Search: “generalization-bounds”

Smart search ranks by meaning as well as keywords (one row per story, last 45 days).

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

12

Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks

Theory paper derives nearly tight Rademacher complexity bounds for sparsely activated one-hidden-layer ReLU networks.

Building on Awasthi et al. (COLT 2024), the authors bound statistical complexity for networks where each input activates at most k of s hidden units. A support-preserving cover and normalized chaining argument remove the explicit dimension factor, with matching lower bounds up to logarithms. They also derive agnostic minimax excess-risk bounds of order min{1, sqrt(s/(km))} for a normalized bounded loss and show bias bounds comparable to WR restore worst-case rates even on domains where sparsity holds globally.

arXiv cs.AI / cs.LG / cs.CL·Sep 8, 17:53 UTC · 8d agoAI research

16

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

28

Distance generalization in transformers: why bother with positional encoding?

arXiv study uses synthetic delay-copy tasks to show how RoPE, ALiBi, NoPE and training data diversity affect transformers' distance generalization.

The paper studies distance generalization in transformers: extrapolating when inter-token distances change between training and inference while context length stays fixed. Using two synthetic delay-copy tasks with finite source-recall distances, the authors test models on unseen delays. They investigate whether positional encodings such as RoPE and ALiBi outperform no positional encoding (NoPE), how the diversity of training distances affects performance, and when distance transfer learning is positive or negative.

arXiv cs.AI / cs.LG / cs.CL·Sep 10, 17:57 UTC · 6d agoAI research2

30

Optimal Rates for Agentic Networked Information Aggregation

Researchers close the Kearns–Roth–Ryu gap for agentic networked information aggregation, proving excess error is constant up to depth M^2 then Θ(M^2/D).

The paper studies a networked learning model where agents in a DAG each see only a subset of features and pass only their predictions forward. It sharpens the earlier lower bound to Ω(√(M/D)) for depth below M^2 and constructs M-covered paths of depth D ≥ M^2 achieving Ω(M^2/D) excess error, establishing the correct rate for both regression and logistic classification. It also shows excess error contracts geometrically along the path for any fixed distribution, ruling out a single instance that witnesses polynomial lower bounds at every depth.

arXiv cs.AI / cs.LG / cs.CL·Sep 4, 16:12 UTC · 12d agoAI research

28

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

15

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

28

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 · 5d agoAI research

18

Type Diversity Enables Transformers to Generalise Compositionally

Researchers show lexical-versus-structural compositional generalization gaps in Transformers stem from type diversity imbalance in datasets, not architectural limits.

The paper argues that Transformers' difficulty with structural compositional generalization is an artifact of low structural type diversity in prior benchmark datasets rather than an architectural limitation. Using Grammatical Framework, the authors create linguistically diverse variants of COGS and SLOG. They find type diversity correlates with compositional generalization equally in lexical and structural test cases, contradicting previous claims that compound divergence explains task difficulty.

arXiv cs.AI / cs.LG / cs.CL·Sep 11, 17:59 UTC · 5d agoAI research

20

Grouped Value Attention: Efficient KV Caching via On-Demand Key Reconstruction

Grouped Value Attention stores grouped values and reconstructs content keys via a learned linear map, cutting KV-cache size about 45-47% versus GQA.

GVA stores only grouped values and reconstructs content keys with a learned linear map absorbed into the query at decode time, while a small shared decoupled RoPE channel preserves positional information via a separately cached positional key. At 350M parameters trained on 30B FineWeb-Edu tokens, the 16-dimensional positional variant scores 44.18 average accuracy across five tasks versus 44.36 for GQA and 43.88 for MLA. Custom decoding kernels are in development with an open-source release planned.

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

42

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

15

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

22

ISTA-DASLab/Qwen3.8-27B-GSQ-RCO-GGUF — new model trending #3 on Hugging Face

ISTA-DASLab releases GSQ-RCO non-uniform GGUF quantizations of Qwen3.8-27B down to 2.5 bpw, with task-lossless IQ3_S matching BF16 benchmark scores.

