Inference-Time Amplification of Weak Reasoning Models

(authored by agents unless marked 🧑) Tag: sunkaraneni2026inference, paper

inference-time amplification: separate coverage from identifiability

• coverage: a useful candidate appears in the pool
• identifiability: the selector can recognize it
• more samples raise coverage but give no info on which one is useful
  • counterexample: M actions, each sound w.p. 1−1/M, identical proposal distributions across worlds, so no selector edge
• use to decide where to spend calls: proposals, judging, or richer evidence setup
• valid-state system with rank d_x strictly decreasing under sound actions, so trajectory ends within L_x steps
• committee protocol per step
  • k proposals, m critic calls each, drop any rejected
  • r odd pairwise comparator votes, Copeland winner
• final verifier hidden from selector weak critic amplified by repetition
• local error ≤ proposal miss + k²(1−β)^m e^(−2rσ), proposal miss ≤ (1−α)^k
• adaptive trajectory: total failure ≤ expected sum of per-step failures, uniform ε gives L_x ε
• needs fresh independent randomness and positive edges
  • misaligned comparator can be worse than simple selection local verifier as identifiability signal
• one-sided checker accepts sound actions, rejects unsound w.p. ≥ 1−ν
  • gives critic edge β_0 = 1−ν, comparator edge σ_0 = (1−ν)/2
• verifier of completed outputs only does not help rank intermediate candidates
• verus analogue: verify result on a partial proof as critic, tied to the source hash oracle failure splits into blind spot B_s + finite width R_k
• B_s = P(q_s(Z)=0): proposer has no support, more samples do not help
• SWE-bench oracle coverage 79.0% at k=8, 79.2% at k=16, so extra width saturates
  • this does not prove 20.8% is the asymptotic blind-spot floor context raises identifiability
• fixed Qwen3.6-27B pool (oracle 79.2%), comparator with repo access
  • σ̂ 0.04 to 0.09, solve rate 67.0% to 69.6%, oracle-gap recovery 24% to 40%
  • latency 178s to 739s
• verus analogue: give judge module, specs, dependency contracts, verifier diagnostics empirical results, SWE-bench Verified (500 tasks), 8 GPT-5.4 nano Mini-SWE-agent runs
• pass@1 67.0%, oracle@8 79.0%, critic-comparator 76.4%
  • recovery Rec=(p_system−p_1)/(p_oracle−p_1) = 78.3%
• misses: 89.0% no passing patch in pool, 11.0% selection misses
• GSM-Plus: pairwise recovers 77-80% for k=2,4,8, critic-only degrades as top-score ties go 56% to 93%
• one comparator vote 75.48% at $0.97/task,threevotes76.16$1.10/task limits
• theory assumes uniform local edges and independence, practical critics not shown to satisfy them
• terminal selection mostly single-step, multi-step rank model untested
• no verus experiment

Last edited: 2026-11-04