNs (e.g., PyTorch or TensorFlow). We present two applications: (i) recognition of handwritten digits projected on the sphere; (ii) estimation of cosmological parameter from Cosmic Microwave Background (CMB) simulated maps. We have built a simple NN architecture, consisting in four convolutional+pooling layers, and have used it for all the applications explored herein. For what concerns the handwritten digits, our CNN reaches an accuracy of about 95%, comparable with other existing spherical CNNs. For CMB applications, we have tested the CNN on the estimation of a "mock" parameter, defining the angular scale at which the power spectrum of a Gaussian field projected on the sphere peaks. We have estimated this parameter directly from maps, in several cases: temperature and polarization, presence of noise and partial sky coverage. In all the cases, the NN performances are comparable with those from standard spectrum-based bayesian methods. We demonstrate, for the first time, the capability of CNNs to extract information from polarization fields and to distinguish between E and B-modes. Lastly, we have applied our CNN to the estimation of the Thomson scattering optical depth at reionization (tau) from simulated CMB maps. Even without any specific optimization of the NN architecture, we reach an accuracy comparable with standard bayesian methods. This work represents a first step towards the exploitation of NNs in CMB parameter estimation and demonstrates the feasibility of our approach.

The growing scale of deep learning models has rendered standard hyperparameter (HP) optimization prohibitively expensive. A promising solution is the use of scale-aware hyperparameters, which can enable direct transfer of optimal HPs from small-scale grid searches to large models with minimal performance loss. To understand the principles governing such transfer strategy, we develop a general conceptual framework for reasoning about HP transfer across scale, characterizing transfer as fast when the suboptimality it induces vanishes asymptotically faster than the finite-scale performance gap. We show formally that fast transfer is equivalent to useful transfer for compute-optimal grid search, meaning that transfer is asymptotically more compute-efficient than direct tuning. While empirical work has found that the Maximal Update Parameterization (μP) exhibits fast transfer when scaling model width, the mechanisms remain poorly understood. We show that this property depends critically on problem structure by presenting synthetic settings where transfer either offers provable computational advantage or fails to outperform direct tuning even under μP. To explain the fast transfer observed in practice, we conjecture that decomposing the optimization trajectory reveals two contributions to loss reduction: (1) a width-stable component that determines the optimal HPs, and (2) a width-sensitive component that improves with width but weakly perturbs the HP optimum. We present empirical evidence for this hypothesis across various settings, including large language model pretraining.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

We present cosmological analysis of 12 nearby (z<0.06) Type IIP supernovae (SNe IIP) observed with the ROTSE-IIIb telescope. To achieve precise photometry, we present a new image differencing technique that is implemented for the first time on the ROTSE SN photometry pipeline. With this method, we find up to a 20\% increase in the detection efficiency and significant reduction in residual RMS scatter of the SN lightcurves when compared to the previous pipeline performance. We use the published optical spectra and broadband photometry of well studied SNe IIP to establish temporal models for ejecta velocity and photospheric temperature evolution for our SNe IIP population. This study yields measurements that are competitive to other methods even when the data are limited to a single epoch during the photospheric phase of SNe IIP. Using the fully reduced ROTSE photometry and optical spectra, we apply these models to the respective photometric epochs for each SN in the ROTSE IIP sample. This facilitates the use of the Expanding Photosphere Method (EPM) to obtain distance estimates to their respective host galaxies. We then perform cosmological parameter fitting using these EPM distances from which we measure the Hubble constant to be 72.9^{+5.7}_{-4.3}~{rm kms^{-1}~Mpc^{-1}}, which is consistent with the standard Lambda CDM model values derived using other independent techniques.

In this work, we embark on the thermodynamic investigation concerning a family of primary charged black holes within the context of shift and parity symmetric Beyond Horndeski gravity. Employing the Euclidean approach, we derive the functional expression for the free energy and derive the first thermodynamic law, offering a methodology to address the challenge of extracting the thermal quantities in shift-symmetric scalar tensor theories characterized by linear time dependence in the scalar field. Following the formal analysis, we provide some illustrative examples focusing on the thermal evaporation of these fascinating objects.

In the present work, we study the dynamical evolution of an homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to an homogeneous and isotropic NC Friedmann-Robertson-Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor a(t) and the two parameters beta_pm (t), which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model where the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe.

