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Tuc Nguyen

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Published work

2 published item(s)

preprint2026arXiv

ATLAS: Adaptive Test-Time Latent Steering with External Verifiers for Enhancing LLMs Reasoning

Recent work on activation and latent steering has demonstrated that modifying internal representations can effectively guide large language models (LLMs) toward improved reasoning and efficiency without additional training. However, most existing approaches rely on fixed steering policies and static intervention strengths, which limit their robustness across problem instances and often result in over- or under-steering. We propose Adaptive Test-time Latent Steering, called (ATLAS), a task-specific framework that dynamically controls steering decisions at inference time using an external, lightweight latent verifier. Given intermediate hidden states, the verifier predicts the quality of ongoing reasoning and adaptively selects whether and how strongly to apply steering, enabling per-example and per-step adjustment with minimal overhead. To our knowledge, ATLAS is the first method to integrate learned latent verification into test-time steering for enhancing LLMs reasoning. Experiments on multiple mathematical reasoning benchmarks show that ATLAS consistently outperforms both vanilla decoding and fixed steering baselines, achieving higher accuracy while substantially reducing test-time token usage. These results demonstrate that verifier-guided latent adaptation provides an effective and scalable mechanism for controlling reasoning efficiency without sacrificing solution quality. All source code will be publicly available.

preprint2026arXiv

Spectral Flattening Is All Muon Needs: How Orthogonalization Controls Learning Rate and Convergence

Muon orthogonalizes the momentum buffer before each update, replacing its singular values with ones via Newton-Schulz iterations. This simple change lets Muon tolerate far larger learning rates and converge faster than other optimizers, but why? We show that the mechanism is spectral flattening, and develop two results around it. First, we prove that Muon's maximal stable step size scales with the average singular value of the gradient rather than the largest, which bottlenecks standard gradient descent. Second, we recast Muon as a preconditioned gradient method and show, under a Kronecker-factored curvature model, that it improves the effective convergence factor, with the improvement controlled by the spectrum of the gradient covariance. Extensive experiments validate both results: Muon remains stable at learning rates that cause SGD to diverge within the first few iterations, and reaches accuracy milestones several epochs earlier even at identical step sizes. Taken together, our results offer a principled, geometric explanation for Muon's empirical success.