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Predicting LLM Reasoning Performance with Small Proxy Model

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Routing, pruning and distillation for reasoning

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Proposes rBridge, a proxy evaluation metric that uses frontier-model reasoning traces as gold labels with token-level NLL weighted by frontier-model confidence, so ≤1B proxies can predict reasoning performance of 13B/32B targets and transfer zero-shot across pre-training datasets.

Problem

Small proxy models (≤1B) are unreliable predictors of large-model reasoning performance because reasoning is emergent and target metrics like accuracy/pass@k are noisy and misaligned with the next-token-prediction objective at small scale.

Approach

Use frontier-model reasoning traces as in-distribution gold labels for NLL, and reweight each token's NLL by the frontier model's token probability (letter-averaged, MinMax-normalized) so that task-critical tokens dominate the proxy signal.

Key results

• On dataset ranking at 1.2B target, rBridge reaches about 80.8% decision accuracy across 25 pre-training datasets and reduces compute by 100.2x to 733.4x versus the best baseline.
• For 1B to 13B, rBridge achieves average train R^2 of 0.874 and test MAE of 1.384, best among six baselines in 10/12 cases on R^2 and MAE.
• Zero-shot transfer from OLMo-Mix-1124 to an alternative dataset at 1B to 7B ranks all 5 benchmarks correctly (5/5) versus 4/5 for R-phi, with average MAE 2.490 vs 3.425.

Surprising findings

• Standard accuracy/pass@1 at 1B fits target performance poorly (average train R^2 about 0.31 at 1B to 13B), and NLL on the raw benchmark gold answers is worse than reasoning-trace NLL.
• Using MMLU Pro-style noisy benchmarks at the smallest proxy scale is unreliable, so the ranking experiment uses ARC-C and CQA instead.

Limitations

• Frontier-model reasoning traces may be incorrect; the method uses unfiltered traces and post-hoc filtering showed minimal gains.
• Frontier models sometimes fail the required JSON output format, requiring retries or exclusion.
• Evaluated only on short-CoT reasoning; not tested on long-CoT models, and the zero-shot transfer experiment covers only one alternative dataset and a single 1B-to-7B scale.

Experimental setup

Datasets: OLMo-Mix-1124 GSM8K MATH500 ARC-C MMLU Pro (STEM) CommonsenseQA HumanEval DataDecide 25 pre-training datasets

Benchmarks: GSM8K MATH500 ARC-C MMLU Pro (STEM) CQA HumanEval

Metrics: decision accuracy Kendall's Tau train R^2 test MAE FLOPs saving

Baselines: Acc./p@1 intermediate SFT (iSFT) Token Edit Distance (TED) Model Probability of Correct Answer (MPCA) NLL R-phi (ScalingBench-style reasoning trace NLL) Correct Probability Normalized Correct Probability Total Probability Margin CF Accuracy

Builds on: DataDecide ScalingBench OLMo 2 decision accuracy metric emergence literature

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