We investigate scale-dependent modifications to the primordial scalar power spectrum as potential solutions to the Hubble tension. We use the Fisher-bias formalism, recently adapted to examine perturbed recombination solutions to the Hubble tension, and extend its range of validity with an iterative method. We first analyze the Planck cosmic microwave background (CMB) anisotropy data, demonstrating the existence of modifications to the primordial power spectrum capable of fully resolving the tension between Planck and SH0ES. As a proof of concept, we interpret these solutions in terms of small, time-dependent variations in the first slow roll parameter or in the sound speed of curvature perturbations during a stage of primordial inflation. However, these solutions are associated with a low total matter density Ω_m, which makes them inconsistent with baryon acoustic oscillations (BAO) and uncalibrated supernovae (SNIa) data. When incorporating additional BOSS and PantheonPlus data, the solutions that reduce the Hubble tension tend to overfit Planck CMB data to compensate for the worsened fit to BAO and SNIa data, making them less compelling. These findings suggest that modifying the primordial power spectrum alone is unlikely to provide a robust resolution to the tension and highlight how the viability of such data-driven solutions depends on the specific datasets considered, emphasizing the role of future high-precision observations in further constraining possible resolutions to the tension.

Our knowledge of supermassive black holes (SMBHs) and their relation to their host galaxies is still limited, and there are only around 150 SMBHs that have their masses directly measured and confirmed. Better black hole mass scaling relations will help us reveal the physics of black holes, as well as predict black hole masses that are not yet measured. Here, we apply symbolic regression, combined with random forest to those directly-measured black hole masses and host galaxy properties, and find a collection of higher-dimensional (N-D) black hole mass scaling relations. These N-D black hole mass scaling relations have scatter smaller than any of the existing black hole mass scaling relations. One of the best among them involves the parameters of central stellar velocity dispersion, bulge-to-total ratio, and density at the black hole's sphere-of-influence with an intrinsic scatter of epsilon=0.083, dex, significantly lower than epsilon sim 0.3, dex for the M-sigma relation. These relations will inspire black hole physics, test black hole models implemented in simulations, and estimate unknown black hole masses on an unprecedented precision.

In this article, we claim that axion-like particles (ALPs) with MeV masses can be produced with semi-relativistic velocities in core-collapse supernovae (SNe), generating a diffuse galactic flux. We show that these ALPs can be detected in neutrino water Cherenkov detectors via a , p rightarrow p , gamma interactions. Using Super-Kamiokande data, we derive new constraints on the ALP parameter space, excluding a region spanning more than one order of magnitude in the ALP-proton coupling above cooling bounds for ALP masses in the range of 1-80 MeV and ALP-proton couplings between 6times10^{-6}-2times10^{-4}. We show that the future Hyper-Kamiokande will be able to probe couplings as small as 2times10^{-6}, fully closing the allowed region above SN 1987A cooling bounds.

Critical temperature, T_c, and the transition width, ΔT_c, are two primary parameters of the superconducting transition. The latter parameter reflects the superconducting state disturbance originating from the thermodynamic fluctuations, atomic disorder, applied magnetic field, the presence of secondary crystalline phases, applied pressure, etc. Recently, Hirsch and Marsiglio (2020 arXiv:2012.12796) performed an analysis of the transition width in several near-room-temperature superconductors (NRTS) and reported that the reduced transition width, ΔT_c/T_c, in these materials does not follow a conventional trend of transition width broadening on applied magnetic field observed in low- and high-T_c superconductors. Here we present thorough mathematical analysis of the magnetoresistive data, R(T,B), for the high-entropy alloy (ScZrNb)_{0.65}[RhPd]_{0.35} and hydrogen-rich superconductors of Im-3m-H_{3}S, C2/m-LaH_{10} and P63/mmc-CeH_9. We found that the reduced transition width, ΔT_c/T_c, in these materials does follow a conventional broadening trend on applied magnetic field.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

Transformers have become the predominant architecture in foundation models due to their excellent performance across various domains. However, the substantial cost of scaling these models remains a significant concern. This problem arises primarily from their dependence on a fixed number of parameters within linear projections. When architectural modifications (e.g., channel dimensions) are introduced, the entire model typically requires retraining from scratch. As model sizes continue growing, this strategy results in increasingly high computational costs and becomes unsustainable. To overcome this problem, we introduce TokenFormer, a natively scalable architecture that leverages the attention mechanism not only for computations among input tokens but also for interactions between tokens and model parameters, thereby enhancing architectural flexibility. By treating model parameters as tokens, we replace all the linear projections in Transformers with our token-parameter attention layer, where input tokens act as queries and model parameters as keys and values. This reformulation allows for progressive and efficient scaling without necessitating retraining from scratch. Our model scales from 124M to 1.4B parameters by incrementally adding new key-value parameter pairs, achieving performance comparable to Transformers trained from scratch while greatly reducing training costs. Code and models are available at https://github.com/Haiyang-W/TokenFormer.

