arXiv subjects

Noel Thomas

Publications and source records attributed to Noel Thomas.

6 recordsLinked to original sources

arXiv2026

No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training

Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked. We show that beyond a small reproducible core, there is no such object. Two estimates of the top-r subspace computed at the same step from disjoint minibatches disagree as much as estimates computed T steps apart (0.73 vs 0.74 of the maximal chordal distance sqrt(2r), at Pythia-160M with r=128): the apparent rotation at each refresh is dominated by estimator noise. This holds across four model families in three architecture classes from 70M to 6.9B parameters, strengthening with scale, and more weakly in a vision transformer. Only ~39 of 128 directions are reproducible across minibatches, and averaging cannot recover the rest: under N-fold averaging the gradient's spectral tail shrinks as N^(-1/4) rather than the N^(-1/2) of pure noise, so no averaging budget makes the subspace well defined. What helps instead follows from treating each refresh as a change of coordinates for Adam's state. Carrying the second moment blindly is provably about (r-k*)/2 worse than the best rotation-blind estimator, while the first moment transports exactly through the rotation, the optimal linear map under isotropic gradients and the rule LDAdam uses. At 1B over 40k steps (3 seeds), full LDAdam reaches 18.7 perplexity at beta2=0.999, beating untransported GaLore after its best beta2 fix (19.3); shortening the second-moment memory to beta2=0.99 helps the refreshing optimizers, though for canonical GaLore the effect is small and a full-rank control reverses it. One measurable fact, subspace non-identifiability, clarifies why GaLore works, which patches work, and what to check before trusting a low-rank assumption: the reproducible rank k*.

cs.LG↗

arXiv2026

FormInv: A Measurement Protocol for Semantic Invariance in Mathematical Reasoning Benchmarks

A paraphrase-quality audit of MathCheck (ICLR 2025) detected 4 semantically incorrect paraphrases in 129 groups (3.1%); removing them drops GPT-4o from rank 2 to rank 4 and elevates Claude Haiku and DeepSeek V3 above it; these ranking changes are invisible to any single-model evaluation. Cross-model unanimity found these errors automatically (>= 3/4 models for MathCheck; >= 6/9 for our primary evaluation) for under $10; in our own dataset the same protocol found that 47% of auto-generated connective-variation paraphrases were semantically incorrect. That flaw compounds a deeper measurement gap: Claude Haiku 4.5 achieves 86% accuracy yet SCR=50%, meaning half its theorems are answered differently under semantically equivalent restatements, while aggregate accuracy across 9 models spans only 86-96% yet Semantic Consistency Rates (SCR) span 50-82% -- a 32-point gap invisible to standard benchmarks. Formally, for any target ranking over 9 frontier models there exists a weighting over paraphrase families that realizes it (No-Free-Benchmark corollary), because no model Pareto-dominates all families -- so benchmark designers who select families are implicitly choosing which model wins. FormInv supplies the audit protocol (replicated on external benchmarks at 100% recall), SCR and per-theorem Cochran's Q as primary invariance measures evaluated on 9 models across 366-811 items (on Lean4-verified theorems), and FormInvSelector for regime-aware model selection.

cs.LG↗

arXiv2026

ChaosBench-Logic v2: Evaluating LLM Logical Reasoning over Dynamical Systems at Scale

Standard accuracy on binary reasoning benchmarks hides critical failure modes: prior collapse, inconsistency under paraphrase, and inability to reason about parameter-dependent dynamics. We present ChaosBench-Logic v2, a 40,886-question benchmark over 165 dynamical systems with 27 FOL predicates and 78 axiom edges, together with CARE (Calibration- and Adversarial-Robust Evaluation), a protocol that surfaces these pathologies. Evaluating 14 models, we find that regime-transition reasoning remains near random (MCC = 0.05) even for frontier models, whereas FOL deduction with given premises reaches MCC = 0.52. Per-family decomposition shows that the proprietary-model advantage concentrates on cross-indicator (+0.40) and consistency tasks, while open-source Qwen 2.5-32B dominates indicator diagnostics (0.91 vs. 0.45). Two models exhibit negative MCC on bifurcation questions, confirmed as systematic anti-correlation via confusion-matrix analysis.

cs.LG↗

arXiv2026

BioXArena: Benchmarking LLM Agents on Multi-Modal Biomedical Machine Learning Tasks

