Shu Zhou, K. Y. Michael Wong, Juntao Wang, David Shui Wing Hui, Daniel Ebler, Jie Sun
Recently proposed analog solvers based on dynamical systems, such as Ising machines, are promising platforms for large-scale combinatorial optimization. Yet, given the heuristic nature of the field, there is very limited insight on optimality guarantees of the solvers, as well as how parameter schedules shape dynamics and outcomes. Here, we develop a dynamical mean-field framework to analyze Ising-machine dynamics for finding the ground state energy of the Sherrington-Kirkpatrick(SK) model of spin glasses and identify mechanisms that enable rapid convergence to provenly near-optimal energies. For a fixed target energy density Ec, we show that solutions are typically reached within O(1) matrix vector multiplications, indicating constant time complexity. We further delineate theoretical limitations arising from different parameter-scheduling trajectories and demonstrate a pronounced benefit of temperature-only annealing for the Coherent Ising Machine. Building on these insights, we propose a general framework for designing optimized parameter schedules, thereby improving the practical effectiveness of Ising machines for complex optimization tasks. The superior performance of the dynamical solvers is illustrated by the attainment of the ground state energy of the SK model.
Shu Zhou, Jinman Leng, Yufei Song, Xin Wang, Tao Fan Nanjing University of Finance and Economics, Hao Wang
Scaling laws have enabled predictable compute allocation for pre-training and for RL in reasoning tasks. However, research on retrieval reinforcement generation (RAG) remains insufficient and there is a lack of fundamental understanding of the interaction between retrieval quality and reinforcement learning computation. We present the first systematic study of RL scaling for RAG across three knowledge-intensive benchmarks. We introduce the Retrieval Bottleneck Hypothesis and derive sigmoidal scaling laws showing that retrieval quality, not RL compute, determines the asymptotic performance ceiling. Our analysis reveals three principles: (1) retrieval quality bounds achievable performance, with improving retrieval yielding larger gains than algorithmic innovations; (2) design choices (training objectives, rewards, off-policy methods) primarily modulate compute efficiency, with secondary effects on the ceiling that are substantially smaller than retrieval quality improvements; and (3) stable configurations enable extrapolation with 3.1% error at 4x compute. We further uncover RAG-specific dynamics: optimal document count increases with training, and RL algorithm effectiveness depends critically on retrieval quality. These insights yield RAG-ScaleRL, achieving strong performance on knowledge-intensive benchmarks while providing the predictable scaling long available for pre-training but previously absent in RAG-RL.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表