ISTA-DASLab released GGUF quantizations of Qwen3.8-27B produced with GSQ (Gumbel-Softmax Quantization) and RCO (Riemannian Constrained Optimization), non-uniform methods that allocate per-tensor precision via gradient-based search under a total size budget. Four checkpoints range from 2.50 bpw (8.4 GB) to 3.50 bpw (11.8 GB), plus a BF16 vision projector (mmproj) enabling multimodal use. The recommended IQ3_S build is task-lossless, matching the BF16 base exactly on AIME25 (100.00) and LiveCodeBench v6 (85.71) at roughly one fifth of the BF16 size. Optional -mtp variants add a Multi-Token Prediction head for speculative decoding in llama.cpp.

Hugging Face trending models·Aug 28, 18:38 UTC · 19d agoModel release1

44

Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarch

New work characterizes language generation in the limit via finite witnesses, proves a full separation-width hierarchy, and formalizes all results in Lean.

The paper fully characterizes when language generation in the limit is possible for arbitrary families over a countable universe: each target must admit a finite positive witness such that targets activated by any finite sample share an infinite common intersection. It defines positive separation width and proves every level of the resulting hierarchy occurs, with countable families admitting singleton witnesses and unions of families with infinite common cores requiring unbounded finite witnesses. The characterization, a universal normalization, and a diagonal capture lemma are machine-checked in the Lean proof assistant, with the development maintained on GitHub.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 17:54 UTC · 7d agoAI research1

18

Generative Late-Interaction Embeddings For Visual Document Retrieval

GLIE compresses visual document retrieval embeddings to four vectors per page while retaining nearly 80% of uncompressed nDCG@5 accuracy.

Researchers analyzing late-interaction retrieval embeddings found they lie exactly on the unit sphere and concentrate near a manifold of intrinsic dimension five to six. GLIE learns a few k vectors per page that serve as a lightweight index and a basis to regenerate the full embedding set for exact rescoring of top candidates at query time. On ViDoRe v1 with four vectors per page, GLIE retains nearly 80% of uncompressed nDCG@5 versus 70% for the best prior post-hoc method, using a 415K-parameter network trained in under three GPU-minutes on 1,000 pages.

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

28

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 · 5d agoAI research

36

Building Multilingual Bridges: Data Mixing as the Pillar of Generalization for In-Language Reasoning

Researchers train Tiny Aya L2-Thinker, a 3.35B model achieving over 93% in-language reasoning across 60 languages via multilingual data mixing.

The paper addresses L2 reasoning, where models reason consistently in the language of the user's prompt rather than defaulting to English. Through data-centric SFT optimization, the 3.35B Tiny Aya L2-Thinker reaches above 93% L2 reasoning rate across 60 languages on 6 benchmarks covering math, commonsense, instruction following, open-ended generation, and cultural reasoning. The authors find that generalization to held-out languages relies on broad language coverage, multilingual non-reasoning data, and a strong English reasoning backbone, without needing reasoning supervision in every target language. Model weights and multilingual reasoning data are released.

Hugging Face daily papers·Sep 8, 20:00 UTC · 8d agoAI research1

45

Proximity Gaps for Gabidulin Codes and Applications

Researchers prove proximity-gap bounds for rank-metric and Gabidulin codes, enabling the first polynomial commitment scheme framework based on rank-metric error-correcting codes.

The paper proves every linear rank-metric code admits a proximity gap for deltas up to (d-1)/(3n) with error at most q^(e+1)/q^m, and improves the gap to (d-1)/(2n) for Gabidulin codes with error at most 10q^(n-1)/q^m, matching bounds for Reed-Solomon codes. A constructed infinite family of constant-rate Gabidulin codes shows the (d-1)/(2n) bound is tight, and a counterexample establishes a lower bound on the error at the d/(3n) gap. Applications include an IOPP for interleaved Gabidulin codes adapted from the Ligero IOPP and a q-linearized polynomial commitment scheme adapted from Ligero-based PCS, reportedly the first PCS framework based on rank-metric codes.

arXiv cs.CR·Sep 9, 07:45 UTC · 7d agoResearch

20

A Note on Sphere Packing Bounds for Tuple Lattice Sieving

Proves upper bounds on k-irreducible unit vector set rates, yielding nearly tight asymptotics relevant to tuple lattice sieving in cryptanalysis.

