Fan Chang, Joseph Slote, Chun-Kai Tseng, Alexander Volberg, Haonan Zhang
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and isoperimetric properties of the class, especially bounds on average sensitivity, one of the central themes in the study of PTFs since the Gotsman--Linial conjecture recently solved by OpenAI, \cite{GLsol}. In this work we study PTFs through the lens of the Boolean surface area (or Talagrand boundary) \[ \mathbf{BSA}[f]=\mathbb{E}|\nabla f|=\mathbb{E}\sqrt{s_{f}(x)}, \] a natural measure of vertex-boundary complexity on the discrete cube. Our main result is that every degree-$d$ PTF has polylogarithmic Boolean surface area: \[ \mathbf{BSA}[f]\le C_d(\log(en))^{C_d}. \] The proof is based on the PTF Restriction Lemma of Kabanets, Kane, and Lu \cite{KKL2017} and proceeds through a tail bound for the pointwise sensitivity. In particular, it controls all subcritical fractional moments of the sensitivity. We also record a random block partition principle for Boolean surface area and an alternative recursive argument following Kane's work \cite{DK} on average sensitivity, which independently yields the second bound \[ \mathbf{BSA}[f]\le \exp(C(d)\sqrt{\log n}). \] This bound was obtained in \cite{FSVZ} without clarifying the magnitude of $C(d)$, which we do below. For lower moments $\bE |\nabla f|^η \le C(d, η)$ there is no dependence on $n$ for $0<η<1$.
Haonan Zhang Nanyang Technological University and Zhejiang University, Dongxia Wang Zhejiang University, Yi Liu Quantstamp, Kexin Chen, Wenhai Wang Zhejiang University
Safety-aligned LLMs suffer from two failure modes: jailbreak (responding to harmful inputs) and over-refusal (declining benign queries). Existing vector steering methods adjust the magnitude of answer vectors, but this creates a fundamental trade-off—reducing jailbreak increases over-refusal and vice versa. We identify the root cause: LLMs encode the decision to respond (answer vector v_a) and the judgment of input safety (benign vector v_b) as nearly orthogonal directions, treating them as independent processes. We propose LLM-VA, which aligns v_a with v_b through closed-form weight updates, making the model’s willingness to respond causally dependent on its safety assessment—without fine-tuning or architectural changes. Our method identifies vectors at each layer using SVMs, selects safety-relevant layers, and iteratively aligns vectors via minimum-norm weight modifications. Experiments on 12 LLMs demonstrate that LLM-VA achieves 11.45% higher F1 than the best baseline while preserving 95.92% utility, and automatically adapts to each model’s safety bias without manual tuning.Code and models are available at https://hotbento.github.io/LLM-VA-Web/.
尚无 AI 解读，展示原文摘要
cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表
Feiteng Fang, Dingwei Chen SUN YAT-SEN UNIVERSITY, Xiang Huang, Ting-En Lin, Yuchuan Wu Alibaba Group, Xiong Liu Alibaba Group, Jing Ye Institute of automation, Chinese academy of science, Chinese Academy of Sciences, Ziqiang Liu 等 13 位作者
Currently, most reinforcement learning tasks focus on domains like mathematics and programming, where verification is relatively straightforward. However, in subjective tasks such as role-playing, alignment techniques struggle to make progress, primarily because subjective reward modeling using the Bradley-Terry model faces significant challenges when dealing with ambiguous preferences. To improve reward modeling in subjective tasks, this paper proposes AAM (Act-Adaptive Margin), which enhances reward modeling by dynamically calibrating preference margins using the model’s internal parameter knowledge. We design two versions of AAM that efficiently generate contextually-appropriate preference gaps without additional human annotation. This approach fundamentally improves how reward models handle subjective rewards by better integrating generative understanding with preference scoring. To validate AAM’s effectiveness in subjective reward modeling, we conduct evaluations on RewardBench, JudgeBench, and challenging role-playing tasks. Results show that AAM significantly improves subjective reward modeling performance, enhancing Bradley-Terry reward models by 2.95% in general tasks and 4.85% in subjective role-playing tasks. Furthermore, reward models trained with AAM can help downstream alignment tasks achieve better results. Our test results show that applying rewards generated by AAM-Augmented RM to preference learning techniques (e.g., GRPO) achieves state-of-the-art results on CharacterEval and Charm. The code and dataset will be released upon acceptance.
尚无 AI 解读，展示原文摘要
cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表