Search: “convex-analysis”

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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 · 4d agoAI research

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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 · 7d agoAI research

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Nonmaximal sums of maximally monotone operators under Rockafellar's constraint qualification

Mathematical paper constructs counterexamples on c0 and l1 disproving Rockafellar's conjecture that sums of maximally monotone operators remain maximally monotone.

The authors build counterexamples where two maximally monotone operators satisfy the interior-domain condition yet their sum is not maximally monotone, refuting Rockafellar's sum conjecture. One counterexample is constructed on c0 and another on l1 with its usual norm. A general construction theorem computes the monotone polar of a class of graphs, gives necessary and sufficient conditions for maximal monotonicity, and shows how a positive rank-one perturbation yields a nonmaximal sum.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:26 UTC · 6d 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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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 · 6d agoAI research

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MAxBench: A Multinomial Concept Recovery Benchmark

MAxBench evaluates multinomial concept recovery methods, finding affine subspaces steer most reliably but none consistently beats prompting.

MAxBench is a geometry-agnostic evaluation framework for multinomial concept representations in language models, based on sampling from recovered concept representations. It compares 10 localization methods covering 5 geometry types across 6 concepts and 4 models. Findings show affine subspaces steer more reliably than rank-one or linear subspaces due to better non-zero offsets, manifold steering is competitive where applicable, and no method consistently outperforms prompting.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:08 UTC · 4d agoAI research

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TransNormal-2: Geometry-Grounded Rectified Flow with Edge-Aware Decoding for Precise Normal Estimation

TransNormal-2 improves monocular surface-normal estimation by fixing VAE edge degradation with geometry-aware losses and refinement, matching MoGe-2 with 1.4% of annotations.

TransNormal-2 is a FLUX.2-based rectified-flow framework for monocular surface-normal estimation with single-step deterministic inference. The authors quantify that VAE 8x spatial compression introduces 1.3-8.5 degrees of mean angular error even on ground-truth normals, with edge error up to 2.8x the global error. The method adds geometry-aware pixel-space losses and an RGB-guided Geometric Refinement Module to correct boundary-localized decoding errors. It matches or exceeds MoGe-2 on all eight reported metrics using only 1.4% as many task-specific annotations, and cuts transparent-object MAE by 4.2 degrees on ClearGrasp and 3.1 degrees on ClearPose.

Hugging Face daily papers·Sep 5, 20:00 UTC · 10d 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 · 7d agoAI research

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Marigold V2: Revisiting Diffusion Transformers for Monocular Depth Estimation

Marigold V2 adapts diffusion transformers for monocular depth estimation, improving AbsRel 16-26% over the previous best on KITTI and ETH3D.

Huawei's Bayer lab revisits the Marigold approach to repurpose image generation and editing models built on the diffusion transformer (DiT) architecture into monocular depth estimators. The recipes target single-step inference from pretrained multi-step flow-matching models, with remedies including alignment to ground-truth semantic features and a two-stage fine-tuning protocol using a Sinkhorn-based loss. The resulting model produces crisper depth maps that generalize out-of-distribution and also achieves state-of-the-art results on surface normals estimation and intrinsic image decomposition.

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 · 5d 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 · 6d agoAI research

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Unsolved Problem by Fields Medalist Breached by Two High School Students

Two high school students used Claude Opus 5 and GPT-5.6 Sol to help solve an open Lorentzian polynomials problem, posting a 75-page arXiv proof.

Aayush Bathija and Prince Rohatgi of Oak Park High School, mentored by UCLA postdoc Daniel Soskin, published the 75-page paper 'Bounded Ratios for Lorentzian Polynomials' (arXiv 2609.05341), solving an open problem in Fields Medalist June Huh's Lorentzian polynomial theory. The main structural theorem extends bounded coefficient-ratio characterization from quadratic to arbitrary-degree polynomials via discrete convexity conditions. The students used Claude Opus 5 and GPT-5.6 Sol for exploration and proof ideas but independently verified all arguments; the result follows an open letter from 25 Fields Medalists voicing concerns about AI's impact on mathematical rigor.

Hacker News · security·Sep 14, 12:23 UTC · 2d agoAI researchHN 22↑ · 19 comments

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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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DataFlex-RL: An Evaluation Platform for RLVR Data Policies

DataFlex-RL benchmark of 13 RLVR data policies on Qwen2.5-7B finds none reproducibly beats uniform sampling under matched GRPO training.

DataFlex-RL is an evaluation platform comparing rollout-selection, reweighting, and mixture data policies for RLVR under a common GRPO recipe. Across 13 configurations and 12 matched seeds with Qwen2.5-7B-Base on 12 math, logic, and science benchmarks, uniform GRPO improved domain-balanced accuracy by 7.76 points, but no alternative policy achieved a statistically significant improvement. A corrected 12-seed Llama-3.1-8B-Base extension found no consistent winner, and math-heavy evaluation summaries were negatively correlated (-0.33) with domain-balanced summaries.

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

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Steering Geometry: Validating Human Value Geometry in LLM Steering Space

Researchers show LLM activation steering vectors encode human value geometry predicted by Schwartz's theory, with fidelity improving at scale but degrading after instruction tuning.

