Zero-freeness for Random Regular Graphs up to the Replica Symmetry Breaking Threshold
Zejia Chen, Chunyang Wang, Xinyuan Zhang
AI 速览：作者在随机 d-正则图上证明硬核模型与反铁磁 Potts 模型（含正常 q-染色）在副本对称区内具有零点自由区域，并由此得到多项式时间近似配分函数的算法。
We study antiferromagnetic spin systems on random regular graphs through the lens of the phase transitions characterized by the complex zeros of the partition function. Our motivating examples include the hardcore model and the antiferromagnetic Potts model (including proper $q$-colorings at $β=0$). For both models on random $d$-regular graphs, we establish, with high probability over the graph, zero-free regions throughout the interior of the replica-symmetric regime. Asymptotically, this regime extends up to tree occupation density $$α< α_{\mathrm{RSB}}(d) = (2\log d - 2\log\log d + 2 - 2\log 2 + o_d(1))/d$$ for the hardcore model and up to degree $$d < d_{\mathrm{RSB}}(q) = (2q-1)\log q - 2\log 2 + o_q(1)$$ for proper $q$-colorings. Leveraging the standard algorithmic implications of zero-freeness, we obtain deterministic polynomial-time algorithms that multiplicatively approximate the corresponding partition functions at fixed rational parameters throughout this regime, with high probability over the graph. Our algorithmic guarantees significantly improve upon prior work and extend beyond the parameter ranges reached by previously known search algorithms. To establish our results, we first develop reinforced small subgraph conditioning, which resolves short-cycle fluctuations in the complex plane by lifting classical small subgraph conditioning on random regular graphs to random holomorphic functions. Second, we overcome the standard second-moment barrier caused by the exponential blowup of the bare second moment inside the replica-symmetric phase, by showing that replica symmetry implies a nonpositive Bethe functional and upgrading planted overlap concentration to an exponentially small bound, which enables a typical-graph truncation that controls complex second moments up to the replica symmetry breaking threshold.
Liuji Chen, Zeyu Zhang, Xinyuan Zhang, Shuai Nie, Qiang Liu, Shu Wu, Liang Wang
Personalized text generation requires models to capture user-specific writing styles from historical data. Existing approaches based on retrieval, parameter-efficient fine-tuning, or activation steering either introduce inference and storage overhead or struggle to separate stylistic signals from semantic content. We propose GLASS, a training-free framework for personalized generation via Global-Local Activation Steering with Sparse priors. GLASS uses sparse autoencoders to extract a global user-style prior from historical responses and constructs local contrastive style vectors over clustered interaction scenarios. During inference, it jointly injects global and local vectors into different model layers, enabling context-aware personalization without retrieval or parameter updates. Experiments on LaMP and LongLaMP show that GLASS outperforms retrieval-, fine-tuning-, and steering-based baselines across ROUGE metrics and LLM-as-judge evaluations. Further analyses show that SAE-based representations are more robust to topic and length shifts, suggesting better disentanglement of stylistic information from semantic residue.
Raymond Alavo University of Notre Dame, Xinyuan Zhang University of Notre Dame, Gemza Ademaj, Junhui Cai University of Notre Dame, Hyeokhyen Kwon Emory University, Robert Cotes Emory University, Gari D. Clifford Emory University and Georgia Institute of Technology, Ahmed Abbasi University of Notre Dame
We present Dash-M5H, an interactive dashboard for multi-modal, multi-model mental health assessment that helps clinicians and researchers jointly inspect multimodal behavioral data with multi-model signal outputs of recorded clinical interviews. Guided by signal detection and integrated sensemaking theories, Dash-M5H synchronizes transcript text, audio, and facial behavior (action units and gaze) to support overview-to-detail evidence tracing; and it integrates extracted signals (e.g., sentiment and facial activity) with a clinically grounded VLM prediction pipeline that produces DSM-5-aligned depression predictions. Dash-M5H (https://dash-m5h.io) is implemented in a lightweight, browser-based stack (Quarto + Observable JS + D3), supports local data import and time-synced clinical annotation with export. We demonstrate Dash-M5H through a depression screening scenario, evaluate its note-taking and screening capabilities through a user experiment, and release a live demo (https://youtu.be/w3qCJ02k6bw) and code (https://github.com/nd-hal/M5H-Dashboard-VLM) to facilitate reproducible evaluation.
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cs.CL · cs.CV
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 3: System Demonstrations) · 2026 · 正式发表