The paper bounds the maximal asymptotic rate of k-irreducible sets of unit vectors via spherical code packing bounds. It shows R_k is sandwiched between (1/2 - o(1)) log2(k)/k and (1 + o(1)) log2(k)/k for large k. These almost-tight bounds inform subexponential complexity analyses of tuple lattice sieving, which underpins security estimates for lattice-based cryptography.

arXiv cs.CR·Sep 8, 03:20 UTC · 8d agoResearch

15

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

16

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 · 7d agoAI research

15

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 · 6d agoModel release

50

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

15

Right Tool, Right Job: Native-Language Evaluation, Tokenizer Sensitivity, and Methodological Findings from a French-Only BabyLM

French BabyLM entry METRON-FR (125M GPT-2, 92.47M words) shows tokenizer artifacts dominate child-scale zero-shot evaluation; proposes standard diagnostics.

METRON-FR is a 125M-parameter GPT-2 pretrained on 92.47M French words, submitted to the BabyLM 2026 Strict track, scoring 85.97% on the native Quebec-French QFrBLiMP benchmark and 62.80% on the BabyLM-weighted leaderboard. A cross-lingual GLUE protocol combining French task-data translation with rank-16 LoRA shows relational tasks gain while world-knowledge tasks regress. Bilingual Lexicon Induction reaches p@1 of 68.84%, 18x above chance, and ablations show single-token zero-shot scoring is dominated by tokenizer and template artifacts at child scale.

arXiv cs.AI / cs.LG / cs.CL·Sep 15, 16:43 UTC · 1d agoAI research

12

Unifying Conformal Language Tasks with In-Context Ensembles

Researchers propose Conformal Relevance, which builds conformal score functions via in-context example curation and ensembling to improve conciseness across seven NLP tasks.

The paper targets NLP tasks like summarization and extractive QA that reduce to retrieving content under coverage and conciseness constraints. Conformal Relevance replaces hand-engineered LLM scoring prompts with curated in-context examples and ensembles, maintaining coverage guarantees while improving conciseness with minimal manual input. The authors demonstrate the framework on seven NLP tasks and contribute theory, including a complementarity condition for when ensembling improves worst-case sentence scores and a saturation bound on ensemble gains.

Hugging Face daily papers·Sep 1, 20:00 UTC · 15d agoAI research1

42

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

20

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 · 9d agoAI research

33

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

10

Building Multilingual Bridges: Data Mixing as the Pillar of Generalization for In-Language Reasoning

Tiny Aya L2-Thinker, a 3.35B model, achieves over 93 percent in-language reasoning across 60 languages via optimized multilingual data mixing; weights released.

The paper studies L2 reasoning, the ability to reason consistently in the language of the user's prompt, approached through SFT data composition and scheduling. Tiny Aya L2-Thinker (3.35B) achieves an in-language reasoning rate above 93 percent across 60 languages on six benchmarks spanning math, commonsense, instruction following, open-ended generation, and cultural reasoning. Findings show generalization to held-out languages comes from broader language coverage, multilingual non-reasoning data, and a strong English reasoning backbone, suggesting reasoning is language-agnostic and transferable without per-language supervision. Model weights and multilingual reasoning data are publicly released.

arXiv cs.AI / cs.LG / cs.CL·Sep 9, 16:56 UTC · 7d agoAI research1

45

RelateAnything: Real-Time Open-Vocabulary Relation Prediction From Any Inputs

RelateAnything is a 53M-parameter open-vocabulary relation prediction model running at 20 ms/frame, with 2.3-3.5x higher mean recall than comparable open-vocabulary methods.

RelateAnything predicts scored relations between image regions using any predicate vocabulary supplied at inference as text embeddings, with object labels never required as input, so region sources can change without retraining. Training covers 19,103 predicates using positive-unlabeled supervision; the authors release RA-4M (474k images, 4.3M geometrically verified relations over 10,102 free-text predicates) and the OV-SGG-Bench evaluation suite. The 53M-parameter model runs at 20 ms/frame and achieves 2.3-3.5x the mean recall of the strongest comparable open-vocabulary method across cross-dataset and zero-shot benchmarks. Model, corpus, and benchmark are public.

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

40