Mirror Horizon: Viable Path Entropy as a Measure of Bounded Reflection
Introduces Mirror Theory and Viable Path Entropy (VPE) as a metric for measuring bounded reflection and coherent continuation capacity in intelligent systems. VPE decomposes capability into the probability of reaching a viable continuation and the diversity of verified continuation modes, moving beyond simple accuracy metrics. Experiments on GSM8K with Qwen2.5-Instruct models show that increasing token budget from 96 to 160 significantly improves verified reachability and smoothed VPE. The Qwen2
Analysis
TL;DR
- Introduces Mirror Theory and Viable Path Entropy (VPE) as a metric for measuring bounded reflection and coherent continuation capacity in intelligent systems.
- VPE decomposes capability into the probability of reaching a viable continuation and the diversity of verified continuation modes, moving beyond simple accuracy metrics.
- Experiments on GSM8K with Qwen2.5-Instruct models show that increasing token budget from 96 to 160 significantly improves verified reachability and smoothed VPE.
- The Qwen2.5-1.5B model achieved the strongest mirror horizon at 160 tokens, outperforming the larger 3B model, demonstrating that accessible verified continuation capacity matters more than parameter count.
Why It Matters
This research shifts the focus from static performance metrics like pass@k to dynamic measures of an AI's ability to sustain coherent reasoning over multiple reflection steps. For practitioners, it highlights that model efficiency and reasoning stability can be optimized through better reflection protocols rather than just scaling parameter counts. It offers a new theoretical framework for evaluating and improving the robustness of LLMs in complex reasoning tasks.
Technical Details
- Viable Path Entropy (VPE): A finite-budget measure defined by four components: mirror state, rollout protocol, verifier, and mode map. It quantifies both the likelihood of success and the diversity of successful strategies.
- Theoretical Scaffold: The paper defines intuition as local underdetermining constraints, taste as invariant-selecting pressure, reflection as taste-guided resolution, and geometry as the learned structure enabling stable future reflection.
- Experimental Setup: Evaluated on GSM8K using Qwen2.5-Instruct models (1.5B and 3B). Each problem involved 32 sampled rollouts across two reflection horizons.
- Key Findings: Increasing the token budget from 96 to 160 reduced zero-reachability and increased verified-mode entropy. The 1.5B model surpassed the 3B model in mirror horizon strength, proving that bounded reflection capacity is distinct from raw model size.
Industry Insight
- Rethinking Model Evaluation: Developers should consider dynamic reasoning capabilities and continuation stability alongside traditional accuracy benchmarks when selecting models for complex, multi-step tasks.
- Efficiency Over Scale: Smaller models can outperform larger ones in specific reasoning protocols if they possess higher verified continuation capacity. Optimizing reflection budgets and verifiers may yield better results than simply deploying larger models.
- Protocol Design Importance: The effectiveness of AI systems is heavily dependent on the rollout and verification protocols used. Investing in better "taste" mechanisms and reflection horizons can unlock latent capabilities in existing models.
Disclaimer: The above content is generated by AI and is for reference only.