The free energy principle (FEP), as an encompassing framework and a unified brain theory, has been widely applied to account for various problems in fields such as cognitive science, neuroscience, social interaction, and hermeneutics. As a computational model deeply rooted in math and statistics, FEP posits an optimization problem based on variational Bayes, which is solved either by dynamic programming or expectation maximization in practice. However, there seems to be a bottleneck in extending the FEP to machine learning and implementing such models with neural networks. This paper gives a preliminary attempt at bridging FEP and machine learning, via a classical neural network model, the Helmholtz machine. As a variational machine learning model, the Helmholtz machine is optimized by minimizing its free energy, the same objective as FEP. Although the Helmholtz machine is not temporal, it gives an ideal parallel to the vanilla FEP and the hierarchical model of the brain, under which the active inference and predictive coding could be formulated coherently. Besides a detailed theoretical discussion, the paper also presents a preliminary experiment to validate the hypothesis. By fine-tuning the trained neural network through active inference, the model performance is promoted to accuracy above 99\%. In the meantime, the data distribution is continuously deformed to a salience that conforms to the model representation, as a result of active sampling.

翻译：自由能原理作为一个包容性框架和统一大脑理论，已被广泛用于解释认知科学、神经科学、社会互动和诠释学等领域的各类问题。作为根植于数学与统计学的计算模型，自由能原理提出了基于变分贝叶斯的优化问题，在实践中通过动态规划或期望最大化求解。然而，将自由能原理扩展至机器学习并利用神经网络实现此类模型似乎存在瓶颈。本文通过经典神经网络模型——亥姆霍兹机，初步尝试衔接自由能原理与机器学习。作为一种变分机器学习模型，亥姆霍兹机通过最小化其自由能进行优化，这与自由能原理的目标一致。尽管亥姆霍兹机不具有时序性，但它为原始自由能原理和大脑层级模型提供了理想的平行框架，在此框架下主动推理与预测编码可被统一表述。除详细的理论探讨外，本文还通过初步实验验证假设：通过主动推理微调训练后的神经网络，模型性能提升至99%以上的准确率。同时，作为主动采样的结果，数据分布持续形变至符合模型表征的显著分布。