Search: “convex-optimization”

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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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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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Bellman Policy Optimization

Bellman Policy Optimization, a critic-free RLVR method derived from Policy Mirror Descent, improves LLM mathematical reasoning without intermediate state-value estimation.

The paper introduces Bellman Policy Optimization (BPO), a critic-free reinforcement learning method for LLMs with verifiable rewards, derived from Policy Mirror Descent. BPO uses the Bellman equations to reformulate PMD as a trajectory-level objective for autoregressive generation with terminal rewards, avoiding state-value estimation at intermediate states. The authors prove BPO shares the same unique optimal solution as PMD and validate it on mathematical reasoning benchmarks.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:59 UTC · 2d 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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A Unified and Constrained View of Regularization-Based Robust Reinforcement Learning

Paper unifies regularization-based robust RL methods via new performance-gap upper bounds and jointly learned Lagrange multipliers.

The authors derive new upper bounds on the gap between nominal and worst-case deep RL policies, each expressible as an existing regularization objective plus a KL-divergence penalty. Robust training is reformulated as constrained optimization, where prior methods correspond to a fixed Lagrange multiplier. The multiplier is instead updated jointly with the policy, auto-tuning the regularization weight. Adversarial evaluations across several continuous control tasks validate the theory.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 16:45 UTC · 5d agoAI research1

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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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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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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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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 · 8d agoAI research

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Drift-Constrained Optimization: Only Direction Matters in Fine-Tuning Instruct Models

Drift-Constrained Optimization reformulates fine-tuning as update-direction selection, letting Qwen3 models improve target tasks within a behavioral drift budget.

The paper specifies a behavioral drift budget before optimization and shows that update direction is the remaining degree of freedom, reformulating fine-tuning as a direction-selection problem. In a stringent QA-only setting where instruct models must still generate multi-step reasoning at inference, a coarse layer-selective probe reverses the failure of QA-only fine-tuning. Across Qwen3-8B and Qwen3-14B, these directions substantially improve scientific reasoning and multilingual translation, matching or outperforming dedicated translation systems over 100+ languages and giving stronger initialization for reinforcement learning.

Hugging Face daily papers·Sep 11, 20:00 UTC · 4d 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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Ask Before You Optimize: Dynamic Pre-Formulation Clarification for Interactive Optimization

Researchers release OR-Clarify, a benchmark testing whether LLM agents ask clarifying questions before formulating optimization models from incomplete requests.

OR-Clarify evaluates pre-formulation clarification in operations research: each task gives a partial problem description, withholds structured hidden slots, and scores agents via bounded interaction with a simulated user, measuring slot recovery, stopping behavior, silent assumptions, and interaction cost. The authors also propose InterOPT, a two-stage framework that identifies formulation-critical gaps to decide when to ask or stop. In choice-based experiments InterOPT substantially outperforms all baselines in exact slot recovery and remains competitive in the open-ended setting.

Hugging Face daily papers·Sep 3, 20:00 UTC · 12d agoAI research1

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A Generalization of Amari's Bayesian Duality

Paper generalizes Amari's Bayesian duality by connecting it to a convex duality of Bayes' rule.

The authors revisit Amari's less-known work on Bayesian duality from information geometry. They connect Bayesian duality to a convex duality formulation of Bayes' rule and present a generalization of it. The paper is purely theoretical and discusses relevance for modern AI, with no experiments or model releases.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:51 UTC · 8d 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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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 · 8d 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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Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start

Thin-shell stability proof along the Gaussian cooling path improves cold-start logconcave sampling complexity to near n^2.5 from n^2.75.

The authors prove that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This yields improved complexity for sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions the complexity is nearly n^2.5, improving the previous n^2.75 bound and matching the abstract Speedy walk.

arXiv cs.AI / cs.LG / cs.CL·Sep 14, 17:10 UTC · 2d 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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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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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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A positive resolution of the gap-entropy conjecture

New proof resolves the gap-entropy conjecture for Gaussian bandits, bounding optimal best-arm identification samples by H(log(1/delta)+Ent(I)) up to constants.

