#01Aug 11, 2026
cs.AI
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
Alan Li, Rahul Saha, Anton Xue and 4 more
AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant $K_G$, which captures the hardness between combinatorial problems and their continuous relaxations. Specifically, while the precise value of $K_G$ is not known, we recently tightened the best known bounds to \[ \frac{6π}{11} \;\le\; K_G \;\le\; \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Crucially, these improvements were achieved using an AI research system that could arrive at insights deemed novel by domain experts. We give a detailed discussion of our experience using AI for mathematics research, particularly touching upon its strengths and weaknesses, as well as our experience with creating ideal conditions for AI to arrive at breakthrough insights.
#02Aug 11, 2026
stat.ME
Goodness-of-Fit Tests and Calibration Machine-Learning Algorithms for Logistic Regression with Sparse Data
Ebrahim Khaled Ebrahim
Assessing the goodness-of-fit of a logistic regression model is a critical prerequisite before the model is used for inference. However, goodness-of-fit (GOF) tests such as the chi-square and deviance tests often give invalid results when the data are "sparse" -- a common issue with continuous predictors like age or weight, where the asymptotic distributional assumptions are not satisfied. This thesis studies classical GOF tests for binary logistic regression under both grouped and sparse data, comparing about 30 statistical tests and machine-learning calibration algorithms. These span the classical chi-square and Hosmer-Lemeshow variants, standardized Pearson statistics, covariate-space partitioning, smoothing-based methods, and contemporary calibration machine-learning and bootstrap procedures. At a fixed size, the GiViTI calibration test (2016), McCullagh (1989), Osius-Rojek (1992), le Cessie (1995) and Stute-Zhu (2002) proved empirically powerful, balancing correct identification of bad models (high empirical power) against not raising false alarms on good models (correct empirical Type I error). Relying on formal methods alone is insufficient: visual diagnostics such as calibration plots are a vital exploratory step for detecting model deficiencies that formal tests often overlook. An application to real data (the Low Birth Weight dataset) shows that many of these tests fail to give valid conclusions when exposed to the complexities of actual datasets. The main conclusion is that model assessment requires a combination of several powerful statistical tests alongside careful visual inspection of model calibration.
#03Aug 11, 2026
cs.CC
How to Verify Consistency of Probabilistic Claims
Orr Paradise, Oliver Richardson, Yoshua Bengio and 1 more
When a probabilistic predictor answers many conditional-probability queries, are its answers self-consistent, and can this be verified in polynomial time? This problem is of interest for AI safety, where safety is derived from honesty about probabilistic predictions of unwanted outcomes potentially caused by an AI action. We construct an interactive PCP as follows. Let a predictive model be specified by a probability circuit P and a circuit Q which outputs confidence in predictions. Together, P and Q implicitly specify exponentially many probabilistic claims. We show a protocol in which a polynomial-time verifier can verify the approximate consistency of (P,Q). The verifier is given the pair of circuits (P,Q), which it evaluates at only a few points; alongside them it is given a proof oracle, an encoding of a witnessing probability distribution allegedly consistent with the predictions of (P,Q), which it reads at a few locations while interacting with a single untrusted prover. En route, we must ensure the existence of a sparse witnessing distribution consistent with the model's predictions. To do so, we first consider witness distributions for the consistency of explicit probabilistic claims, rather than claims specified by a predictor: say m claims, each of the form Pr[Y = 1 | X = x] = p, over n Boolean variables. Building on work initiated by Nilsson (Artif. Intell., 1986), we place l_2-approximate probabilistic consistency of explicit claims in NP, with certificates of length O(mn + log B) in the input bit-precision B; we further show how a small additive completeness-soundness gap removes the dependence on B. Together these results provide a complexity-theoretic foundation for certifying the self-consistency of probabilistic predictors. We view our interactive PCP as a first step toward training predictive models to prove their own consistency.
#04Aug 11, 2026
cs.CL
Attention-Path Fragility as an Uncertainty Signal in Large Language Models
Minsoo Kim, Sungyoung Ji, Kisung Moon and 1 more
We propose that a model's uncertainty about a token is reflected not only in the breadth of its output distribution but also in whether a confident prediction is \emph{fragile} under perturbation of its attention pathways. We instantiate this as ASMI (Attention-Subnetwork Mutual Information), a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks, with a semantic-agreement kernel to discount surface-form disagreement. The signal is not a restatement of output confidence: on grounded QA an out-of-fold test shows it adds error-predictive information beyond single-pass confidence and entropy, concentrated in \emph{confident-but-fragile} predictions, where acting on it roughly halves the retained error of a confidence filter. The distinctness is regime-graded, so ASMI predicts its own domain of applicability, strong where answers are routed through provided context and bounded by design where they are recalled from parametric knowledge. Sem-ASMI reads the signal from a single greedy response, without the stochastic generations the strongest baselines require, and ties or beats Semantic Entropy on ten of the twelve grounded benchmark-backbone settings. Across the same twelve settings, the best ASMI variant, typically the adaptive one reusing the ten samples already drawn for the baselines, ties or leads the strongest baseline in eight, significantly in three under a paired test. On parametric QA all variants revert to or below the zero-cost MSP baseline, exactly as predicted, and the estimates are near-deterministic across reruns. A head-level analysis shows that what tracks this boundary is not the presence of head-level fragility but whether that fragility couples to errors.
#05Aug 11, 2026
cs.CL
From Interpretability to Control: Insights from Six Years of the TrustNLP Workshop
Rahul Gupta, Abhinav Mohanty, Anaelia Ovalle and 10 more
The Workshop on Trustworthy Natural Language Processing (TrustNLP), co-located with major ACL conferences since 2021, has grown from 8 proceedings papers to 41 over six editions, documenting a field-wide transition from post-hoc interpretability of static models to mechanistic understanding and proactive control of generative systems. We synthesize insights from all 144 proceedings papers, classifying them along six trust dimensions grounded in established frameworks (TrustLLM, DecodingTrust). We observe co-occurrences with capability emergence. The release of the first high-impact chat models activated all trust dimensions simultaneously, while subsequent model generations shifted focus toward truthfulness and safety alignment. Analysis from the classification study reveals that truthfulness is the fastest-growing dimension (absent in 2021-2022, comprising 37% of papers by 2025-2026), fairness remains the most consistent theme, and explainability exhibits a U-shaped trajectory; declining as post-hoc methods lost relevance but resurging in 2026 through mechanistic interpretability. A cross-venue comparison with ACL, NAACL, EACL, and EMNLP (~2K papers) in the same period shows that TrustNLP's topical distribution closely follows the field average. We identify four structural insights and conclude with actionable directions for the research community.