Yunpeng Li | Search arXiv

arXiv2026

A proof of Ross's conjecture for two-site moving-target search

A target moves between two sites according to a discrete-time Markov chain with a $2\times2$ transition matrix $M$. At each epoch one site is searched at positive cost, and a search may overlook a target that is present. Ross conjectured that an optimal policy is threshold in the posterior probability that the target is at site~1. MacPhee and Jordan proved the conjecture throughout the nonpositive-determinant ($\det M\le0$) regime and for part of the positive-determinant ($\det M>0$) regime, leaving the remaining cases open. We prove threshold optimality throughout the positive-determinant regime, completing Ross's conjecture for all parameter values.

math.PR↗

arXiv2026

Why Are LLM Backdoor Defenses Fragmented? A Feature-Level Explanation with Sparse Autoencoders

Backdoor attacks pose a serious threat to large language models (LLMs), but existing defenses remain fragmented, failing to pro?vide unified defense against both dirty-label and clean-label attacks. To investigate why such fragmentation arises, we present the first systematic feature-level mechanistic analysis of LLM backdoors using sparse autoencoders (SAEs). Starting from a 2 x 2 comparison of clean and poisoned models on clean and triggered inputs, we trace backdoor-induced logit shifts to high-contributing SAE features and categorize them into four roles: interac?tion, suppressed, mixed, and weight-modified features. This taxonomy reveals system?atic encoding differences: dirty-label back?doors are dominated by isolated interaction features, whereas clean-label backdoors rely more on heterogeneous mixtures of mixed and weight-modified features. These differ?ences explain why existing defenses remain fragmented across attack paradigms. We val?idate this hypothesis through inference-time feature clamping, which reduces ASR to at most 10.8% in most dirty-label settings and at most 15.4% in the majority of clean-label settings, while preserving benign-task perfor?mance. These results show that SAE-based analysis can explain defense fragmentation and guide interpretable backdoor mitigation.

cs.CR↗