Peng Ye

Jie-Yu Zhang, Peng Ye

In topological phases of matter, fusion rules dictate how anyonic topological charges combine. However, the transformation of quasiparticle mobility under fusion remains largely unexplored. In this letter, we reveal that restricted mobility classes obey their own complex multi-channel fusion algebras. We introduce a family of exactly solvable models with $\mathbb{Z}_2$ topological order enriched by subsystem symmetries to explicitly demonstrate these structures. Within this framework, mobility constraints arise from enforcing symmetries supported on specific subsets. When excitations fuse, these rigid geometric constraints interfere spatially. At the macroscopic level, this deterministic geometric interference manifests as a multi-channel fusion ring. We present three explicit mobility fusion phenomena realized in distinct models: (i) Fibonacci fusion rules; (ii) tensor products of Fibonacci rules; and (iii) lineon period transmutation.

Jianhao Chen, Chenxu Wang, Gengrui Zhang et al.

Recent years have witnessed a surge in the number of large language models (LLMs), yet efficiently managing and utilizing these vast resources remains a significant challenge. In this work, we explore how to learn compact representations of LLM abilities that can facilitate downstream tasks, such as model routing and performance prediction on new benchmarks. We frame this problem as estimating the probability that a given model will correctly answer a specific query. Inspired by the item response theory (IRT) in psychometrics, we model this probability as a function of three key factors: (i) the model's multi-skill ability vector, (2) the query's discrimination vector that separates models of differing skills, and (3) the query's difficulty scalar. To learn these parameters jointly, we introduce a Mixture-of-Experts (MoE) network that couples model- and query-level embeddings. Extensive experiments demonstrate that our approach leads to state-of-the-art performance in both model routing and benchmark accuracy prediction. Moreover, analysis validates that the learned parameters encode meaningful, interpretable information about model capabilities and query characteristics.