SPIRE: Let the Student Choose Its Own Supervision for Implicit Reasoning

Implicit chain-of-thought reasoning compresses explicit reasoning traces into a short sequence of latent states. Recent methods enrich latent supervision with teacher key–value (KV) states, but identifying informative teacher states does not determine which states best supervise each student step. We investigate this allocation problem and find that teacher-state utility depends on the receiving student step, while preserving the teacher’s reasoning order improves performance. We introduce SPIRE (Student-Selected Supervision for Implicit Reasoning), a framework in which the student chooses its own supervision. Given a compact pool of teacher states, SPIRE uses the student’s current representations to jointly select an ordered, non-reusing supervision path, assigning a distinct teacher target to each active student step. We solve this selection exactly with dynamic programming and characterize its stability under score noise. SPIRE introduces no additional trainable routing parameters and leaves the latent inference procedure unchanged. Experiments on three arithmetic reasoning benchmarks and three model backbones demonstrate performance gains over implicit CoT baselines.