In this paper, we emphasise the recent observational findings from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI DR2), which provide compelling evidence for a possible deviation from the standard ΛCDM (Cold Dark Matter) cosmology, suggesting the presence of a dynamically evolving effective dark energy component. Motivated by this, we construct a theoretical framework in which a massive cosmological vector field, B^μ, couples non-minimally to the background curvature through marginal interactions, offering a controlled mechanism to realise the deviation from the ΛCDM model. A detailed analysis of the effective Equation of State (EoS) parameter w(tilde H) reveals a narrow region of parameter space consistent with current cosmological observations presented by DESI. The analysis yields a stringent upper bound for the coupling constant λ to be λ<2.98times10^{-11}, a very strong bound on mass 3.1356times10^{-66}~g leq m leq 3.3627times10^{-66}~g, and the admissible range -0.405 leq log_{10}tildeγleq -0.38 for which present-day value w_0 = w(tilde H = 1) corresponding to a deviation δ= w_0 + 1 that lies within the region 0.107 leq δleq 0.217. This interval reproduces the deviation inferred from the combined DESI, Cosmic Microwave Background (CMB), and Pantheon+ data, reflecting a controlled departure from the ΛCDM behaviour. In summary, the results suggest that the proposed framework of a massive vector field can account for the departure from ΛCDM behaviour highlighted by DESI in the current cosmic acceleration. Furthermore, the framework approaches the ΛCDM behaviour in late-time tgtrsim28 Gyr, establishing a direct phenomenological link between the underlying parameters and the observed dynamical nature of dark energy.

One of the current goals of neutrino experiments is to precisely determine standard unknown oscillation parameters such as the leptonic CP phase and mass hierarchy. Lorentz invariance violation represents a potential physics factor that could influence the experiment's ability to achieve these precise determinations. This study investigates the influence of Lorentz invariance violation (LIV) on oscillation dynamics, particularly through non-isotropic CPT-violating (a^{X}_{emu}, a^{X}_{etau}, a^{X}_{mutau}) and CPT-conserving (c^{XY}_{emu}, c^{XY}_{e tau}, c^{XY}_{mu tau}) parameters within the Deep Underground Neutrino Experiment (DUNE). We analyze the impact of these parameters on the mass hierarchy (MH) and Dirac CP phase sensitivity measurements. Our findings indicate that while MH sensitivity remains relatively unaffected, only the presence of c^{XY}_{mu tau} significantly deteriorates MH sensitivity, albeit remaining above the 5 sigma threshold. Additionally, we observe a substantial compromise in CP sensitivity due to the c^{XY}_{e mu} and c^{XY}_{e tau} parameters.

We study the inflationary phenomenology of a rescaled Einstein-Gauss-Bonnet gravity. In this framework, the gravitational constant of the Einstein-Hilbert term is rescaled due to effective terms active in the high curvature era. Basically, the total theory is an F(R,G,phi) theory with the Gauss-Bonnet part contributing only a non-minimal coupling to the scalar field, so it is a theory with string theory origins and with a non-trivial F(R) gravity part. The F(R) gravity part in the high curvature regime contributes only a rescaled Einstein-Hilbert term and thus the resulting theory is effectively a rescaled version of a standard Einstein-Gauss-Bonnet theory. We develop the formalism of rescaled Einstein-Gauss-Bonnet gravity, taking in account the GW170817 constraints on the gravitational wave speed. We show explicitly how the rescaled theory affects directly the primordial scalar and tensor perturbations, and how the slow-roll and observational indices of inflation are affected by the rescaling of the theory. We perform a thorough phenomenological analysis of several models of interest and we show that is it possible to obtain viable inflationary theories compatible with the latest Planck data. Also among the studied models there are cases that yield a relatively large blue tilted tensor spectral index and we demonstrate that these models can lead to detectable primordial gravitational waves in the future gravitational wave experiments. Some of the scenarios examined, for specific values of the reheating temperature may be detectable by SKA, LISA, BBO, DECIGO and the Einstein Telescope.

Non-linear interactions during inflation generate non-Gaussianities in the distribution of primordial curvature. In many theories, the physics is scale-invariant, such that the induced three-point function depends solely on a dimensionless shape function S(x,y)sim k^6B_ζ(kx,ky,k). To confront such models with observations, one typically builds specialized estimators for each shape, then applies them to cosmic microwave background datasets at significant computational expense. In this Letter, we take a different approach, directly reconstructing S(x,y) from observations using an efficient logarithmically-binned estimator in primordial-space (motivated by the modal program). Applying this to temperature and polarization maps from Planck, we obtain high-resolution shape measurements across the full (x,y)-plane, including squeezed limits. Our approach is close-to-optimal, highly interpretable, and preserves the information content on (optimally-analyzed) standard templates within approx 10%; moreover, we can use it to assess the scale-dependence of our constraints, finding that Planck is sensitive to approx 6 e-folds of non-Gaussian evolution with a peak sensitivity around 0.1h,Mpc^{-1}. Since we work directly in shape-space, data and theory can be compared in milliseconds. As an example, we perform a search for massive particle exchange using a suite of over 20,000 theoretical templates computed with exact bootstrap methods (for the first time) across a wide range of masses, spins, and sound-speeds; the spin-two analysis yields a maximum significance of 2.6σ. Our approach can be used to probe a wide range of scale-invariant models in orders-of-magnitude less time than with direct estimators, allowing the inflationary paradigm to be explored in new ways.

