We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex distributions, a far wider range of distributions than just computable ones. By focusing on computable distributions, machine learning models can better manage complexity via probability. We abstract away from specific learning mechanisms, modeling machine learning as producing P/poly-computable distributions with polynomially-bounded max-entropy. We illustrate how learning computable distributions models complexity by showing that if a machine learning model produces a distribution $μ$ that minimizes error against the distribution generated by a cryptographic pseudorandom generator, then $μ$ must be close to uniform.

翻译：我们通过计算复杂性的视角来理解机器学习模型的能力，特别是它们模拟复杂系统的能力。机器学习模型通常基于从可采样分布或更复杂分布中提取的数据进行训练，这些分布的范围远超可计算分布。通过聚焦于可计算分布，机器学习模型能够借助概率更好地管理复杂性。我们抽象掉具体的学习机制，将机器学习建模为生成具有多项式有界最大熵的P/poly-可计算分布。我们通过展示以下结果来说明学习可计算分布如何建模复杂性：若机器学习模型生成的分布μ在对抗密码学伪随机生成器所生成的分布时具有最小误差，则μ必然接近均匀分布。