The study tests whether latent geometry of activation steering vectors reflects theory-specified structure in human values, using Schwartz's Theory of Basic Human Values and a new 26K-sample benchmark spanning 20 values. Distribution-driven methods (CAA, SphericalSteer, ODESteer) recover predicted value topologies with Spearman correlation up to 0.51 (p < 10^-13), while behavior-centric methods (COLD-Steer, BiPO) steer comparably but show little geometric fidelity. Geometric alignment improves with model scale but drops after instruction tuning. Better geometric alignment also yields more human-consistent cross-value transfer, steering one value lifting compatible values and suppressing opposing ones.

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

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Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs

Theoretical tutorial establishes equivalence between covariance neural networks and PCA, with stability and transferability bounds and brain-age applications.

The paper reviews the theory of coVariance neural networks (VNNs), graph neural networks that operate on covariance matrices as graphs. It derives a conceptual equivalence between VNNs and PCA-based information processing, refined stability bounds under finite-sample covariance perturbations, and transferability characterizations across multiscale datasets. Demonstrated applications include brain age gap estimation for neurodegenerative conditions from neuroimaging data.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:28 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 · 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 · 4d 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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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 · 1d agoAI research

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Decomposition Buys Integrity, Not Yield

Study of 600 production deep-research traces finds agent-tree decomposition loses findings at rate N^(1-δ); flat architectures maximize yield.

The paper models multi-agent decomposition as a tree where an agent holding b items retains each with probability r(b); with r(b)=1/b every tree delivers exactly one finding regardless of shape. Analysis of 600 production deep-research traces estimates delta=0.34 retention decay, and 1,012 annotated traces show one brief in sixteen goes off-target per tier, giving an alignment penalty of 0.536. Depth still cuts root context exposure from N to N^(1/k) and is cheaper at scale, with a hazard model over 743,819 production tool calls showing delegation is an opening move rather than a response to filling context.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 17:04 UTC · 20h 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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VDiff-Bench: A Challenging Benchmark for Fine-Grained Image Difference Identification

VDiff-Bench, a 1,756-question benchmark, shows multimodal LLMs struggle with fine-grained image-difference identification, scoring as low as 8.7% on low-level changes.

VDiff-Bench is a multiple-choice benchmark of 1,756 four-way questions over image pairs covering 10 change categories including position, motion, color, texture, OCR/text and illumination, with curated hard negatives. Evaluation of 11 state-of-the-art open- and closed-source MLLMs shows fine-grained visual comparison remains brittle: 7-8B-scale open-source models score 52.5-70.6% on semantic changes but only 8.7-33.3% on low-level changes like noise and texture. Notably, Grok 4.3 shows a sharp performance drop on noise and texture differences, falling behind large open-source models like Kimi K2.5 and K3.

Hugging Face daily papers·Sep 4, 20:00 UTC · 11d 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 · 4d agoAI research1

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Privacy Failure in Split-LLM Training, The Returned Gradient Nullifies the Decoys

Researchers show split-LLM training leaks privacy via zero-valued gradients on decoy rows, exposing which activations are real despite passing forward-channel checks.

A systems-security case study of a two-node split-LLM training setup found that the returned output gradient from an Untrusted Cloud Node is exactly zero for decoy rows, revealing which rows are real. Across nine seeds, zero patterns identified real rows in 4,096 of 4,096 frames per run, and an attack on frame contents recovered 0.65 to 1.50 percentage points of extra tokens over a baseline. Both datasets passed forward-channel privacy and quality checks but failed once the returned gradient was included. Row-wise gradient clipping and noise closed the leak for roughly 0.01 nats of held-out cross-entropy, though five unmeasured attack classes remain.

Hugging Face daily papers·Sep 2, 20:00 UTC · 13d agoAI safety & security

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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 · 1d agoAI research1

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Disentangling Representation Evolution in Transformers through Directional Decomposition

Researchers decompose transformer updates into parallel and perpendicular components, linking representation geometry to editing robustness, compression diagnosis, and training interventions.

The paper studies transformer representation evolution as functional geometry, decomposing learned updates into parallel and perpendicular components across attention/MLP and value-aggregation spaces. Targeted edits reveal a space-dependent asymmetry: exclude-self value-space parallel manipulation is markedly more robust than residual-space and perpendicular counterparts. Full-aggregate parallel suppression during from-scratch pretraining lowers validation-loss trajectories and improves downstream averages, with the value-space variant strongest. Code is released on GitHub.

Hugging Face daily papers·updated Sep 14, 17:56 UTC · 1d ago·first Sep 13, 20:00 UTC · 2d agoAI research 2 sources

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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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TempCloze: Can Video-LLMs Identify the Missing Middle?

TempCloze benchmark tests Video-LLMs' temporal reasoning with 1,521 videos, finding temporal alignment is the primary failure mode across 31 models.

TempCloze is a video cloze benchmark in which models must identify the true missing middle clip given the beginning and ending clips, using 1,521 carefully filtered videos from seven sources, mostly long-take and egocentric footage. Distractors are constructed along three dimensions: Semantic, Alignment and Progression, with shared scenes and objects to reduce appearance cues. Evaluation of 10 proprietary and 21 open-source Video-LLMs found Alignment is the primary bottleneck, with models often recognizing plausible semantics and local event progression but struggling with temporal alignment.

Hugging Face daily papers·Aug 31, 20:00 UTC · 15d agoAI research

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