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements.

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t to lambda^z t, x to lambda x; we focus on the case with z=2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.

Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H_0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and ΛCDM-dependent baryon acoustic oscillation observations. The inferred H_0 values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are H_0= 66 pm 6, km,s^{-1},Mpc^{-1}, H_0= 67 pm 10, km,s^{-1},Mpc^{-1} and H_0= 69 pm 6, km,s^{-1},Mpc^{-1}, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with ln R=12.17pm 0.02.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

An accurate description of the scalar potential at finite temperature is crucial for studying cosmological first-order phase transitions (FOPT) in the early Universe. At finite temperatures, a precise treatment of thermal resummations is essential, as bosonic fields encounter significant infrared issues that can compromise standard perturbative approaches. The Partial Dressing (or the tadpole resummation) method provides a self consistent resummation of higher order corrections, allowing the computation of thermal masses and the effective potential including the proper Boltzmann suppression factors and without relying on any high-temperature approximation. We systematically compare the Partial dressing resummation scheme results with the Parwani and Arnold Espinosa (AE) ones to investigate the thermal phase transition dynamics in the Two-Higgs-Doublet Model (2HDM). Our findings reveal that different resummation prescriptions can significantly alter the nature of the phase transition within the same region of parameter space, confirming the differences that have already been noticed between the Parwani and AE schemes. Notably, the more refined resummation prescription, the Partial Dressing scheme, does not support symmetry non-restoration in 2HDM at high temperatures observed using the AE prescription. Furthermore, we quantify the uncertainties in the stochastic gravitational wave (GW) spectrum from an FOPT due to variations in resummation methods, illustrating their role in shaping theoretical predictions for upcoming GW experiments. Finally, we discuss the capability of the High-Luminosity LHC and proposed GW experiments to probe the FOEWPT-favored region of the parameter space.

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call muTransfer: parametrize the target model in muP, tune the HP indirectly on a smaller model, and zero-shot transfer them to the full-sized model, i.e., without directly tuning the latter at all. We verify muTransfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup and installable via `pip install mup`.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

On-policy distillation (OPD) is widely used for LLM post-training. When pushed with a reward-extrapolation coefficient lambda > 1, the student can lift past the teacher in domain, but past a threshold lambda* the same step violates the output contract on structured-output tasks. In a single-position Bernoulli reduction, we derive a closed-form base-relative clip-safety threshold lambda*(p,b,c) determined by three measurable quantities: the teacher modal probability, the warm-start mass, and the importance-sampling clip strength. Above lambda*, the extrapolated fixed point exits the clip-safe region, changing training from format-preserving to format-collapsing. We extend the rule to calibrated K-ary listwise JSON tasks where a single binding equivalence class dominates the output contract and SFT retains parse headroom. On Amazon Fashion, three pre-registered tests--a fine-grid cliff interval, a budget-extension test, and a small-clip cross-prediction--fall within their locked prediction windows, with the small-clip value matching the closed-form prediction below grid resolution. Operating just below lambda*, ListOPD brings a 1.7B Qwen3 student to in-domain parity with an 8B-SFT baseline at one-fifth the parameters. The gain is driven primarily by format adherence: NDCG@1 on parsed outputs remains flat across lambda, while parse validity sharply changes at the predicted boundary. The cliff diagnostic is rubric-independent, whereas the parity claim uses a Gemini-graded rubric and inherits that evaluator's exposure.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning can be employed to learn such parameters from data. However, neither exact function values nor exact gradients with respect to the hyperparameters are attainable, necessitating methods that only rely on inexact evaluation of such quantities. State-of-the-art inexact gradient-based methods a priori select a sequence of the required accuracies and cannot identify an appropriate step size since the Lipschitz constant of the hypergradient is unknown. In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point. Furthermore, the proposed algorithm determines the required accuracy dynamically rather than manually selected before running it. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation on a range of relevant problems in imaging and data science such as total variation and field of experts denoising and multinomial logistic regression. Particularly, the results show that the algorithm is robust to its own hyperparameters such as the initial accuracies and step size.

This paper introduces a structural equation formulation that gives rise to a new family of quasi-periodic Gaussian processes, useful to process a broad class of natural and physiological signals. The proposed formulation simplifies generation and forecasting, and provides hyperparameter estimates, which we exploit in a convergent and consistent iterative estimation algorithm. A bootstrap approach for standard error estimation and confidence intervals is also provided. We demonstrate the computational and scaling benefits of the proposed approach on a broad class of problems, including water level tidal analysis, CO_{2} emission data, and sunspot numbers data. By leveraging the structural equations, our method reduces the cost of likelihood evaluations and predictions from O(k^2 p^2) to O(p^2), significantly improving scalability.

