Tiantian Zhang introduced the concept of Mirror Horizon in a recent paper titled Mirror Horizon: Viable Path Entropy as a Measure of Bounded Reflection, submitted on July 11, 2026. This study explores how intelligent systems can be analyzed not just by their representations but by their ability to sustain coherent continuations through repeated reflection.
Understanding Viable Path Entropy
The paper presents viable path entropy (VPE), a measure that quantifies the continuation capacity of intelligent systems under a bounded reflection protocol. VPE breaks down capability into two components: the likelihood of achieving a viable continuation and the variety of verified continuation modes achieved during successful rollouts.
The theoretical framework behind VPE includes several key concepts: intuition as a local underdetermining constraint, taste as invariant-selecting pressure, reflection as taste-guided resolution, and geometry as the learned structure that stabilizes future reflections. By applying these concepts, the paper aims to provide a comprehensive understanding of how intelligent systems can improve their reasoning capabilities.
Experimental Findings on Language-Model Reasoning
In experiments conducted using the GSM8K dataset, the study analyzed the performance of different Qwen2.5-Instruct models. With an increase in token budget from 96 to 160 tokens, results showed significant improvements:
