Search: “stochastic-gradient-descent”

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Double descent is the principle of least action

A statistical mechanics analysis explains double descent: finite-time diffusion induces effective weight decay that regularizes models as parameters grow.

The paper models stochastic gradient-based training as a particle diffusing over the training-loss energy landscape at an induced temperature, sampling parameters via a Boltzmann distribution. Finite training time carries an effective weight decay, making every parameter a quadratic degree of freedom governed by the equipartition theorem. Adding parameters at fixed training loss lowers the temperature and the L2 norm of the stationary path, increasing effective regularization and explaining the double descent phenomenon.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:17 UTC · 12h agoAI research

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Quantile-based Loss Filtering for Outlier-Robust Stochastic Gradient Descent

Quantile-k-Loss SGD filters corrupted component losses by quantile sampling, proving linear convergence while outperforming standard and min-k-loss SGD.

The paper proposes Quantile-k-Loss SGD (Q(k)L-SGD), a loss-filtering framework for finite-sum optimization with corrupted components that samples k losses per iteration and updates using an index from the lower empirical q-quantile. The authors prove linear convergence under standard convexity, requiring sample size to scale with the number of corruptions, plus a complementary small-sample probabilistic analysis. Experiments on polynomial regression, regularized logistic regression, and hinge loss show intermediate quantiles often outperform both standard SGD and min-k-loss SGD.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:38 UTC · 5d agoAI research

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A Theoretical Analysis of Generalization Dynamics in Neural Networks under Gradient Descent with Weight Decay

Theoretical framework bounds generalization for gradient descent with weight decay, deriving conditions that explain delayed generalization and grokking.

The paper proves convergence of gradient descent with weight decay to a neighborhood of global minimizers of the empirical l2 loss for a broad class of neural networks. It decomposes population error into data, optimization, and prediction variation errors, deriving cellwise and layerwise approximate-homogeneity bounds on prediction variation along the training trajectory. The resulting necessary and sufficient conditions explain layerwise generalization differences and provide a theoretical characterization of grokking.

arXiv cs.AI / cs.LG / cs.CL·Sep 7, 16:59 UTC · 9d agoAI research

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Local gradient neural operator

Researchers propose LGNO, a lightweight interpretable neural operator using learnable local stencils, matching global-operator accuracy on PDE benchmarks with fewer parameters.

LGNO builds on nonlinear gradient discretization priors and uses multilayer perceptron convolutional layers to learn translation-invariant local kernels resembling discrete stencils. A zero consistent stencil factorization separates coefficient learning from field reconstruction, and network folding shares equivalent components to cut parameter counts for symmetric problems. Evaluations on linear and nonlinear, static and dynamic, and low- and high-dimensional PDE benchmarks show maintained accuracy, parameter efficiency, and rollout stability, with applicability to diffusion, flow, and quantum problems.

arXiv cs.AI / cs.LG / cs.CL·Sep 7, 16:53 UTC · 9d agoAI research1

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Silver Rate Is (Almost) Optimal for Gradient Descent Acceleration

New optimization theory paper proves near-optimal lower bounds for gradient descent with predetermined stepsizes, confirming silver-schedule optimality.

The paper studies the limits of accelerating gradient descent using predetermined nonnegative stepsizes in smooth convex optimization, with the key constant p_sil = log2(1 + sqrt(2)). It proves a non-anytime lower bound of Omega(n^(-p_sil - O(sqrt(log log n / log n)))) on the error achievable by any such stepsize schedule. In the anytime setting, it shows every infinite nonnegative schedule must incur error Omega(n^(-2*p_sil/(1+p_sil) - O(sqrt(log log n / log n)))) at infinitely many horizons. Combined with the silver-schedule upper bound of Altschuler and Parrilo (2025) and the anytime upper bound of Zhang et al. (2025), these results determine the optimal polynomial convergence exponents in both settings.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:59 UTC · 8d agoAI research

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When Does Scale-Invariant Optimization Become Unstable? An Exact Schedule Law with Weight Decay

Researchers derive an exact law linking learning-rate schedules and weight decay in normalized networks, pinpointing when scale-invariant optimization destabilizes.

The paper shows that normalization makes large parts of neural networks scale-invariant, creating a hidden feedback loop where learning-rate schedules and weight decay interact through the parameter norm to control the effective optimizer step. An exact discrete-time law with a single scalar quantity separates contraction- and expansion-dominated effective learning-rate regimes, and the balance point is intrinsically unstable, so constant learning rate with weight decay produces recurrent behavior instead of a stable equilibrium. A unified homogeneous-optimizer framework explains why adaptive methods stabilize more weakly under normalization. The law is validated with high precision on MLPs, CNNs, and GPT-2 across MNIST, CIFAR, WikiText, and OpenWebText, with code released on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:46 UTC · 8d agoAI research

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Bridging Control, Inference, Transport, and Thermodynamics: From Theory to Applications in Learning

Review connects control theory, optimal transport, probabilistic inference, thermodynamics, and machine learning via free-energy optimization under constraints.

The review unifies five fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. The common conceptual thread is optimization of free-energy-like functionals under dynamical or statistical constraints. Selected applications are presented in reinforcement learning, variational inference, and generative modeling. The tutorial-style text assumes no prior familiarity and begins from physics principles.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:16 UTC · 2d agoAI research

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Fast Learning Rates for Physics-Informed Kernel Methods

Theoretical analysis proves finite-sample learning rates for physics-informed kernel estimators, showing differential observations can improve rates from n^-1/4 to n^-1/2.

The paper analyzes a physics-informed kernel estimator combining n value observations and m differential observations for a linear differential operator D, asking how much differential information improves prediction. The authors prove finite-sample bounds, supported by simulations, revealing a two-regime structure: when m is limited the rate depends jointly on n and m, and when m exceeds a problem-dependent threshold the rate saturates to the oracle rate. Examples in Sobolev spaces, including partial Laplacian constraints on the torus and gradient observations on bounded domains, illustrate improvements from the nonparametric n^-1/4 rate to the parametric n^-1/2 rate, plus physically consistent rates in a stronger norm.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 16:39 UTC · 13h agoAI research

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Probabilistic Linear Explanations

Researchers introduce a unified probabilistic explainability framework using sparse anchored linear models that outperforms LIME and MAPLE on relevance error.

The paper proposes probabilistic explanations based on sparse, anchored linear models applicable to both binary classification and continuous regression. It proves that minimizing relevance error for neural-network models is NP-hard and relates it to a tractable fidelity-error surrogate. Solutions are computed via a mixed integer programming formulation with provably optimal empirical solutions and a polynomial-time iterative hard thresholding algorithm with approximation guarantees. Empirical evaluations show lower relevance error than LIME and MAPLE while satisfying anchoring and sparsity constraints by construction.

arXiv cs.AI / cs.LG / cs.CL·Sep 16, 17:18 UTC · 12h agoAI research

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SQS: Bayesian DNN Compression through Sparse Quantized Sub-distributions

SQS unifies weight pruning and low-bit quantization via Bayesian variational learning, compressing Llama3.2 and Qwen2.5 at higher rates with comparable accuracy.

SQS introduces a unified Bayesian variational framework performing simultaneous pruning and low-bit quantization, using a spike-and-slab prior for sparsity and Gaussian Mixture Models to model quantized weights. The authors derive an efficient approximation for the intractable objective and provide a consistency result for the variational approach. Experiments on ResNet, BERT-base, Llama3.2, and Qwen2.5 show higher compression rates than prior baselines with comparable performance drops.

Hugging Face daily papers·Sep 6, 20:00 UTC · 10d agoAI research

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Understanding the Impact of Model Pruning on Long-Tail Forgetting and Explanation Reliability in Medical Imaging

Systematic study finds model pruning causes frequency-dependent long-tail forgetting in medical imaging and that gradient-informed methods best preserve explanations.

Across two long-tailed medical imaging datasets, two CNN architectures, four pruning methods, and sparsity up to 95%, the study measures predictive performance, explanation stability, and faithfulness. Rare classes degrade earlier and more severely than frequent ones, while explanation reliability depends mainly on the pruning strategy, with gradient-informed methods degrading least. Mechanistic analysis ties explanation collapse to loss of class-discriminative gradients rather than vanishing feature activations, recommending class- and explanation-aware evaluation of compression.

arXiv cs.AI / cs.LG / cs.CL·Sep 7, 17:44 UTC · 9d agoAI research

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StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean

StochBench introduces 450 graduate-level stochastic-processes problems in Lean 4; an Opus 4.8-based agent proved 34.9% under a 15-minute limit.

StochBench is a Lean 4 benchmark of 450 graduate stochastic-processes problems, each paired with its natural-language source, covering Markov chains, renewal processes, martingales, Brownian motion, stochastic calculus, weak convergence, and Poisson and continuous-time Markov processes. The benchmark addresses field-specific applied mathematics underrepresented in Mathlib, unlike competition-math-dominated suites such as IMO and Putnam collections. An Opus 4.8-based agent achieved a 34.9% proof rate (157/450) under a 15-minute per-problem limit, showing the benchmark remains challenging for advanced provers.

Hugging Face daily papers·Sep 7, 20:00 UTC · 9d agoAI research

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The Price of Sparsity: Sufficient Conditions for Sparse Recovery using Sparse and Sparsified Measurements

Researchers derive sufficient sample-size conditions for recovering sparse binary signals from sparse Gaussian measurements, quantifying an information-theoretic threshold of order slog(p/s)/log(ds/p).

The paper studies support recovery of sparse binary signals from noisy linear measurements. For sparse Gaussian designs, the authors identify sufficient minimal sample sizes for maximum-likelihood recovery in the high-SNR regime d*s/p -> infinity, yielding an information-theoretic threshold of order slog(p/s)/log(ds/p) that makes the price of measurement sparsity explicit. They also show a regime where the sample-complexity loss from sparsity is only logarithmic while computational gains are nearly linear, and prove that for independently sparsified dense Gaussian designs a sample size of order p/ψ² suffices for support recovery at any fixed error level.

Hugging Face daily papers·Sep 7, 20:00 UTC · 9d agoAI research

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General Quantification of Covariate and Concept Shifts

Paper proposes γ*-concept shifts via entropic optimal transport, deriving estimable generalization bounds unifying covariate and concept shift under distribution shift.

The authors show existing definitions of concept shift break when source and target supports mismatch and propose γ*-concept shifts grounded in entropic optimal transport. They derive a general error bound covering broad loss functions, label spaces and stochastic labeling, plus estimators with concentration guarantees. The resulting DataShifts algorithm quantifies distribution shifts and estimates the error bound in most applications, addressing learning bounds that were previously non-estimable from samples.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:57 UTC · 6d agoAI research1

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Learning Sparse Decision Trees via Transformer Variational Auto-Encoders

TREVIS uses a Tree Transformer VAE latent space to learn decision trees matching near-optimal predictive performance while improving structural sparsity.

TREVIS learns decision trees optimized for complex objectives by exploring the latent space of a Tree Transformer Variational Auto-Encoder (TTVAE). Mapping trees to continuous latent representations replaces the discrete search space with a continuous one, enabling gradient-based optimization through a differentiable surrogate model. Experiments show TREVIS matches the predictive performance of near-optimal algorithms while improving structural sparsity, targeting high-stakes contexts needing transparent decision logic.

Hugging Face daily papers·Aug 31, 20:00 UTC · 16d agoAI research1

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AdamX: Cosine similarity meets gradient descent

Researchers propose AdamX, a cosine-similarity-based first-order optimizer with variance rectification that matches Adam-class convergence across benchmark datasets and architectures.

The paper introduces AdamX, a first-order optimizer that uses cosine similarity as an adaptive mechanism for controlling update magnitudes, plus a variance rectification scheme for smoother optimization early in training. The method is described as scalable, model-agnostic, and straightforward to integrate into existing pipelines. Empirically, AdamX shows competitive convergence rates measured by epochs to reach performance thresholds under a fixed hyperparameter budget, with code and experiments released on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:42 UTC · 6d agoAI research

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Near-Optimal Reinforcement Learning with Multi-Step Transition Lookahead

Theorists prove multi-step lookahead RL planning is NP-hard for every fixed rational discount factor yet give a randomized polynomial-time approximation scheme.

The paper resolves open questions about reinforcement learning with multi-step transition lookahead. It shows exact planning remains NP-hard for every fixed rational discount factor in (0,1), not just discounts arbitrarily close to one, and introduces a randomized polynomial-time approximation scheme for every fixed lookahead depth. Extending to unknown transitions and stochastic rewards via optimism and variance-adaptive confidence bounds, the algorithm achieves cumulative regret matching classical tabular discounted RL up to logarithmic factors.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 16:58 UTC · 6d agoAI research1

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Cascading Gradient Inversion via LT-Code Inspired Peeling in Federated Learning

New gradient inversion attacks tied to erasure-coding theory recover 94–100% of ImageNet batches, showing federated learning privacy leakage is underestimated.

The paper connects gradient inversion in federated learning to erasure-correcting code theory, constructing analytic attacks that exceed previously known recovery bounds. The attacks recover batches exactly, with every sample's label, from a single FedSGD round, and certify each recovery without ground-truth data. On eight image and tabular benchmarks, even a passive attacker observing an honestly trained network recovers 94–100% of ImageNet batches up to size 128, and more than 90% actively at batch sizes of several hundred. The authors conclude that federated learning's privacy leakage has been underestimated.

arXiv cs.CR·Sep 9, 03:17 UTC · 8d agoResearch

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AgentGrad: Intervention-guided Prompt Optimization for Multi Agent Systems

AgentGrad introduces intervention-guided prompt optimization for LLM multi-agent systems, achieving state-of-the-art results with 2.5x faster optimization.

