#01Nov 5, 2026
cs.AI
The Gold Rush in AI4Math, II: What are signatures of AI-assisted Proofs?
Yuanchuan Guo, Jiashun Jin, Zheng Tracy Ke and 1 more
The growing use of AI in mathematics raises a question: can we detect AI involvement in proofs, separately from AI assistance with writing? Historical arXiv papers, recent papers disclosing substantive AI use, and manuscripts released by OpenAI provide a rich empirical basis for studying this question. However, several challenges remain: lack of matched case-control pairs; potential incompleteness of disclosure; and lack of ready-to-use features designed to capture signals of AI involvement in proofs. To address these challenges, we construct five cohorts comprising 8,281 papers by combining existing manuscripts with those we produced using generative AI. These cohorts span different levels of AI involvement and include matched pairs of papers addressing the same research problems. We then introduce ProofTrace, a framework that represents each paper as a graph of immediate proof support (GIPS) and extracts interpretable features of mathematical organization. Our study yields three discoveries. First, principal-component projections of our features reveal a qualitative gradient of AI involvement, where AI-reworded papers remain close to human papers, the two AI-generated cohorts depart in broadly shared directions, and papers disclosing substantive AI use occupy intermediate positions which shifts toward AI-generated cohorts over time. Second, we identify recurring signatures of AI-generated proofs, such as fewer externally cited results, greater reliance on intermediate conclusions, and altered graph connectivity; many of these signatures persist under controls for research field, manuscript length, or graph size. Finally, in a separate detection experiment, ProofTrace distinguishes human-written papers from those disclosing substantive AI use. Its performance remains stable under AI rewording, whereas the performance of state-of-the-art text-based detectors declines sharply.
#02Nov 5, 2026
cs.RO
Failure Prediction and Classification in Vision-Language-Action Models Via Calibrated Latent Probing
Michal P. Podolinsky, Yunhao Yang, Daniel Little and 6 more
Vision-Language-Action models (VLAs) enable general-purpose embodied intelligence, but their performance is brittle under distribution shift, where unanticipated failures can damage equipment or endanger people. Deploying VLAs in real-world systems therefore requires a runtime monitor that is timely, calibrated, and informative while being efficient enough to run on the edge. Existing methods fail to fulfill these requirements. We present VLA-Tug, a lightweight probe over the latent layers of a VLA backbone that improves early failure detection and bounds the missed-detection and false-alarm rates, with minimal inference overhead. We show that supervising on the pre-failure segment of a trajectory increases early failure detection at matched false-positive rates by up to 30% over the strongest learned baseline. Under shift to unseen tasks, the bounds on missed-detection and false-alarm rates remain valid in up to 86% of runs, versus at most 21% for baselines. Unlike existing methods, VLA-Tug predicts the failure mode to enable corrective actions, raising top-3 accuracy on unseen tasks by up to 44% over a majority baseline. VLA-Tug enables real-time monitoring where the well-timed and informative probe supports lightweight steering that improves task success. We release a dataset of 3,180 annotated manipulation episodes to support future work on latent failure detection in VLAs at https://vla-tug.github.io.
#03Nov 5, 2026
cs.LG
Adversarial Training with Large Step Sizes: Implicit Bias, Optimization, and Sharpness
Yi Feng, Andrea Paudice
Adversarial Training (AT) is an important method for improving model robustness. We study the dynamics of deterministic Gradient Descent (GD) in AT. Most existing works in this direction focus on the small or vanishing step sizes regime, where GD resembles a continuous-time flow. However, such step sizes can make training inefficient and are rarely used in practice. In this paper, we study the AT dynamics of GD with large constant step sizes. We first study GD in adversarial linear logistic regression, focusing on two aspects: where the model parameters converge (implicit bias) and how quickly the losses decrease (optimization). We then turn to neural networks training and study how the sharpness of losses evolve during AT. Our results advance the understanding of the behaviors of GD with large step sizes in AT and highlight three key differences from its behavior in Standard Training (ST): (i) the implicit bias gap between AT and ST, previously established only for small step sizes, persists for arbitrarily large constant step sizes, (ii) different from ST, there is no uniform rate of convergence for the optimization error in AT, and (iii) sharpness can exhibit two-stage dynamics that differ from the Edge-of-Stability behavior observed in ST.
#04Nov 5, 2026
cs.LG
Towards interpreting any residual stream direction by scaling activation inversion
Celeste De Schamphelaere, Juan J. Vazquez, Ari Spiesberger and 4 more
To interpret a direction in a language model's residual stream, we can look for text that strongly activates it. But when such text is found by scanning a corpus, it is limited to what that corpus contains. We develop Maximally-Activating Example Metamodels (MAEMs), language models which map residual stream directions from a subject model to text exemplars that strongly activate those directions. Our objective is to maximise the cosine similarity of a supplied residual stream direction with the activations of the text generated by the MAEM. This label-free RL objective helps to scale MAEMs on diverse sources of residual stream directions. Empirically, we find the resultant metamodel produces informative exemplars: a Qwen3.6-27B MAEM inverts held-out activations better than corpus search or a natural-language autoencoder (NLA), beats corpus search (at 10M tokens) on a majority of held-out languages/domains, and activates 89% of held-out SAE features. It also identifies concepts behind steering vectors about as well as NLAs, recovers the payloads of LoRA backdoors more often than corpus search, and can even verbalise some model workspace inner monologue. Unlike explanations produced by other metamodels (e.g. NLAs), MAEM exemplars can be verified with a forward pass on the subject model, making the MAEM objective a grounded alternative for scaling the training of metamodels.
#05Nov 5, 2026
cs.LG
Spectral and Subspace Dynamics of LoRA in Supervised Fine-Tuning and Reinforcement Learning
Chenruo Liu, Zihan Wang, Yijun Dong and 1 more
Low-rank adaptation (LoRA) is commonly used in both supervised fine-tuning (SFT) and reinforcement learning (RL), often under similar optimizer settings. Yet, how the different dynamics of the two stages manifest in the low-rank increment that LoRA optimizes remains unclear. Tracking the singular spectrum and subspaces of LoRA updates on mathematical reasoning tasks, we find that RL concentrates the spectrum at every learning rate, while SFT expands it at moderate learning rates; moreover, RL rotates the singular subspaces much faster than SFT at small learning rates. Interpolating between SFT and RL one ingredient at a time, we pinpoint group-mean baseline subtraction as the source of both contrasts. A quadratic multi-index model updated via LoRA unveils the underlying mechanism: group-mean baseline subtraction tilts the balance between two competing forces, coherent fitting and gradient noise, toward spectral concentration and faster subspace rotation, while forcing the risk-favorable learning rate to be low. Guided by these dynamics, we tailor LoRA updates to each stage: in SFT, we flatten the spectrum of the full update to spread adaptation across singular directions, whereas in RL, we flatten the part of the update outside the current LoRA increment span to promote subspace rotation. Experiments on mathematical reasoning tasks across multiple models show that the respective configurations for SFT and RL yield the best performance among the compared methods in most evaluated settings.