Search: “optimization-theory”

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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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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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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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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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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 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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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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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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Generalized Agent Iteration: One Formal Framework for Iterative Policy Improvement and Recursive Self-Improvement

Generalized Agent Iteration formally unifies iterative policy improvement and recursive self-improvement, defining axes that distinguish anchored, goal-drifting, and self-referential agents.

The paper proposes Generalized Agent Iteration (GAI), a formal framework that models learning as a cycle of agent evaluation and agent improvement, defining the agent as a configuration of modifiable components. Two dials—whether the improving mechanism is part of the agent and whether the evaluation standard is grounded outside it—separate generalized policy iteration (GPI) from recursive self-improvement (RSI) and classify systems as anchored, goal drift, or fully self-referential. The framework places existing systems on shared axes and makes defects of recursive self-improvement statable one condition at a time.

Hugging Face daily papers·Sep 10, 20:00 UTC · 5d 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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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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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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Reduced-Space Multi-Fidelity Bayesian Optimization of Process Simulation Models

RS-MFBO couples global sensitivity analysis with fidelity-augmented Gaussian processes to slash costly high-fidelity simulation runs in industrial flowsheet optimization.

The paper presents RS-MFBO, a reduced-space multi-fidelity Bayesian optimization framework for high-dimensional, expensive black-box functions. It integrates Global Sensitivity Analysis for dimensionality reduction with a fidelity-augmented Gaussian process and a cost-aware acquisition strategy featuring cooldown and promotion mechanisms. Validation on a plasmid DNA bioprocess (SuperPro Designer) and a green fuel synthesis plant (Aspen HYSYS) shows substantial reductions in high-fidelity evaluations while remaining competitive with single-fidelity baselines.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 16:46 UTC · 1d 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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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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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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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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ScienceBuddy: Recursive-in-Recursive Self-Improvement for Interactive Scientific Agents

ScienceBuddy couples harness evolution with model reinforcement learning so scientific agents continually self-improve from researcher feedback in an interactive workspace.

The authors release ScienceBuddy, an interactive scientific research workspace that transforms researcher requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. Its recursive-in-recursive self-improvement paradigm couples harness evolution (inner recursion, model fixed) with model reinforcement learning under the improved harness (outer recursion). Case studies span four scientific task families, and the system is released to the scientific community as a research product.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 17:55 UTC · 1d agoAI research 2 sources

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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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Design Docs Are All You Need: An AI-native Machine-Learning Performance Tool

Researchers present SMART, an ML performance-modeling library regenerated by AI coding agents from natural-language design docs instead of code.

The paper describes SMART, a symbolic performance-modeling library whose main branch contains almost no code: the repository is a DAG of self-contained design documents, and coding sub-agents regenerate implementations from only the docs on version updates. Reliability rests on a worked-example doc style used as in-context demonstrations and a minimal operator IR with SymPy cost expressions, offering both fast analytical roll-up and fine-grained modulo-scheduling modes. Regenerated implementations reproduce hand-audited reference models, including DeepSeek-V3 serving on a TPU pod slice, to round-off precision.

arXiv cs.AI / cs.LG / cs.CL·Sep 4, 17:08 UTC · 12d agoAI research1

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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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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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Training Specialist Models without Reasoning Trajectories for Domain Expert Distillation

Study shows specialists trained on question-answer pairs implicitly select latent reasoning trajectories, and tuning choices control the precision-generalization trade-off in distillation.

The work demonstrates that specialist optimization implicitly selects from a latent trajectory space when specialists are trained only on question-answer pairs without explicit reasoning supervision. Using student distillation as an agnostic probe across 27 specialist-student pairings, specialization-generalization profiles correlate exceptionally strongly. Explicitly controlling the specialist's distributional drift systematically shifts both teacher and distilled student along a controllable trade-off between domain precision and general-capability retention across chemistry, physics, and multilingual settings, even across divergent model families.

Hugging Face daily papers·Sep 11, 20:00 UTC · 4d agoAI research

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Differential Privacy Meets Fixed Parameter Tractability: Algorithms and Lower Bounds

Theory paper combines differential privacy with fixed-parameter tractable encoders, improving approximation guarantees for combinatorial optimization and proving new lower bounds.