AgentGrad is a prompt optimization framework for LLM-based multi-agent systems that addresses limitations in textual gradient extraction and aggregation. It uses sequential intervention to identify the agent whose prompt modification resolves a given failure, then applies agent-level supervision and semantic gradient clustering to build generalized gradients. Experiments report state-of-the-art performance across five MAS benchmarks and a 2.5x average reduction in wall-clock optimization time versus the next-fastest baseline.

Hugging Face daily papers·Sep 7, 20:00 UTC · 9d agoAI research

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Algorithmic stability via ensembling

Theoretical work derives a general framework quantifying stability guarantees for averaging-based ensembles under arbitrary data perturbations via covariance operator norms.

The paper develops a framework for quantifying algorithmic stability of ensembling strategies defined via averaging, for varied types of data perturbation. The main result bounds the stability of the ensembled algorithm in terms of the norm of a covariance operator describing the ensembling process. The framework yields interpretable insights across practical perturbation examples and provides sharper guarantees than those derived from differential privacy considerations.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 16:39 UTC · 7d agoAI research

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Benign Loss Landscapes Can Coexist with Worst-Case Hardness

Theory paper shows tree tensor networks contain worst-case hard targets yet benign loss landscapes, with difficulty arising from degenerate saddles.

The paper studies tree tensor networks (TTNs), which generalize deep linear networks and Tucker decompositions and embed arbitrary read-once Boolean formulas. It proves that every local minimum that is minimum-norm is global for every realizable target, so bad local minima do not distinguish typical from worst-case problems. Instead, learning difficulty arises from high-order degenerate saddle points caused by rank-deficiency, illustrated via a parity function case study, linking landscape geometry to computational hardness.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:57 UTC · 5d agoAI research

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Model-Aware Schedules Improve Generation via Fiberwise Optimal Transport

Researchers introduce model-aware diffusion schedules via fiberwise optimal transport, cutting flow-matching FID on CIFAR-10 by 38.6% at 16 function evaluations.

The paper proposes constructing diffusion and flow-matching sampling schedules from a fiberwise prediction risk defined via optimal transport, combined with coefficient-path kinetic action, yielding a closed-form time allocation. Across DDPM and flow-matching experiments spanning targets, datasets, and architectures, the schedules beat model-agnostic baselines, including a 38.6% relative FID reduction for flow matching on CIFAR-10 at 16 function evaluations. Normalized fiberwise-risk profiles from independently trained models align closely, suggesting empirical universality, and a frozen analytic allocation template retains most of the gains.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:30 UTC · 6d agoAI research

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Likelihood-free inference with nuisance parameters through normalizing flows

Researchers decompose normalizing flows to derive near-pivotal statistics for likelihood-free inference with nuisance parameters, recovering the t-test and beating Welch limits.

A new paper decomposes neural-network normalizing flows to uncover pivotal statistics in the presence of nuisance parameters using only a sample generator from the distribution of interest. The statistic is near-pivotal in the sense of minimum average KL-divergence of its p-values and can incorporate prior knowledge of group invariances such as translation and scale. Experiments show it recovers the one-sample t-test almost exactly, outperforms the Welch test on worst-case size over a constrained variance-ratio range, and delivers higher power and much faster runtime than profile likelihood-ratio techniques on small-to-moderate samples.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:58 UTC · 7d agoAI research

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Quenched Ensemble Sampling

Quenched Ensemble Sampling generalizes nested sampling's hard energy constraint to repulsive potentials, traversing first-order phase transitions where tempering fails.

Quenched Ensemble Sampling generalizes nested sampling's hard energy constraint into a family of repulsive potentials at the energy boundary, preserving monotone energy descent while making the constrained target amenable to scalable gradient-based kernels. On synthetic phase-transition models it estimates marginal likelihood and draws posterior samples across first-order transitions where popular alternatives such as tempering fail. Applications include marginal likelihood estimation for Bayesian neural network architecture comparison and partition function estimation in a high-dimensional continuous lattice field theory.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:16 UTC · 2d agoAI research1

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VC-Attention: Value Smoothing and Softmax Casting for Low-bit Attention

VC-Attention is a training-free low-bit attention method for diffusion transformers, achieving 1.46-1.59x kernel speedups on datacenter GPUs with higher fidelity.