Hyperparameters are a critical factor in reliably training well-performing reinforcement learning (RL) agents. Unfortunately, developing and evaluating automated approaches for tuning such hyperparameters is both costly and time-consuming. As a result, such approaches are often only evaluated on a single domain or algorithm, making comparisons difficult and limiting insights into their generalizability. We propose ARLBench, a benchmark for hyperparameter optimization (HPO) in RL that allows comparisons of diverse HPO approaches while being highly efficient in evaluation. To enable research into HPO in RL, even in settings with low compute resources, we select a representative subset of HPO tasks spanning a variety of algorithm and environment combinations. This selection allows for generating a performance profile of an automated RL (AutoRL) method using only a fraction of the compute previously necessary, enabling a broader range of researchers to work on HPO in RL. With the extensive and large-scale dataset on hyperparameter landscapes that our selection is based on, ARLBench is an efficient, flexible, and future-oriented foundation for research on AutoRL. Both the benchmark and the dataset are available at https://github.com/automl/arlbench.

Within the context of a Chern-Simons running-vacuum-model (RVM) cosmology, one expects an early-matter dominated (eMD) reheating period after RVM inflation driven by the axion field. Treating thus in this work Chern-Simons RVM cosmology as an effective f(R) gravity theory characterized by logarithmic corrections of the spacetime curvature, we study the gravitational-wave (GW) signal induced by the nearly-scale invariant inflationary adiabatic curvature perturbations during the transition from the eMD era driven by the axion to the late radiation-dominated era. Remarkably, by accounting for the extra GW scalaron polarization present within f(R) gravity theories, we find regions in the parameter space of the theory where one is met with a distinctive induced GW signal with a universal f^6 high-frequency scaling compared to the f^7 scaling present in general relativity (GR). Interestingly enough, for axion masses m_a higher than 1 GeV and axion gauge couplings f_a above 10^{-3} Planck mass, one can produce induced GW spectra within the sensitivity bands of future GW observatories such as the Einstein Telescope (ET), the Laser Interferometer Space Antenna (LISA), the Big Bang Observer (BBO) and the Square Kilometer Arrays (SKA).

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.

In this work, we compute multi-field core and halo properties in wave Dark Matter models. We focus on the case where Dark Matter consists of two light (real) scalars, interacting gravitationally. As in the single-field Ultra Light Dark Matter (ULDM) case, the scalar field behaves as a coherent BEC with a definite ground state (at fixed total mass), often referred to in the literature as a gravitational soliton. We establish an efficient algorithm to find the ground and excited states of such two-field systems. We then use simulations to investigate the gravitational collapse and virialization, starting from different initial conditions, into solitons and surrounding halo. As in the single-field case, a virialized halo forms with a gravitational soliton (ground state) at the center. We find some evidence for an empirical relation between the soliton mass and energy and those of the host halo. We use this to then find a numerical relation between the properties of the two. Finally, we use this to address the issue of alleviating some of the tensions that single-field ULDM has with observational data, in particular, the issue of how a galaxy's core and radius are related. We find that if galaxies of different masses have similar percentages of the two species, then the core-radius scaling tension is not addressed. However, more general possibilities occur if the relative abundance of species in each halo correlates with the total mass of the galaxy. If this is the case, the model predicts several other phenomenological signatures.

Studies show that the model-independent, fully non-perturbative covariant cosmographic approach is suitable for analyzing the local Universe (zlesssim 0.1). However, accurately characterizing large and inhomogeneous mass distributions requires the fourth-order term in the redshift expansion of the covariant luminosity distance d_L(z,n). We calculate the covariant snap parameter S and its spherical harmonic multipole moments using the matter expansion tensor and the evolution equations for lightray bundles. The fourth-order term adds 36 degrees of freedom, since the highest independent multipole of the snap is the 32-pole (dotriacontapole) (ell=5). Including this term helps to de-bias estimations of the covariant deceleration parameter. Given that observations suggest axially symmetric anisotropies in the Hubble diagram for z lesssim 0.1 and theory shows that only a subset of multipoles contributes to the signal, we demonstrate that only 12 degrees of freedom are needed for a model-independent description of the local universe. We use an analytical axisymmetric model of the local Universe, with data that matches the Zwicky Transient Facility survey, in order to provide a numerical example of the amplitude of the snap multipoles and to forecast precision.

