LLM Self-Consistency Calibration for Math Reasoning Confidence
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Solution Overview
Problem
Large language models (LLMs) lack adequate calibration, leading to poorly aligned probabilities of model predictions with actual accuracy, which affects their performance in math reasoning tasks, especially in scenarios with slight question changes.
Innovation Solution
A method involving generating multiple sample responses using an LLM, organizing them into clusters, and performing a calibration process to output a response based on the calibration, leveraging self-consistency to improve confidence estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LLMs are used for math reasoning tasks without specific training, then they can solve many math reasoning tasks with reasonable accuracy, but they lack adequate calibration where prediction probabilities are poorly aligned with actual accuracy
Solution Approach 1:
The system generates multiple sample responses and uses self-consistency calibration to create feedback loops. By organizing responses into clusters and performing calibration processes, the system continuously adjusts prediction probabilities to better align with actual accuracy, transforming the uncalibrated LLM into a calibrated system through iterative feedback from multiple sampling rounds.
Solution Approach 2:
Before final output, the system performs preliminary actions by generating N sample responses and organizing them into clusters. This preliminary calibration process prepares the prediction probabilities in advance, ensuring they are better aligned with actual accuracy before the final response is selected and outputted.
2Reliability
If conventional models are fine-tuned on GSM8K training set, then they achieve specific task performance, but they report accuracies around 10% to 20% which is lower than LLMs with chain-of-thought prompting
Solution Approach 1:
The system dynamically adapts to different math reasoning questions by generating multiple sample responses for each query. Instead of relying on static fine-tuning that degrades with question changes, the dynamic self-consistency calibration process adjusts to each specific question, maintaining high accuracy across varied math reasoning tasks through adaptive sampling and clustering.
3Measurement precision
If LLMs produce responses without calibration, then they can answer questions directly, but they cannot precisely indicate how likely their responses are correct, limiting handling of low-confidence responses
Solution Approach 1:
The calibration process provides precise confidence estimation feedback by comparing multiple sample responses and their cluster distributions. This feedback mechanism enables the system to accurately determine how likely responses are correct, which then enables flexible handling of low-confidence responses through options like refusal or resampling.
Data Source
AI summary
A method includes receiving an input query; generating N sample responses based on the input query using a large language model (LLM), N being an integer greater than zero; organizing the N sample responses into one or more clusters; performing a calibration process on the one or more clusters; and outputting a response to the input query based on the calibration process.