One Checkpoint, Many Speeds: Healing Depth Prefixes to Unlock Vertical Compute Control in Reasoning LLMs

Efficient-reasoning research controls test-time compute almost exclusively along the length axis—generating fewer chain-of-thought (CoT) tokens. We study the orthogonal depth axis: executing fewer transformer layers per token, within a single checkpoint. We first establish that this axis is locked in modern reasoning models: decoding Qwen3-8B (36 layers) from any truncated layer prefix collapses math accuracy to ≤4.2%—even dropping just four top layers—and a logit-lens analysis shows only 6.9% of CoT token predictions have stabilized by layer 24 (numeric tokens: 0.1%). We then show the axis can be unlocked cheaply: LoRA self-distillation on 9k of the model's own rejection-sampled correct CoT traces (20 H100-hours) turns the 28-layer prefix into a capable fast reasoner on GSM8K/MATH-500-level problems (GSM8K 0%→91.2% vs. full 95.2%; MATH-500 0%→72.8% vs. 94.6%; hard benchmarks stay depth-hungry: AIME'24 20.4% vs. 68.3%), while the full-depth path stays bit-identical and the fast path decodes measurably faster (1.21× at d=28, 1.38× at d=24). Ablations show what healing needs: the model's own long-CoT traces beat its own short answers and generic instruction data by 22–28 GSM8K points at equal budget, and recovery exhibits a sharp cliff below d=26 that more training does not fix. Finally, we place healed prefixes in a {shallow, full} × {think, no-think} compute grid governed by one hidden-state probe router: the router recovers 94.0% GSM8K accuracy at 33% of always-think cost (a length-only result the four-mode set does not improve), and depth modes extend the grid's oracle frontier by up to 25% additional savings that realizable probes do not yet capture—though we find, honestly, that on Qwen3 the built-in length axis remains the dominant lever, with depth contributing a latency-optimal serving mode and a small-but-real slice of the cost frontier. We release recipes, laws, and accounting to guide depth-elastic reasoning.