Tootfinder

Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces
Minju Gwak, Guijin Son, Jaehyung Kim
https://arxiv.org/abs/2510.06953 https://

Revisiting the Uniform Information Density Hypothesis in LLM Reasoning Traces
The Uniform Information Density (UID) hypothesis suggests that effective communication maintains a stable flow of information. In this work, we revisit this principle in the context of large language model (LLM) reasoning traces, asking whether step-level uniformity reflects reasoning quality. To this end, we propose an entropy-based stepwise information density metric and introduce two complementary measures of uniformity, local and global uniformity scores. Across the experiments on six diffe…

Artificial intelligence as a surrogate brain: Bridging neural dynamical models and data
Yinuo Zhang, Demao Liu, Zhichao Liang, Jiani Cheng, Kexin Lou, Jinqiao Duan, Ting Gao, Bin Hu, Quanying Liu
https://arxiv.org/abs/2510.10308

Artificial intelligence as a surrogate brain: Bridging neural dynamical models and data
Recent breakthroughs in artificial intelligence (AI) are reshaping the way we construct computational counterparts of the brain, giving rise to a new class of ``surrogate brains''. In contrast to conventional hypothesis-driven biophysical models, the AI-based surrogate brain encompasses a broad spectrum of data-driven approaches to solve the inverse problem, with the primary objective of accurately predicting future whole-brain dynamics with historical data. Here, we introduce a unified framewo…

On modular invariants of the truncated polynomial ring in rank four
Dang Vo Phuc
https://arxiv.org/abs/2510.11464 https://arxiv.org/pdf/2510.11464

On modular invariants of the truncated polynomial ring in rank four
We prove the rank-4 case of the conjecture of Ha-Hai-Nghia for the invariant subspace of the truncated polynomial ring $\mathcal{Q}_m(n)=\mathbb{F}_q[x_1,\dots,x_n]/(x_1^{q^m},\dots,x_n^{q^m}),$ under a new, explicit technical hypothesis. Our argument extends the determinant calculus for the delta operator by deriving crucial rank-4 identities governing its interaction with the Dickson algebra. We show that the proof of the conjecture reduces to a specific vanishing property, for which we intro…