We study and explore the low scale implications of Yukawa unification in the minimal gauge mediated supersymmetry breaking models. We also assume non-zero non-holomorphic terms, with which the YU solutions can be accommodated in the cases with μ> 0. These results can be considered a direct effect from the non-holomorphic terms, but they also lead to testable low scale implications compatible with YU. We observe abundant solutions consistent with the Higgs boson mass. This constraint leads to heavy strongly interacting supersymmetric particles, while the electroweak sector can be realized relatively lighter and they can be probed by several experiments. We find that the chargino can be lighter than 1 TeV and it is degenerate with the lightest neutralino in most of such solutions. Consistent solutions in this region can accommodate charginos as light as about 120 GeV, and they will be tested more likely soon by the analyses over the compressed spectra. These solutions are also be subjected in the lifetime analyses. Our analyses identify such light charginos decaying in about 10^{-2} ns. Probing such points may need a slight improvement in sensitivity of the analyses, and one can expect them to be tested very soon. In the same region, stau is realized to be another light supersymmetric particle, and some of the solutions can be inconsistently lighter. We find that it can weigh as light as about 600 GeV consistently, and it can be tested also soon over its lifetime. We summarize and also exemplify our findings with five benchmark scenarios. Most of the benchmark solutions also reveal that the solutions can be tested in heavy Higgs boson searches, which shape the whole Higgs boson spectrum in models.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

We apply the Weibull distribution -- a two-parameter family from extreme-value theory -- as a diagnostic framework for element-wise weight magnitude distributions in transformers. At initialization, i.i.d. Gaussian weights give |w| ~ HalfNormal, yielding k ~ 1.20 via middle-80% probability-plot fit (the protocol used throughout this work). This anchor makes k a principled, architecture-independent measuring stick for training dynamics; fitting each weight matrix independently at every layer at every checkpoint enables per-component, per-layer, and per-step diagnostics that aggregate statistics cannot resolve. Applying this framework to 12 model entries spanning 7 architectural families (Pythia, OLMo-1/2, LLaMA-3, Mistral, Qwen2.5/3) reveals three findings. First, FFN modules and the attention output projection W_o -- the Transmission Class -- fall in a narrow k band: median terminal k in [1.186, 1.204] across 12 entries (cross-family CV = 0.51%), shared across SwiGLU/GeLU activations, Pre-LN/QK-Norm placements, and 70M-14B sizes. Second, the attention input projections W_q, W_k -- the Selection Class -- depart from the Weibull family, with severity shaped by storage: separately-stored Q/K (OLMo-1, OLMo-2) yields k in [0.76, 0.99] (deep); GQA models yield k in [1.10, 1.16] (mild); Pythia's merged W_qkv occupies a transitional zone tracking training budget T/tau monotonically. Third, lambda grows substantially during training and scales with sqrt(eta/lambda_wd) within the Pythia family (Pearson r = 0.94, three Transmission kinds), directionally consistent with Fan et al. (2025). The two parameters carry independent information: k labels the functional class, lambda labels training progress. We release npm-weibull-py v0.4 (Python library) and DATABASE_v9_1 at https://github.com/tiexinding/NPM-Weibull-public .

Mixture-of-Experts (MoE) layers have emerged as an important tool in scaling up modern neural networks by decoupling total trainable parameters from activated parameters in the forward pass for each token. However, sparse MoEs add complexity to training due to (i) new trainable parameters (router weights) that, like all other parameter groups, require hyperparameter (HP) tuning; (ii) new architecture scale dimensions (number of and size of experts) that must be chosen and potentially taken large. To make HP selection cheap and reliable, we propose a new parameterization for transformer models with MoE layers when scaling model width, depth, number of experts, and expert (hidden) size. Our parameterization is justified by a novel dynamical mean-field theory (DMFT) analysis. When varying different model dimensions trained at a fixed token budget, we find empirically that our parameterization enables reliable HP transfer across models from 51M to over 2B total parameters. We further take HPs identified from sweeping small models on a short token horizon to train larger models on longer horizons and report performant model behaviors.

We propose a quark flavor model based on modular S'_4 with a general CP symmetry. CP violation in the quark sector is entirely realized by the modulus langle τrangle. We show that the canonical normalization induced by the Kähler metric plays a crucial role in reproducing the observed hierarchies, while maintaining coupling constants of order O(1). The minimal model achieves a great fit to the quark sector data, which we take as the PDG 2024 data extrapolated to the GUT scale.

Parameter inference is a crucial task in modern cosmology that requires accurate and fast computational methods to handle the high precision and volume of observational datasets. In this study, we explore a hybrid vision transformer, the Convolution vision Transformer (CvT), which combines the benefits of vision transformers (ViTs) and convolutional neural networks (CNNs). We use this approach to infer the Omega_m and sigma_8 cosmological parameters from simulated dark matter and halo fields. Our experiments indicate that the constraints on Omega_m and sigma_8 obtained using CvT are better than ViT and CNN, using either dark matter or halo fields. For CvT, pretraining on dark matter fields proves advantageous for improving constraints using halo fields compared to training a model from the beginning. However, ViT and CNN do not show these benefits. The CvT is more efficient than ViT since, despite having more parameters, it requires a training time similar to that of ViT and has similar inference times. The code is available at https://github.com/Yash-10/cvt-cosmo-inference/.

