Baharan Mirzasoleiman

While next-token prediction (NTP) has been the standard objective for training language models, it often struggles to capture global structure in reasoning tasks. Multi-token prediction (MTP) has recently emerged as a promising alternative, yet its underlying mechanisms remain poorly understood. In this paper, we study how MTP facilitates reasoning, with a focus on planning. Empirically, we show that MTP consistently outperforms NTP on both synthetic graph path-finding tasks and more realistic reasoning benchmarks, such as Countdown and boolean satisfiability problems. Theoretically, we analyze a simplified two-layer Transformer on a star graph task. We prove that MTP induces a two-stage reverse reasoning process: the model first attends to the end node and then reconstructs the path by tracing intermediate nodes backward. This behavior arises from a gradient decoupling property of MTP, which provides a cleaner training signal compared to NTP. Ultimately, our results highlight how multi-token objectives inherently bias optimization toward robust and interpretable reasoning circuits.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a highly effective framework for improving LLM reasoning, with methods such as GRPO among its most successful instantiations. However, GRPO relies on repeated generation of long chain-of-thought rollouts. Training time scales with the number of rollouts, a large fraction of which are uninformative. Thus, GRPO is computationally expensive and unstable. To mitigate this, existing approaches either generate a larger pool of rollouts and filter the most informative prompts, or leverage historical signals for filtering at later stages of training. These strategies offer modest performance gains, but slow down the overall process. To address this, we propose VarIance Guided Online Rollout allocation (VIGOR) which instead of allocating a fixed rollout budget per example, begins with a small number of rollouts for all examples in a batch and iteratively allocates additional rollouts to those with the highest group reward variance until a fixed total rollout budget is reached. Theoretically, we show that under RLVR, reward variance controls the gradient magnitude, and derive VIGOR's closed-form speedup ratio over GRPO, which grows with refinement rounds under Pareto-distributed reward variance. Experiments on mathematical reasoning and coding tasks show that VIGOR reaches target accuracy with up to 2.3$\times$ fewer rollouts on math, reaches GRPO's final coding full pass rate with 1.49$\times$ fewer rollouts, and improves the coding average test pass rate by 3.4 points.