Kaiyi Zhang

Kaiyi Zhang, Xueliang Zhao, Zhuocheng Gong et al.

Model routing balances solution accuracy and computational cost by selecting among models of varying capabilities. While recent multi-round frameworks interleave reasoning and planning, we identify a structural failure mode termed Trust Region Collapse. We demonstrate that the deep coupling of reasoning and routing, exacerbated by the dominance of strong pre-training priors under sparse supervision, leads to degenerate local optima where capable experts are systematically suppressed. To decouple these processes, we propose $\textbf{EntroRouter}$, a single-round routing framework that treats entropy regulation as a core objective. We first initialize the policy via Soft Supervision, fitting a distribution of suitable models to establish a high-entropy prior for exploration. Subsequently, we stabilize Reinforcement Learning using a Soft Anchor, which utilizes offline capability estimates to orchestrate controlled entropy contraction within a safe trust region. Extensive experiments demonstrate that EntroRouter retains 98.3% of the strongest expert's accuracy while reducing computational costs by 48.25%.

Kaiyi Zhang, Wei Wu, Yankai Lin

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose $\textbf{DelTA}$, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.