Large language model (LLM) agents are increasingly capable of automating components of machine learning development, yet existing biomedical benchmarks mainly focus on question answering, reasoning, and tool usage, or evaluate only narrow aspects of biomedical ML coding. We present BioXArena, a biomedical machine learning benchmark designed to evaluate whether agents can generate task-specific model training pipelines for heterogeneous and multi-modal biomedical datasets. BioXArena contains 76 end-to-end tasks across 9 domains, including sequence modeling, single-cell analysis, structural biology, network biology, chemical biology, perturbation dynamics, phenotype-disease modeling, biomedical imaging, and text-integrated learning. Each task is curated from primary biomedical sources into a unified evaluation framework with hidden labels, held-out graders, and biology-aware metrics normalized to a 0 to 1 scale. Agents are required to write executable code, train predictive models, and generate submissions for private test samples. Most tasks involve multiple input modalities, including tabular data, images, natural language, molecular sequences, omics matrices, and protein structures. We evaluate 11 agent configurations in a standardized 2-hour single-GPU environment. MLEvolve with Gemini-3.1-Pro achieves the highest average score of 0.666, followed by GPT-5.4 with 0.636, while no single agent consistently dominates across all domains. We additionally perform extensive ablation studies, robustness evaluations, scaling analyses, cost analyses, and failure-mode investigations to better understand how model backbones, agent scaffolds, inference budgets, and biomedical domains influence BioML coding performance. We will publicly release all benchmark tasks, graders, execution runners, leaderboard results, and agent trajectories.

cs.CE↗

arXiv2026

Regime-Conditioned Evaluation in Multi-Context Bayesian Optimization

Published transfer-BO comparisons often estimate an average treatment effect of acquisition choice over hidden regime variables, while practitioners need the conditional effect for their specific prior quality, budget ratio, and metric. An audit of 40 transfer-BO papers from NeurIPS, ICML, ICLR, AISTATS, UAI, TMLR, JMLR, and AutoML-Conf (2022-2025) finds that 98% never vary B/|A| as a controlled axis. On the same GDSC2 benchmark, changing only the budget reverses the ranking: at B=50, Greedy outperforms UCB by 0.050 Hit@1, while at B=100, UCB outperforms Greedy by 0.035. We capture this transition with the Portable Regime Score PRS=(B/|A|)(1-rho), where rho is the prior rank correlation and can be estimated from pilot contexts before the main comparison. Across 79 conditions spanning chemistry, drug-response biology, and HPO, a hierarchical model gives beta=0.50 (p=1.1e-9), and 19% of conditions fall in an equivalence zone where |advantage|<0.01 Hit@1. In five published reversal cases, PRS predicts the winner from pre-comparison observables. A No-Free-Leaderboard proposition explains why unconditional rankings are unstable: when CATE changes sign across regimes, the reported ATE becomes a function of benchmark mixture. RegimePlanner, which estimates rho online and switches acquisition accordingly, wins all 16 HPO-B search spaces at B=100 and exceeds the matched {Greedy,UCB} per-context oracle on GDSC2 by 18%. Pre-registered predictions achieve 27/40=67.5% overall accuracy and above 90% within EMA prior families. The practical protocol is simple: report B/|A|, rho, K, and metric alongside any claimed acquisition advantage.

cs.LG↗

arXiv2026

ChaosBench-Logic: A Benchmark for Logical and Symbolic Reasoning on Chaotic Dynamical Systems

Large language models (LLMs) excel at natural language tasks but remain brittle in domains requiring precise logical and symbolic reasoning. Chaotic dynamical systems provide an especially demanding test because chaos is deterministic yet often misinterpreted as randomness or complexity. We introduce ChaosBench-Logic, a benchmark that evaluates LLM reasoning across 30 diverse dynamical systems using a unified first-order logic (FOL) ontology. Each system is annotated with truth assignments for 11 semantic predicates, and 621 questions are generated across seven reasoning categories, including multi-hop implications, cross-system analogies, counterfactual reasoning, bias probes, and multi-turn dialogues. We define metrics for logical accuracy, implication consistency, dialogue coherence, and contradiction, and we release an open-source evaluation pipeline. Initial experiments show that frontier LLMs such as GPT-4, Claude 3.5 Sonnet, Gemini 2.5 Flash, and the open-source LLaMA-3 70B achieve 91-94% per-item accuracy, yet still score 0% on compositional items and exhibit fragile global coherence. Dialogue-level accuracy ranges from 53.1% (GPT-4 CoT) to 75.5% (LLaMA-3 zero-shot). ChaosBench-Logic provides a rigorous testbed for diagnosing such failures and a foundation for developing neuro-symbolic approaches that improve scientific reasoning in LLMs.

cs.AI↗