The paper studies combinatorial optimization under epsilon-differential privacy within the implicit encoder-decoder framework of Gupta et al. (SODA 2010), generalizing it to allow fixed-parameter tractable encoders. This circumvents approximation barriers inherent to polynomial-time algorithms and yields improved guarantees for fundamental combinatorial optimization problems. The authors establish the first representation-independent lower bounds: assuming a non-uniform variant of the Gap Exponential Time Hypothesis, no epsilon-DP encoder-decoder pair can achieve certain approximation guarantees with a subexponential-time decoder for sufficiently small epsilon. Representation-dependent lower bounds are also provided for larger epsilon.

arXiv cs.CR·Sep 11, 07:13 UTC · 5d agoResearch

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Dream-RSI: Recursive Self-Improvement through Evolving Worlds

Dream-RSI refines exploration policies by dreaming in replay simulators built from discovery history, cutting discovery costs across coding tasks.

Dream-RSI is a framework for scalable recursive self-improvement in autonomous coding agents, where a lightweight orchestration layer makes exploration explicit and programmable while leaving the underlying agent unchanged. Its core insight is that accumulated discovery history can serve as a replay simulator over the realized search space, providing immediate, low-cost off-policy feedback to evaluate and refine exploration policies without expensive online evaluations. Across algorithm engineering, mathematical optimization, and GPU kernel engineering, Dream-RSI achieves competitive or improved discovery quality at substantially reduced cost.

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

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COBRA-Skills: Contextual Bandit-Guided Evolution for Agent Skill Optimization

COBRA-Skills uses contextual bandits to guide LLM agent skill evolution, cutting optimization cost 55-58% versus SkillOpt while topping six agent benchmarks.

COBRA-Skills formulates LLM agent skill optimization as budgeted sequential optimization over a dynamically evolving candidate space. It couples contextual-bandit-guided prioritization with evidence-grounded skill evolution, selectively spending execution-based evaluations on promising candidates while refining skills from feedback. Across six heterogeneous agent benchmarks and three target models, it achieves the strongest average performance while reducing optimization cost by 55-58% relative to SkillOpt using only 50 unique optimization examples per benchmark. The method remains robust to agent harness changes and works when the target model generates its own skills.

Hugging Face daily papers·Sep 9, 20:00 UTC · 6d agoAI research

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Expert-Space Exploration in MoE Reinforcement Learning

ESRL explores MoE expert-routing space during RL post-training, improving Qwen3-30B-A3B Pass@1 by 3.2 points over GRPO without extra compute.

The paper shows perturbing expert routing increases rollout diversity similarly to higher decoding temperature, but naive perturbation degrades quality. ESRL anchors high-confidence experts, restricts stochastic routing to a plausible candidate pool, adapts perturbation strength via router entropy, and replays recorded expert paths during policy optimization. It achieves the best results across top-K, top-1, and shared-expert MoE backbones on math, science, and code tasks; on Qwen3-30B-A3B it improves average Pass@1 and Pass@8 over GRPO by 3.2 and 4.5 percentage points.

Hugging Face daily papers·updated Sep 11, 16:58 UTC · 5d ago·first Sep 10, 20:00 UTC · 5d agoAI research 2 sources

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ZGCM-1: A Fully Open and Extremely Efficient Foundation Model for Math and Agentic Search

ZGCM-1 is a fully open 7B foundation model with 256K context that stays competitive with frontier models on math reasoning and agentic search.

ZGCM-1 is a fully open 7B dense foundation model trained from scratch using an efficiency-focused recipe: interleaved gated sliding-window and full attention, a stable FP8 Muon optimizer, and MDP-based mid-training with context scaling across 16K, 64K, and 256K. On mathematical reasoning and agentic search suites it remains competitive with much larger frontier models such as Qwen3-235B-A22B and GLM-5.1. The recipe yields a ~4.2x improvement in 16K pre-training time-to-loss, and all weights, checkpoints, training code, data recipes, and W&B logs are open-sourced.

Hugging Face daily papers·Sep 10, 20:00 UTC · 5d agoModel release

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Graph Machine: Towards Better Pretraining via Edges

Researchers propose Graph Machine, an O(n)-state sparse architecture that replaces 75% of Qwen3-0.6B dense layers with only slight loss change.

The paper introduces the Graph Machine (GM), an architecture that maintains an O(n)-sized state accessed through sparse, dynamic routing via pointer-like edges updated differentiably by a referral mechanism resembling pointer chasing. The authors replaced 75% of dense Transformer layers in Qwen3-0.6B with GM sparse layers and pretrained from scratch on 15.7B tokens. Retrieving 2 of 4,096 tokens per KV head in each sparse layer degrades loss only slightly, while retrieving 4 marginally improves loss over the dense baseline.

Hugging Face daily papers·Sep 1, 20:00 UTC · 14d agoAI research

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