Path-Space Uncertainty: Quantifying Uncertainty Across the Entire Reasoning Landscape

TL;DR: Extending HARMONY's approach to combine hidden states and outputs, we'll develop a method to quantify uncertainty not just for the current reasoning path but for the entire space of possible paths that the model represents. This could provide a more comprehensive measure of model confidence.

Research Question: Can we develop a more comprehensive uncertainty measure that accounts for the entire space of reasoning paths represented by the model, rather than just uncertainty along the current path?

Hypothesis: Traditional token-level uncertainty measures underestimate model uncertainty because they only consider the current path, while path-space uncertainty will better predict when models are likely to make errors or when interventions will be effective.

Experiment Plan: Build on HARMONY's transformer-based uncertainty estimation (Mushtaq et al.) by incorporating the path-space representation capabilities discovered by Zur et al. Develop a "Path-Space Uncertainty" metric that combines: traditional token-level uncertainty, diversity of predicted future paths from hidden activations, and confidence distribution across the entire path space. Test this metric on reasoning problems where the correct answer requires exploring multiple reasoning paths before converging. Compare whether path-space uncertainty better predicts final answer correctness than traditional uncertainty measures. Explore whether path-space uncertainty can identify when models are "stuck" in suboptimal reasoning regions. Expected outcome: Path-space uncertainty will correlate more strongly with reasoning accuracy and will better identify when models would benefit from interventions or alternative approaches.

References: ['Mushtaq, E., et al. (2025). HARMONY: Hidden Activation Representations and Model Output-Aware Uncertainty Estimation for Vision-Language Models. 2025 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).', 'Zur, A., Geiger, A., Lubana, E., & Bigelow, E.J. (2025). Are language models aware of the road not taken? Token-level uncertainty and hidden state dynamics.']