Standard reinforcement learning post-training on large language models has a blind spot: it makes easy problems easier and barely touches the hard ones. That is the finding of a new blog post and accompanying paper by researcher Michael Noukhovitch, working with coauthors Hamish Ivison, Nathan Lambert, and Aaron Courville, self-published September 15 on Noukhovitch’s personal blog alongside a companion paper posted to arXiv.

The team names the pattern the “Matthew Effect,” borrowing the term from sociologist Robert Merton’s 1968 work on how advantage compounds, the dynamic often shorthanded as “the rich get richer.” Applied to RL training on language models, the claim is specific: gains on a task scale with the model’s initial competence at that task. Questions the model could already partly answer improve sharply. Questions it starts at zero percent on tend to stay near zero.

The paper backs this with a diagnostic most eval reports skip. Instead of reporting one average accuracy number, the authors split benchmark questions into difficulty tiers using the base model’s pre-training pass rate, then track each tier separately through RL training. Running this analysis on Olmo 3.1’s math RL-Zero training against the AIME 2025 benchmark, they found a model whose pre-RL pass rate was zero on the hardest third of questions finished training with that tier mostly still at zero. The easiest third, meanwhile, climbed from roughly 23 percent toward near-mastery. Repeating the split on two other open-source RL projects, Deepcoder and DeepSWE, produced the same skew.

Their explanation centers on a compute allocation problem inside the standard training algorithm, GRPO. Sampling more completions per prompt is the usual way to find a rare correct answer on a hard question. But it also raises the odds of finding a rare wrong answer on an easy one, burning training signal that could otherwise go toward the harder prompts still unsolved. Testing sample counts from 4 to 32 on GSM8k Platinum, the researchers found that fewer samples per prompt actually solved more hard problems, because it filtered already-solved easy prompts out of the batch faster and freed up compute for the ones the model was still missing.

The fix they propose, called Never Give Up, starts with a small number of completions per prompt and escalates only for the ones the model keeps failing: an unsolved prompt gets resampled with more completions instead of being discarded, accumulating attempts until the model lands a correct answer or the budget runs out. On GSM8k, a small starting sample size combined with a 90 percent retry rate beat every fixed sample-count setting the team tested, with the largest gains concentrated on the hardest problem tier. The authors report similar improvements scaling the method to a larger Qwen 3 4B base model trained on DeepScaler math data for roughly 120 H100 hours, and on a code benchmark called Manufactoria, where standard training stalled on partially passing test suites while the new method kept pushing toward fully solved problems.

These results come from the authors’ own experiments, published as a blog post and preprint rather than through peer review, so treat the specific percentage gains as self-reported until independently replicated. The authors also name a real limitation: the resample-and-retry cycle makes training data increasingly stale the longer a hard prompt resists solving, which can slow learning down on task sets that skew heavily toward very difficult problems from the start.

For teams running reinforcement learning on reasoning or coding models, the operational lesson is to stop trusting one averaged eval curve as proof of progress. A model can look like it is improving overall while all of that lift comes from problems it could nearly solve already, leaving the genuinely hard cases it was supposed to unlock exactly where they started.

Michael Noukhovitch detailed the research in a self-published blog post and companion arXiv paper on September 15, 2026.