热力学过拟合与泛化：预测复杂度的能量极限
Thermodynamic Overfitting and Generalization: Energetic Limits on Predictive Complexity
AI总结：
本文研究信息引擎中复杂预测记忆的能量收益与过拟合风险，提出由物理约束导出的热力学正则化器，证明其能有效提升预测模型泛化性能，揭示物理定律为涌现复杂性与预测智能创造条件。
摘要：
高效获取热力学资源需要对其结构有精确的理解。这一点通过信息引擎——以信息为燃料的热力学引擎——的视角变得明确。利用可用信息最大化所收获的功，是一种物理实例化的机器学习形式，它驱动信息引擎发展出复杂的预测性记忆，以存储环境的时间关联。我们表明，信息引擎的复杂预测性记忆既带来能量上的收益，也带来风险。虽然增加记忆有助于检测环境中的隐藏模式，但它也开启了热力学过拟合的可能性，即引擎在测试中耗散额外的能量。为了解决过拟合问题，我们引入了热力学正则化器，由于信息引擎的物理约束，这些正则化器在训练中会给引擎复杂度带来代价。我们证明，经过正则化的热力学机器学习能够有效泛化。特别是，推导出正则化器的物理约束提高了所学预测模型的性能。这表明物理定律共同为涌现复杂性和预测智能创造了条件。
英文摘要：
Efficiently harvesting thermodynamic resources requires a precise understanding of their structure. This becomes explicit through the lens of information engines -- thermodynamic engines that use information as fuel. Maximizing the work harvested using available information is a form of physically-instantiated machine learning that drives information engines to develop complex predictive memory to store an environment's temporal correlations. We show that an information engine's complex predictive memory poses both energetic benefits and risks. While increasing memory facilitates detection of hidden patterns in an environment, it also opens the possibility of thermodynamic overfitting, where the engine dissipates additional energy in testing. To address overfitting, we introduce thermodynamic regularizers that incur a cost to engine complexity in training due to the physical constraints on the information engine. We demonstrate that regularized thermodynamic machine learning generalizes effectively. In particular, the physical constraints from which regularizers are derived improve the performance of learned predictive models. This suggests that the laws of physics jointly create the conditions for emergent complexity and predictive intelligence.
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