arXiv subjects

Xuntao Lyu

Publications and source records attributed to Xuntao Lyu.

3 recordsLinked to original sources

arXiv2026

Spectral Principal Paths: A Spectral Perspective on Linear Representation Formation in LLMs

High-level representations have become a central focus in enhancing AI transparency and control, shifting attention from individual neurons or circuits to structured semantic directions that align with human-interpretable concepts. While the Linear Representation Hypothesis (LRH) suggests that such directions emerge in representations, it remains unclear how these representations originate and why they become increasingly stable across layers. To solve this issue, we introduce the Input-Space Linearity Hypothesis, positing that concept-aligned directions originate in the input space and are steadily maintained with increasing depth. We then propose the Spectral Principal Path (SPP) framework, which formalizes how deep networks progressively distill linear representations along the spectral principal directions. We provide rigorous stability guarantees for the SPP based on the Wedin $\sinΘ$ perturbation theorem, identifying testable conditions, including spectral gap and context incoherence, that jointly ensure layer-wise directional preservation. By bridging theoretical analysis with empirical evidence, this work identifies a spectral view of how linear representations arise in LLMs, and suggests potential implications for concept-level controllable, robust, and coherent approaches to fairness and transparency in modern AI systems.

cs.CV↗

arXiv2025

CertMask: Certifiable Defense Against Adversarial Patches via Theoretically Optimal Mask Coverage

Adversarial patch attacks inject localized perturbations into images to mislead deep vision models. These attacks can be physically deployed, posing serious risks to real-world applications. In this paper, we propose CertMask, a certifiably robust defense that constructs a provably sufficient set of binary masks to neutralize patch effects with strong theoretical guarantees. While the state-of-the-art approach (PatchCleanser) requires two rounds of masking and incurs $O(n^2)$ inference cost, CertMask performs only a single round of masking with $O(n)$ time complexity, where $n$ is the cardinality of the mask set to cover an input image. Our proposed mask set is computed using a mathematically rigorous coverage strategy that ensures each possible patch location is covered at least $k$ times, providing both efficiency and robustness. We offer a theoretical analysis of the coverage condition and prove its sufficiency for certification. Experiments on ImageNet, ImageNette, and CIFAR-10 show that CertMask improves certified robust accuracy by up to +13.4\% over PatchCleanser, while maintaining clean accuracy nearly identical to the vanilla model.

cs.CV↗

arXiv2025

Why Representation Engineering Works: A Theoretical and Empirical Study in Vision-Language Models

Representation Engineering (RepE) has emerged as a powerful paradigm for enhancing AI transparency by focusing on high-level representations rather than individual neurons or circuits. It has proven effective in improving interpretability and control, showing that representations can emerge, propagate, and shape final model outputs in large language models (LLMs). However, in Vision-Language Models (VLMs), visual input can override factual linguistic knowledge, leading to hallucinated responses that contradict reality. To address this challenge, we make the first attempt to extend RepE to VLMs, analyzing how multimodal representations are preserved and transformed. Building on our findings and drawing inspiration from successful RepE applications, we develop a theoretical framework that explains the stability of neural activity across layers using the principal eigenvector, uncovering the underlying mechanism of RepE. We empirically validate these instrinsic properties, demonstrating their broad applicability and significance. By bridging theoretical insights with empirical validation, this work transforms RepE from a descriptive tool into a structured theoretical framework, opening new directions for improving AI robustness, fairness, and transparency.

cs.LG↗