用可验证路径熵衡量智能体在有限反思下的持续能力，发现小模型反而更优。
Mirror Horizon: Viable Path Entropy as a Measure of Bounded Reflection
- 提出可验证路径熵（VPE），量化有限预算下持续推理的可达性与多样性。
- 在GSM8K上，160词元预算使验证可达率提升，零可达率下降，模式熵增加。
- 小模型（1.5B）在反思能力上优于大模型（3B），证明能力不取决于参数量。
镜像理论认为，应通过智能体在反复反思下能维持的连贯延续路径来评估其能力。本文提出‘可验证路径熵’（VPE），一种有限预算下的验证延续能力度量方法。给定镜像状态、回溯协议、验证器和模式映射，VPE将能力分解为：成功抵达可行延续的概率，以及在成功回溯中达到的验证模式多样性。本文构建了完整的理论框架：局部不确定性作为约束，品味作为不变选择压力，反思作为品味引导的不确定性消解，几何结构则使未来反思稳定。在GSM8K语言模型推理实验中，对Qwen2.5-Instruct系列模型，每题32次采样回溯，两种反思周期下，将词元预算从96增至160显著提升了验证可达性，降低了零可达性，增加了验证模式熵，并改善了平滑后的VPE。在160词元时，尽管参数更少，Qwen2.5-1.5B展现出最强的镜像视野，超越了参数更多的Qwen2.5-3B。这表明镜像视野并非由参数数量决定，而是受限于反射协议下的可访问验证延续能力。结果支持镜像理论作为能力的度量层面解释：能力是可实现的可行延续结构，而非单次准确率或pass@k。
原文摘要 · Abstract (English)
Mirror Theory proposes that an intelligent system should be studied not only by what it represents, but by what coherent continuations it can sustain under repeated reflection. We make this claim operational through \emph{viable path entropy} (VPE), a finite-budget measure of verified continuation capacity. Given a mirror state, a rollout protocol, a verifier, and a mode map, VPE decomposes bounded capability into two parts: the probability of reaching a viable continuation and the diversity of verified continuation modes reached among successful rollouts. This paper restores the full theoretical scaffold behind the measure: intuition as local underdetermining constraint, taste as invariant-selecting pressure, reflection as taste-guided resolution of underdetermination, and geometry as the learned structure that makes future reflection stable. We then instantiate the theory in language-model reasoning experiments on GSM8K. Across Qwen2.5-Instruct models, 32 sampled rollouts per problem, and two reflection horizons, increasing the token budget from 96 to 160 substantially expands verified reachability, reduces zero-reachability, increases verified-mode entropy, and improves smoothed VPE. At 160 tokens, Qwen2.5-1.5B realizes the strongest mirror horizon among the tested models, even though Qwen2.5-3B has more parameters. This shows that mirror horizon is not parameter count, but accessible verified continuation capacity under a bounded reflection protocol. The result supports Mirror Theory as a measure-level account: capability is the structure of viable continuations made reachable, not merely one-shot accuracy or pass@k.
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