We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the mathematical reasoning capabilities of large language models (LLMs).

Models were trained with 32 experts, with experts placed every 2 layers - except where explicitly stated. The learned contrastive temperature parameter is initialised at 10. We train models at batch size 16,384 for 781,250 steps at resolution 224. These are B/16 models trained for 100,000 steps at batch size 8192. The default training data is mixed with data from JFT -4B with a ratio of 3:1.

However, such models are typically trained on a single modality at a time.

Diffusion policies have emerged as a powerful framework for robotic visuomotor control, yet they often lack the robustness to recover from subtask failures in long-horizon, multi-stage tasks and their learned representations of observations are often difficult to interpret. In this work, we propose the Mixture of Experts-Enhanced Diffusion Policy (MoE-DP), where the core idea is to insert a Mixture of Experts (MoE) layer between the visual encoder and the diffusion model. This layer decomposes the policy's knowledge into a set of specialized experts, which are dynamically activated to handle different phases of a task. We demonstrate through extensive experiments that MoE-DP exhibits a strong capability to recover from disturbances, significantly outperforming standard baselines in robustness. On a suite of 6 long-horizon simulation tasks, this leads to a 36% average relative improvement in success rate under disturbed conditions. This enhanced robustness is further validated in the real world, where MoE-DP also shows significant performance gains. We further show that MoE-DP learns an interpretable skill decomposition, where distinct experts correspond to semantic task primitives (e.g., approaching, grasping). This learned structure can be leveraged for inference-time control, allowing for the rearrangement of subtasks without any re-training.Our video and code are available at the https://moe-dp-website.github.io/MoE-DP-Website/.

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6% (8.6% improvement beyond format correction), and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7% (7.0% non-format gain). This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which contains the aforementioned example. Furthermore, RLVR with only two examples even slightly exceeds these results (MATH500: 74.8%, average: 36.6%). Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples. In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-category generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by incorporating entropy loss with an appropriate coefficient) in 1-shot RLVR training. We also further discuss related observations about format correction, label robustness and prompt modification. These findings can inspire future work on RLVR efficiency and encourage a re-examination of recent progress and the underlying mechanisms in RLVR. All resources are open source at https://github.com/ypwang61/One-Shot-RLVR.