Learning from the Gap Between Pass@K and Pass@1

Take three frontier mixture-of-experts models (Alibaba, OpenAI, NVIDIA; 3.6-4.0B active parameters each) and fine-tune them to reason in a low-resource language. On accuracy benchmarks almost nothing happens, and the benchmark itself is noise at this scale: changing only the random seed moves the score by 7.7 points, more than every data and recipe effect we measured. That null is our first result. The real changes live where accuracy cannot see. Base models never think in Greek: 0 of 1,000 reasoning traces, even when the question is Greek, so the model answers correctly while reasoning in a form its user cannot read, audit, or correct. After supervised fine-tuning (SFT), every released checkpoint reasons in the language of the question on ~98% of items, one family at 3x fewer tokens, with judged grammaticality improving on all four models and general ability within a few points of each base: nothing was forgotten, and fluency was gained. We propose six behavioural dimensions that make such changes measurable, each gated to reject any metric that correlates with output length, and we report how our own instruments lied: six failures, each caught by a control. What SFT cannot do is fix its own defects: a quarter of answers skip the requested format, answers leak into the reasoning channel, and an explicit "think in English" is obeyed under half the time. Reinforcement learning with verifiable rewards, pre-registered before training, fixes the first two outright (fallback 24% to 2.5%, leak 3.5% to 0.0%, both against a flat random-reward control) and moves the third (+9.1pp), while the Greek reasoning habit survives an accuracy-only gradient untouched. We release five checkpoints. The instruments, the controls and the pre-registration travel to any low-resource language; Greek is the case that let us measure them.

In verifiable domains such as math and coding, finding one correct solution among many attempts can matter more than the pass rate of each attempt. Post-training can concentrate large language model outputs around a few modes, while increasing sampling temperature has limited effectiveness. We introduce Don't Repeat Yourself Supervised Fine-Tuning (DRY-SFT), a post-training method that increases output diversity and coverage: the probability of at least one correct solution among many attempts. DRY-SFT has two stages. First, for each problem, sequentially generate K solutions, showing the model all prior attempts and asking for a different solution. Second, fine-tune on each attempt independently, removing prior attempts from the context. The process uses no reward, verifier, or correctness filter. On HumanEval+, MBPP+, and DS-1000, DRY-SFT raises pass@100 by 10.8, 12.5, and 12.4 percentage points, respectively, at a small cost to pass@1. Structural diversity, measured by abstract syntax tree edit distance among passing solutions, rises significantly on all three benchmarks. DRY-SFT also solves 244 of 600 problems that the base model did not solve in the same 200 attempts. Across nine open-weight models, lower structural diversity of the base model significantly predicts larger DRY-SFT gains, indicating that the method is especially effective on more mode-collapsed models.

Reinforcement learning post-training drives reasoning and agentic capabilities in modern AI systems, yet a growing body of work shows that it is most effective when used to fine-tune an already capable base model. We question whether existing pipelines yield models that are most suitable for reinforcement learning. Building on prior work highlighting the role of coverage and pass@K as predictors of post-RL performance, we design a simple modification to supervised fine-tuning, TailSFT, which filters out already fit sequences during training, thereby focusing learning on under-modeled regions, or the tail, of the data distribution. We justify and validate the design choices in TailSFT, particularly the specific filtering criteria, through a combination of controlled experiments and theoretical analysis. On OLMo-3 7B, TailSFT often improves pass@16 performance on math and coding evaluations, with gains up to 17% absolute, while incurring minimal computational overhead. These higher-coverage checkpoints consistently translate to up to 4% absolute pass@1 gains in subsequent GRPO runs, demonstrating that TailSFT checkpoints serve as better initializations for RL. We further introduce a lightweight diagnostic for identifying settings where TailSFT is most likely to help. More broadly, our results motivate a principled, stage-aware approach to model development, in which intermediate checkpoints are judged by how effectively they support subsequent training.