VC-Attention is a training-free low-bit attention framework for diffusion transformers that pairs V-Smooth value smoothing via lightweight online clustering with ExpCast-FP8, which maps log-domain scores directly to E4M3 FP8 probability codes and eliminates the FP32 softmax exponential. It is implemented for B200, B300, H200, RTX PRO 6000, and RTX 5090 GPUs. Across Wan2.2, LongCat-Video, HunyuanVideo-1.5, and MiniMax-H3, it improves fidelity over low-bit baselines and speeds attention 1.46-1.59x over BF16 FlashAttention-4 on datacenter Blackwell and Hopper GPUs and 2.3-3.6x on workstation cards, with 1.13-1.70x faster end-to-end clip generation.

Hugging Face daily papers·updated 00:45 UTC · 4h ago·first Sep 13, 20:00 UTC · 3d agoAI research 2 sources

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Unlocking Lossless Speedups in LLMs via Discrete Diffusion

Uno pairs autoregressive LLMs with lightweight diffusion weights to draw multiple tokens in parallel, delivering up to 3x lossless speedup without a draft model.

The paper introduces diffusion-augmented LLMs: autoregressive weights trained with the standard next-token objective plus lightweight diffusion weights trained via a Diffusion Distillation phase to emit multiple tokens in parallel. Psi-Spec samplers enable lossless acceleration without the separate draft model required by speculative decoding. The 8B Uno model outperforms the 26B open DiffusionGemma and proprietary Mercury 2 on agentic tool use, coding, and long-context reasoning benchmarks, with up to 3x throughput gains over the base model at all evaluated batch sizes. Code and checkpoints are released publicly.

Hugging Face daily papers·Sep 2, 20:00 UTC · 14d agoAI research

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Rethinking Heterogeneous System Disaggregation for Subquadratic Attention

SQD disaggregates LLM inference by quadratic versus subquadratic attention layers, improving energy efficiency up to 56% on heterogeneous systems versus GPU-only baselines.

SQD (SubQuadratic Disaggregation) splits decode not by operator type but by quadratic versus subquadratic attention, matching their distinct arithmetic intensity and memory footprints. For sparse attention LLMs it separates top-k selection (requiring full KV indexing) from top-k attention plus FFN; for linear and sliding-window models it separates dense attention layers from subquadratic layers plus FFN. On an adjusted 8xB200 heterogeneous proxy, tokens-per-joule improves 53% on GLM 5.2, 31% on Nemotron 3 Ultra, and 56% on Gemma 4 31B. A Rubin plus LPX analytical model shows 1.2x-1.5x tighter achievable latencies and up to 3.6x higher throughput versus attention-FFN disaggregation.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:55 UTC · 5d agoAI research

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Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult

Lower bounds show heterogeneous asynchronous optimization cannot match homogeneous rates under standard similarity assumptions; strong interpolation plus local PL condition closes the gap.

The paper examines whether pessimistic optimal time complexities for asynchronous distributed optimization with heterogeneous workers (different data distributions) can be overcome. It proves improvement is provably impossible under widely used first- and second-order similarity assumptions for any randomized algorithm, and that the weak interpolation assumption alone is also insufficient. Combining strong interpolation with the local Polyak-Lojasiewicz condition yields a new time complexity bound matching the best-known homogeneous dependence on worker computation times without requiring identical data distributions.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 17:24 UTC · 1d agoAI research

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Learning Multimodal One-step Flow Policy via Value-weighted Optimal Transport

OptiFlow learns one-step multimodal flow policies for offline RL via state-wise entropic optimal transport, avoiding critic overestimation and mode collapse.

The paper introduces OptiFlow, a framework that frames one-step flow policy learning as a structured sample-allocation problem in offline reinforcement learning. It jointly trains a value-aware reference flow policy and a one-step policy, coupling action samples through state-wise entropic optimal transport where critic values set distillation priority and action-distance cost ensures geometrically compatible pairings. By avoiding direct critic maximization, it anchors the policy to high-value dataset-supported modes without out-of-distribution divergence. Code is released on GitHub and the method performs strongly across diverse offline RL benchmarks.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:10 UTC · 2d agoAI research

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Robust Policy Optimization via Adversarial Importance Sampling

Adversarial Importance Sampling estimates worst-case RL returns without extra interactions; authors also release the advrl PyTorch library.

The paper introduces Advis, which uses importance sampling over trajectories from standard training to estimate and optimize verifiable worst-case returns, requiring no additional environment interactions or auxiliary networks. It also releases advrl, a modular PyTorch library of single-file robustness methods and adversarial attacks for reproducible evaluation. The authors show adversarial hyperparameters do not transfer across agents, so they evaluate with 6-14x more attacker configurations than prior work. Effectiveness is demonstrated on continuous control environments.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:40 UTC · 5d agoAI research1

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