Ring-lite: Scalable Reasoning via C3PO-Stabilized Reinforcement Learning for LLMs

We present Ring-lite, a Mixture-of-Experts (MoE)-based large language model optimized via reinforcement learning (RL) to achieve efficient and robust reasoning capabilities. Built upon the publicly available Ling-lite model, a 16.8 billion parameter model with 2.75 billion activated parameters, our approach matches the performance of state-of-the-art (SOTA) small-scale reasoning models on challenging benchmarks (e.g., AIME, LiveCodeBench, GPQA-Diamond) while activating only one-third of the parameters required by comparable models. To accomplish this, we introduce a joint training pipeline integrating distillation with RL, revealing undocumented challenges in MoE RL training. First, we identify optimization instability during RL training, and we propose Constrained Contextual Computation Policy Optimization(C3PO), a novel approach that enhances training stability and improves computational throughput via algorithm-system co-design methodology. Second, we empirically demonstrate that selecting distillation checkpoints based on entropy loss for RL training, rather than validation metrics, yields superior performance-efficiency trade-offs in subsequent RL training. Finally, we develop a two-stage training paradigm to harmonize multi-domain data integration, addressing domain conflicts that arise in training with mixed dataset. We will release the model, dataset, and code.

Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions

We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of $\widetilde{O}\left(n^{-1} t^{-\frac{d+2}{2}}(t^{\frac{d}{2}} \vee 1)\right)$ for the score function of $p_0*\mathcal{N}(0,t\boldsymbol{I}_d)$, where $n$ and $d$ represent the sample size and the dimension, $t$ is bounded above and below by polynomials of $n$, and $p_0$ is an arbitrary sub-Gaussian distribution. As a consequence, this yields an $\widetilde{O}\left(n^{-1/2} t^{-\frac{d}{4}}\right)$ upper bound for the total variation error of the distribution of the sample generated by the diffusion model under a mere sub-Gaussian assumption. If in addition, $p_0$ belongs to the nonparametric family of the $\beta$-Sobolev space with $\beta\le 2$, by adopting an early stopping strategy, we obtain that the diffusion model is nearly (up to log factors) minimax optimal. This removes the crucial lower bound assumption on $p_0$ in previous proofs of the minimax optimality of the diffusion model for nonparametric families.