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To determine why reinforcement learning with verifiable rewards (RLVR) degrades test-time diversity, this work isolates the trajectory-level locus of solution space collapse using an exhaustively enumerated Countdown task and math reasoning benchmarks across Qwen models (3B to 14B) trained with PPO and GRPO. The authors find that RLVR's up to 67% coverage contraction is heavily front-loaded—per-token likelihood shifts are 11x–16x larger before the first arithmetic operation—meaning models maintain downstream execution capability but fail to access alternative reasoning paths. Leveraging this localization, entrance-targeted interventions such as late-layer checkpoint interpolation recover 37% of lost solution diversity with zero penalty to pass@1 accuracy.
RLVR chokes reasoning diversity at the front door rather than during execution: an 11x–16x likelihood collapse occurs before the very first operation, leaving downstream solution paths intact and fully recoverable via targeted late-layer weight interpolation.
Reinforcement learning with verifiable rewards (RLVR) substantially improves single-sample accuracy (pass@1) but causes the policy's solution space to contract, diminishing the returns of test-time scaling. In this work, we investigate where inside a reasoning trajectory this breadth is lost: does the policy fail to access a valid solution family, or does it fail to execute computation once initiated? To disentangle access from execution, we analyze the Countdown task, whose solution space can be exhaustively enumerated into discrete entrance families defined by the first operand and operator, across PPO on Qwen2.5-3B and GRPO on Qwen2.5-3B-Instruct. Across both training setups, solution coverage falls by up to 67%, halving even on problems solved across all checkpoints. We show that this contraction is heavily concentrated at the entrance: per-token likelihood shifts are 11x--16x larger prior to the first arithmetic operation than during downstream reasoning. Supplying only an unselected entrance prefix restores completion rates in low-access families by over an order of magnitude (0.018 ->0.212 under PPO), demonstrating that alternative solutions remain executable but are no longer initiated. Guided by this localization, we find that while surface prompting fails to recover diversity, entrance-targeted interventions succeed: late-layer parameter interpolation with early checkpoints increases solution coverage by 37% at no loss in pass@1. Finally, we show that early-step entropy collapse recurs across six math benchmarks with 7B and 14B models, but is not an inevitable byproduct of reasoning optimization: an SFT baseline preserves more than double the coverage, and staged SFT--DPO--RLVR pipelines retain early-step entropy. In summary, reasoning breadth is lost at the door, not inside the room. Code: https://github.com/ershiyidian/early-branch-locking.