Despite major advances in methodology, hyperparameter tuning remains a crucial (and expensive) part of the development of machine learning systems. Even ignoring architectural choices, deep neural networks have a large number of optimization and regularization hyperparameters that need to be tuned carefully per workload in order to obtain the best results. In a perfect world, training algorithms would not require workload-specific hyperparameter tuning, but would instead have default settings that performed well across many workloads. Recently, there has been a growing literature on optimization methods which attempt to reduce the number of hyperparameters -- particularly the learning rate and its accompanying schedule. Given these developments, how far away is the dream of neural network training algorithms that completely obviate the need for painful tuning? In this paper, we evaluate the potential of learning-rate-free methods as components of hyperparameter-free methods. We freeze their (non-learning rate) hyperparameters to default values, and score their performance using the recently-proposed AlgoPerf: Training Algorithms benchmark. We found that literature-supplied default settings performed poorly on the benchmark, so we performed a search for hyperparameter configurations that performed well across all workloads simultaneously. The best AlgoPerf-calibrated learning-rate-free methods had much improved performance but still lagged slightly behind a similarly calibrated NadamW baseline in overall benchmark score. Our results suggest that there is still much room for improvement for learning-rate-free methods, and that testing against a strong, workload-agnostic baseline is important to improve hyperparameter reduction techniques.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere mathbb S^{d-1}. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on mathbb S^{d-1} to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on (mathbb S^{d-1})^L both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

The impressive capabilities of Large Language Models (LLMs) across diverse tasks are now well-established, yet their effective deployment necessitates careful hyperparameter optimization. Through extensive empirical studies involving grid searches across diverse configurations, we discover universal scaling laws governing these hyperparameters: optimal learning rate follows a power-law relationship with both model parameters and data sizes, while optimal batch size scales primarily with data sizes. Our analysis reveals a convex optimization landscape for hyperparameters under fixed models and data size conditions. This convexity implies an optimal hyperparameter plateau. We contribute a universal, plug-and-play optimal hyperparameter tool for the community. Its estimated values on the test set are merely 0.07\% away from the globally optimal LLM performance found via an exhaustive search. These laws demonstrate remarkable robustness across variations in model sparsity, training data distribution, and model shape. To our best known, this is the first work that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers, as well as establishes optimal hyperparameter scaling laws across diverse data distributions. This exhaustive optimization process demands substantial computational resources, utilizing nearly one million NVIDIA H800 GPU hours to train 3,700 LLMs of varying sizes and hyperparameters from scratch and consuming approximately 100 trillion tokens in total. To facilitate reproducibility and further research, we will progressively release all loss measurements and model checkpoints through our designated repository https://step-law.github.io/

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest varies as amount of compute used for training (or inference), number of model parameters, training dataset size, model input size, number of training steps, or upstream performance varies) for various architectures & for each of various tasks within a large & diverse set of upstream & downstream tasks, in zero-shot, prompted, & finetuned settings. This set includes large-scale vision, language, audio, video, diffusion, generative modeling, multimodal learning, contrastive learning, AI alignment, AI capabilities, robotics, out-of-distribution (OOD) generalization, continual learning, transfer learning, uncertainty estimation / calibration, OOD detection, adversarial robustness, distillation, sparsity, retrieval, quantization, pruning, fairness, molecules, computer programming/coding, math word problems, "emergent phase transitions", arithmetic, supervised learning, unsupervised/self-supervised learning, & reinforcement learning (single agent & multi-agent). When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set. Moreover, this functional form accurately models & extrapolates scaling behavior that other functional forms are incapable of expressing such as the nonmonotonic transitions present in the scaling behavior of phenomena such as double descent & the delayed, sharp inflection points present in the scaling behavior of tasks such as arithmetic. Lastly, we use this functional form to glean insights about the limit of the predictability of scaling behavior. Code is available at https://github.com/ethancaballero/broken_neural_scaling_laws

