A theory of label-free RLVR explains why self-reinforcement collapses as the training set grows, with a critical problem count that scales as the inverse square of coupling strength
AspireAI community · arXiv
A paper submitted October 27, 2026 examines why label-free reinforcement learning with verifiable rewards, which rewards a language model for agreeing with its own majority vote, improves reasoning at first and then collapses, with the self-assessed reward going to one while accuracy falls until the model answers every problem the same way. The authors show the collapse appears only when training uses many problems and explain the dataset-size dependence as a collective instability: per-problem sharpening, slowed by 1/N for N training problems, races against a shared mode that grows at a rate proportional to the square of the coupling strength and is independent of N, yielding a critical number of problems N_c proportional to ln(1/delta) divided by the coupling strength squared times G. Simulations confirm a sharp transition, a single critical amplification across couplings, confidence profiles and training variants, a logarithmic dependence on batch size, and no collapse for confident initial models. In label-free RL of a small Transformer, removing the shared direction prevents collapse entirely and restoring it causes collapse, with collapse growing with training-set size and base-model entropy. The limitation is that the empirical validation is on a small Transformer rather than a frontier-scale model.
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