#01Nov 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.
#02Nov 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.
#03Nov 5, 2026
cs.LG
A Hidden Markov Preference Model for Online Prediction of Adversary Actions
Angel Daruna, Michael Cogswell, Tixiao Shan and 3 more
A defender anticipating an attacker needs a probability distribution over the attacker's next action from information available before that action occurs. Two structures complicate this: the attacker's behavioral regime persists and can switch within an episode, and each action combines an operation with state-dependent arguments whose feasible values change over time. We capture both with a hidden Markov model whose latent state is the active regime and whose regime-conditioned action law is defined on a feasibility-masked tree of executable actions. The same likelihood forms the next-action distribution and updates the regime belief once the action is seen, and a partially observed prefix contributes its resolved local factors. Estimation separates into convex logistic fits that Baum-Welch reuses when regimes are unlabeled. We derive a reach-weighted nodewise KL expression for regime information, a sequence-wise log-loss bound for switching regime paths, and a uniform fallback guarantee. On the CAGE 2 cyber defense benchmark the filtered latent state is worth 0.8 nats per step, and after a controller switch the loss begins to fall in three steps against ten for a recurrent baseline.
#04Nov 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.
#05Nov 5, 2026
cs.RO
T3R: Training-Free Two-Stage Token Refinement Towards Efficient and Robust VLA Models
Mohammed Hassan, Zhenyang Chen, Zheng Wang and 5 more
Vision-Language-Action (VLA) models enable end-to-end robot control, but inference is increasingly expensive. Each decision processes hundreds of visual tokens, often across multiple cameras, leading to substantial computation while allowing irrelevant background content to distract action prediction under distribution shift. We argue that these issues stem from two complementary forms of redundancy: many visual tokens are spatially irrelevant, while attention over the remaining tokens is often misallocated. Based on this observation, we propose T3R, a Training-Free Two-Stage Token Refinement framework. In the first stage, segmentation-guided token pruning removes irrelevant visual patches to reduce computation and eliminate distracting context. In the second stage, saliency-guided attention biasing reallocates attention toward action-critical visual regions and language instructions within the retained tokens. Together, pruning produces a cleaner candidate set, while attention biasing further emphasizes the most decision-relevant evidence, yielding a better accuracy-efficiency frontier than either stage alone. On LIBERO-Spatial, T3R removes 85% of scene-camera visual tokens while essentially matching the unpruned success rate, and improves success by up to 7 percentage points under out-of-distribution object-placement perturbations. The timing comparison attributes 7.8 ms per inference call to pruning and attention-bias application. As input resolution increases, LLM-forward profiling shows up to a 3.3x speedup over the unpruned baseline. Evaluations across LIBERO, SIMPLER, and RoboTwin with three VLA backbones show the strongest accuracy-efficiency benefits in multi-camera settings. These results demonstrate that training-free token refinement is a practical approach to efficient and robust VLA inference.