# SCATR: Simple Calibrated Test-Time Ranking

arXiv: https://arxiv.org/abs/2604.16535 · HTML: https://mlsanity.com/paper/2604.16535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 27 of 27)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Scalable Best-of-N Selection for Large Language Models via Self-Certainty](https://mlsanity.com/paper/2502.18581/) (2025)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [Self-Evaluation Improves Selective Generation in Large Language Models](https://mlsanity.com/paper/2312.09300/) (2023)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Learning to Route LLMs with Confidence Tokens](https://mlsanity.com/paper/2410.13284/) (2024)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [LLMs Can Generate a Better Answer by Aggregating Their Own Responses](https://mlsanity.com/paper/2503.04104/) (2025)
- [Learning to Refine: Self-Refinement of Parallel Reasoning in LLMs](https://mlsanity.com/paper/2509.00084/) (2025)
- [Scalable In-context Ranking with Generative Models](https://mlsanity.com/paper/2510.05396/) (2025)
- [LLMs are Overconfident: Evaluating Confidence Interval Calibration with FermiEval](https://mlsanity.com/paper/2510.26995/) (2025)
- [Optimal Aggregation of LLM and PRM Signals for Efficient Test-Time Scaling](https://mlsanity.com/paper/2510.13918/) (2025)

## Abstract (arXiv)

Test-time scaling (TTS) improves large language models (LLMs) by allocating additional compute at inference time. In practice, TTS is often achieved through parallel scaling: generating multiple candidate responses and selecting the best via a Best-of-N (BoN) strategy. Its effectiveness therefore hinges on the scoring function. Learned scorers such as process reward models (PRMs) can be strong, but they are expensive to train and run. Lightweight confidence heuristics based on token log-probabilities are much cheaper, yet we find that they often perform substantially worse. To improve on lightweight confidence heuristics without incurring the full cost of stronger learned scorers, we introduce SCATR, a simple and efficient BoN ranking method that learns a lightweight scorer from a small calibration set using hidden representations from the base model. Across coding and mathematical reasoning benchmarks, SCATR improves over prior confidence-based baselines by up to 9%. Relative to LoRA fine-tuning on the same calibration data, it achieves comparable accuracy with up to 8000x fewer trainable parameters and much lower compute, reducing training and inference latency by up to 150x and 1000x, respectively. SCATR is also competitive with strong PRM baselines, and in several settings improves accuracy by up to 7.8% on math and 4.2% on coding while enabling up to 1000x faster inference. Overall, SCATR offers a strong accuracy-efficiency trade-off for scalable test-time selection.