#01Nov 5, 2026
cs.AI
StepBack: Step-Level Error-Localized Resampling for Efficient Test-Time Reasoning
Yang Ouyang, Jung-Eun Kim
Self-consistency (SC) is a widely used decoding strategy for improving chain-of-thought reasoning, but it requires sampling many complete reasoning trajectories with a preset budget. Its efficient variants reduce the cost mainly by stopping full-trajectory sampling early or distributing the number of samples across questions. In this paper, we propose StepBack, a step-level error-localized resampling method for efficient test-time reasoning. Given a small set of draft trajectories, StepBack localizes likely first error positions using lightweight signals and then resamples the detected error step and its suffix, followed by majority answer voting. Empirically, StepBack matches the accuracy of SC on average across seven mathematical reasoning and multi-hop QA benchmarks, while reducing token usage by up to 41.26%. In addition, by nature, StepBack can be combined with adaptive inference methods such as Adaptive Consistency, further improving their inference-time efficiency.
#02Nov 5, 2026
stat.ML
Unifying Central Flow, Rod Flow, and the Edge Coupling
Eric Regis, Sinho Chewi
At the edge of stability, the iterates of gradient descent oscillate along the sharp directions of the Hessian. This poses a significant challenge for continuous-time models as the usual continuous-time approximation -- the gradient flow -- admits no oscillations. Several continuous-time models have been proposed to capture the behavior at the edge of stability, among them central flow and rod flow. Although both models can be interpreted as performing a coarse-graining in time, the connection between them remains poorly understood. Here we show that both flows can be derived from a third object, the edge coupling: a functional on consecutive iterates whose critical points are the fixed points and period-two orbits of gradient descent. It is revealed that the two flows correspond to coarse-grainings at different time scales. Rod flow coarse-grains over only the fastest time scale, while central flow coarse-grains over both the fast and intermediate time scales. Furthermore, using the edge coupling, we derive rod flows and central flows for momentum methods such as heavy ball and Adam. We verify the derived flows experimentally on representative neural network architectures, where they track the discrete iterates throughout all phases of training -- including the transition from the stable regime to the edge of stability.
#03Nov 5, 2026
cs.LG
User Embeddings are Superpositions of Interpretable Behavioral Modes
Jonathan Kozaczuk, Zheng Dong, Noyan Evirgen and 7 more
User embeddings are central components of modern recommendation, personalization, and behavioral modeling systems. Though these embeddings can compactly encode rich behavioral information, they are inherently dense and opaque, limiting interpretability. To address this gap, we argue that user embeddings can be understood as sparse superpositions of interpretable behavioral modes. This structure is directly predicted by generative models of user behavior for linear embeddings and extends approximately to deep-learning representations by the superposition hypothesis. Superimposed modes can naturally be recovered by sparse dictionary learning methods, such as sparse autoencoders (SAEs), and recovered modes can be automatically named and queried in natural language. We validate mode recovery against known ground truth on synthetic data, where SAEs recover modes better than classical sparse baselines, including on transformer-encoded embeddings. We then apply the method to classical and transformer-based user embeddings from two real-world datasets. We also show how the corresponding natural-language labels enable zero-shot audience retrieval and characterization over embeddings never trained on text. The framework is post-hoc and model-agnostic, requiring no modification to the upstream embedding system.
#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
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.