A paper proves the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in [0,1], and a unique optimal arm. It shows the optimal expected sample count, averaged over arm-label permutations, is within absolute constant factors of H(log(1/delta)+Ent(I)), where H sums squared gaps and Ent(I) is the instance's gap-entropy. It also gives an instance-independent algorithm bounded by a constant multiple of this quantity plus a g^-2 loglog(e^e/g) term for the smallest gap g.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:57 UTC · 7d agoAI research

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Eliciting Weak-to-Strong Generalization with On-Policy Reverse Distillation

OPRD distillation enables weak-to-strong generalization by amplifying verifier-supported policy updates, outperforming existing RL and distillation methods with fewer student updates.

On-Policy Reverse Distillation (OPRD) evaluates a weak teacher's policy shift relative to its reference policy on student rollouts and amplifies the verifier-supported component of the student's policy gradient. This rescaling preserves the stationary points of policy optimization while letting the student learn beyond the teacher's capacity ceiling. In successive model transfer and multi-teacher distillation, OPRD achieves higher performance with fewer student updates than existing RL and distillation approaches, and response-style analysis shows students remain closer to verifier-RL-trained models than to their weak teachers.

Hugging Face daily papers·Sep 7, 20:00 UTC · 8d agoAI research

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Entropy-Regularized Rank-Masked Policy Optimization for Test-Time Reinforcement Learning in Code Generation

Researchers propose ERPO, enabling test-time reinforcement learning for code generation via probe-executed consensus rewards, rank masking, and entropy regularization.

The paper introduces probe-driven test-time reinforcement learning (TTRL) for code generation, where output-free probe inputs are constructed from problem statements and candidate programs are executed on them to compute a Probe Consensus Reward (PCR). Because PCR can be gamed through spurious consensus, the authors propose Entropy-Regularized Rank-Masked Policy Optimization (ERPO), which turns low-PCR outcomes into conservative negative updates via rank masking and constrains policy drift with an entropy ceiling. On coding benchmarks, ERPO substantially improves pass@1 and pass@k in both in-domain adaptation and zero-shot transfer.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:54 UTC · 8d agoAI research1

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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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Unfold The World: Factorize 4D Properties in Reinforcing Spatial Reasoning

FactoSR factorizes 4D spatial reasoning into XY, Z, and T reinforcement-learning sub-objectives, boosting VLM performance on VSI-Bench by 5.9% and All-Angles-Bench by 4.5%.

Researchers present FactoSR, a factorized reinforcement learning framework that decomposes world-consistent reasoning into planar correspondence, depth consistency, and temporal reversibility sub-objectives. Optimizing these verifiable constraints turns the ill-posed projection recovery problem into tangible reasoning steps. Evaluations show gains of 5.9% on VSI-Bench and 4.5% on All-Angles-Bench for 3D and 4D reasoning, arguing VLMs' spatial bottleneck stems from training on 2D projections versus latent 3D geometry and temporal continuity.

Hugging Face daily papers·Sep 2, 20:00 UTC · 13d 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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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 · 15d agoAI research

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SAS: Simple Attention Sparsification via End-to-End Optimization of Context Ranking

SAS trains attention sparsification end-to-end with the language modeling loss, beating sparse attention baselines especially under tight context budgets.

Simple Attention Sparsification (SAS) injects the selector's continuous scores into attention logits in log form inside the softmax, letting gradients from the language modeling loss directly update the ranking of context units. The method uses normalized softmax gates calibrated against the current block and a memory-efficient Triton kernel integrated into FlashAttention-style computation. Across reasoning, long-context, and agentic tasks, SAS consistently outperforms trainable sparse attention baselines across budgets, with the largest gains under tight attention budgets.

Hugging Face daily papers·updated Sep 11, 17:58 UTC · 5d ago·first Sep 10, 20:00 UTC · 5d agoAI research 2 sources1

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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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Measuring benchmark optimization in speech recognition

Hugging Face examines how much speech recognition systems overfit benchmarks and how to measure benchmark optimization in ASR.

A Hugging Face post on measuring benchmark optimization in automatic speech recognition, analyzing how model improvements on benchmarks reflect genuine capability gains versus overfitting. It is evaluation methodology research with no direct security impact.

Hugging Face Blog·Aug 21, 00:00 UTC · 26d agoAI research

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