Singular limits for the following indirect signalling chemotaxis system align* \left\{ array{lllllll} \partial_t n = \Delta n - \nabla \cdot (n \nabla c ) & in \Omega\times(0,\infty) , \varepsilon \partial_t c = \Delta c - c + w & in \Omega\times(0,\infty), \varepsilon \partial_t w = \tau \Delta w - w + n & in \Omega\times (0,\infty), \partial_\nu n = \partial_\nu c = \partial_\nu w = 0, &on \partial\Omega\times (0,\infty) %(n,c,w)_{t=0} = (n_0,c_0,w_0) & on \Omega, array \right. align* are investigated. More precisely, we study parabolic-elliptic simplification, or PES, varepsilonto 0^+ with fixed tau>0 up to the critical dimension N=4, and indirect-direct simplification, or IDS, (varepsilon,tau)to (0^+,0^+) up to the critical dimension N=2. These are relevant in biological situations where the signalling process is on a much faster time scale compared to the species diffusion and all interactions. Showing singular limits in critical dimensions is challenging. To deal with the PES, we carefully combine the entropy function, an Adam-type inequality, the regularisation of slow evolution, and an energy equation method to obtain strong convergence in representative spaces. For the IDS, a bootstrap argument concerning the L^p-energy function is devised, which allows us to obtain suitable uniform bounds for the singular limits. Moreover, in both scenarios, we also present the convergence rates, where the effect of the initial layer and the convergence to the critical manifold are also revealed.

We develop a novel way to probe subgalactic-scale matter distribution with diffractive lensing on gravitational waves. Five-year observations from Einstein Telescope and DECIGO are expected to probe k= 10^5sim 10^8 ,{rm Mpc}^{-1} down to P(k) = 10^{-16} sim 10^{-14} ,{rm Mpc}^3 level. These results can be interpreted in terms of primordial black holes in the range M_{rm PBH} gtrsim 10^{-3}M_odot down to f_{rm PBH} = 10^{-6} level, or QCD axion minihalos in the range m_a = 10^{-3} sim 10^{-12} ,{rm eV}. A key result of the paper is the approximate relation between the scale k and the gravitational wave frequency f, derived in an ensemble of `multi-lensing' events. This relation enables direct measurement of the power spectrum at specific scales, with sensitivities characterized by model-independent kernels delta P(k). Additionally, we delineate the statistical properties of `multi-lensing' based on the `Fresnel number' N_F. When N_F cal O(1), the statistical significance can be approximately calculated by Variance of lensing effects, which is directly related to the power spectrum among other moments of matter distribution.

The Languini Kitchen serves as both a research collective and codebase designed to empower researchers with limited computational resources to contribute meaningfully to the field of language modelling. We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. The number of tokens on which a model is trained is defined by the model's throughput and the chosen compute class. Notably, this approach avoids constraints on critical hyperparameters which affect total parameters or floating-point operations. For evaluation, we pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. On it, we compare methods based on their empirical scaling trends which are estimated through experiments at various levels of compute. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput. While the GPT baseline achieves better perplexity throughout all our levels of compute, our LSTM baseline exhibits a predictable and more favourable scaling law. This is due to the improved throughput and the need for fewer training tokens to achieve the same decrease in test perplexity. Extrapolating the scaling laws leads of both models results in an intersection at roughly 50,000 accelerator hours. We hope this work can serve as the foundation for meaningful and reproducible language modelling research.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the AdS/CFT correspondence by solving the Einstein-Abelian-Higgs model in an AdS_4 black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

This paper considers the problem of variable selection allowing for parameter instability. It distinguishes between signal and pseudo-signal variables that are correlated with the target variable, and noise variables that are not, and investigate the asymptotic properties of the One Covariate at a Time Multiple Testing (OCMT) method proposed by Chudik et al. (2018) under parameter insatiability. It is established that OCMT continues to asymptotically select an approximating model that includes all the signals and none of the noise variables. Properties of post selection regressions are also investigated, and in-sample fit of the selected regression is shown to have the oracle property. The theoretical results support the use of unweighted observations at the selection stage of OCMT, whilst applying down-weighting of observations only at the forecasting stage. Monte Carlo and empirical applications show that OCMT without down-weighting at the selection stage yields smaller mean squared forecast errors compared to Lasso, Adaptive Lasso, and boosting.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

The superconducting materials that make up an MKID have a significant effect on its performance. The T_c and normal state resistivity ρ_N of the film determine the penetration depth λ and therefore how much kinetic inductance it has. The ratio of kinetic inductance to total inductance (α), the volume of the inductor, and Q_m determines the magnitude of the response to incoming energy. The quasiparticle lifetime τ_qp is the characteristic time during which the MKID's surface impedance is modified by the incoming energy. Many materials have been explored for use in superconducting resonators and MKIDs, but that information is often not published or scattered around the literature. This chapter contains information and references on the work that has been done with thin film lithographed circuits for MKIDs over the last two decades. Note that measured material properties such as the internal loss quality factor Q_i and quasiparticle lifetime τ_qp vary significantly depending on how the MKID superconducting thin film is made and the system they are measured in, so it is best to interpret all stated values as typical but not definitive. Values are omitted in cases when there aren't enough measurements or there is too much disagreement in the literature to estimate a typical value. In order to be as complete as possible some unpublished results from the author's lab are included and can be identified by the lack of a reference. Unless noted all films are polycrystalline or amorphous.