LLM Verification Signals Show Heterogeneity, Limiting Optimization

This research investigates the effectiveness of uncertainty signals in large language model (LLM) systems, particularly when allocating computational resources for tasks like verification. The study reveals a critical flaw: the quality of these uncertainty signals is not uniform across different computational cost levels. This "heteroskedasticity" means that signals that appear equally strong may not carry comparable decision value, especially in regions concentrating many errors. The paper introduces a controlled intervention hierarchy, including a simple cost-stratified thresholding (CST) method. This approach, which avoids complex gradient updates, significantly improves hit rates by up to 17 percentage points in scenarios where signal quality varies widely. The findings suggest that the primary bottleneck in optimizing LLM verification isn't just weak signals or optimizer limitations, but rather the inherent structural heterogeneity in how uncertainty manifests.