SFT and RLVR represent two fundamental yet distinct paradigms for LLM post-training, each excelling in distinct dimensions. SFT expands knowledge breadth while RLVR enhances reasoning depth. Yet integrating these complementary strengths remains a formidable challenge. Sequential training can cause catastrophic forgetting, and joint optimization often suffers from severe gradient conflicts. We analyze SFT and RLVR through the lens of task vectors and reveal three structural properties behind these failures: a 30* magnitude disparity, 45* sign interference, and heterogeneous module-wise update distributions. These findings show SFT and RLVR are difficult to integrate directly, but they also suggest that the two paradigms modify partly complementary components of the model. Motivated by these observations, we propose Decoupled Test-time Synthesis (DoTS), a post-hoc framework allows SFT and RLVR checkpoints to be trained independently and synthesizes their capabilities only at inference time via task vector arithmetic, without updating model parameters. To reduce interference, DOTS applies selective sparsification with norm-preserving rescaling. It then uses Bayesian optimization on a small set of unlabeled queries to search for combination coefficients on the Pareto frontier of consistency and perplexity. Empirically, \ours matches or exceeds the performance of training-based SFT--RLVR integration methods across multiple mathematical reasoning benchmarks, incurring only ∼3% of the computational cost. When applied to stronger post-trained checkpoints, DOTS surpasses SOTA models and generalizes to out-of-domain benchmarks without re-tuning. Code is available at https://github.com/chaohaoyuan/DoTS.
Recent advances in large language models (LLMs) have demonstrated that reinforcement fine-tuning of pretrained base models can lead to significant gains in reasoning performance at inference time. In this work, we theoretically analyze why reinforcement fine-tuning induces better reasoning ability than purely supervised fine-tuning (SFT) methods. We model chain-of-thought (CoT) reasoning as a pathfinding problem on graphs and compare the popular method of reinforcement learning with verifiable rewards (RLVR) against traditional SFT. We prove that SFT, when trained on golden shortest paths without negative examples, fails to learn how to efficiently backtrack. In contrast, an RLVR-trained model can learn how to efficiently backtrack from dead ends using only outcome reward. This leads to an exponential separation in inference-time compute between the two methods, and demonstrates that RLVR leads the model to learn the location of difficult decisions in a reasoning chain, ultimately allowing for better allocation of inference-time compute. Finally, we show that the reasoning traces of an RLVR model can be distilled to train a base model to backtrack efficiently as well.
Recent mixed-policy optimization methods for LLM reasoning that interleave or blend supervised and reinforcement learning signals report improvements over the standard SFT-then-RL pipeline. We show that numerous recently published research papers rely on a faulty baseline caused by two distinct bugs: a CPU-offloaded optimizer bug in DeepSpeed that silently drops intermediate micro-batches during gradient accumulation (affecting multiple downstream frameworks including TRL, OpenRLHF and Llama-Factory), and a loss aggregation bug in OpenRLHF that incorrectly weights per-mini-batch losses. Together they suppress SFT performance, with the optimizer bug accounting for most of the gap and the loss aggregation bug contributing a smaller additional effect. Once corrected, the standard SFT-then-RL pipeline surpasses every published mixed-policy method we evaluate by +3.8 points on math benchmarks with Qwen2.5-Math-7B and by +22.2 points with Llama-3.1-8B. Even a truncated variant with just 50 RL steps outperforms mixed-policy methods on math benchmarks while using fewer FLOPs.
The standard LLM training pipeline applies reinforcement learning (RL) only after pre-training and supervised fine-tuning (SFT). We question this status quo by training a LLM from scratch and applying RL, SFT, and SFT followed by RL directly to intermediate pre-training checkpoints. We find that RL is effective very early, and often matches the full SFT→RL pipeline early as well. Through experiments on harder problems, we find that targeted pre-training data composition is a strong lever for RL effectiveness, even more so than model scale. Beyond reasoning accuracy, applying RL directly to base checkpoints expands the model's distribution; the sharpening effect reported in recent work arises only when RL follows SFT. The general capabilities of the model remain essentially unchanged by RL, while they degrade following SFT. Finally, we merge RL and SFT objectives by parallel averaging, which outperforms across all other training methods discussed, across metrics, while preserving general capabilities. Together, these results suggest that LLM training might benefit from an expanded use of RL.