真正的层次认知模型（一图胜千言）
一图胜千言，一道破万术，花醉三千客，知音有几人。
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出自：A step-by-step tutorial on active inference and its application to empirical data 图12 图13 ，论文提供了代码。
second level A matrix (likelihood mapping) mediates the ascending and descending messages between hierarchical levels. This structure also entails that the second-level model must operate at a slower timescale than the first-level model, because each observation in the second-level model (i.e., each time point in a second-level trial) corresponds to the results of (i.e., posterior beliefs after) a complete trial in the first-level model. Thus, there are as many first-level trials as there are time points in a second-level trial.
This type of model architecture is essential for capturing perceptual phenomena with nested dynamics, or where objects must be recognized before regularities in the behavior of those objects can be detected.
Hierarchical POMDPs also afford further opportunities for simulating neuronal processes. To date, simulations associated with the faster and slower timescales of belief updating have been shown to reproduce an impressive number of task-based electrophysiological findings. For example, empirically observed patterns of ERPs associated with specific cognitive and perceptual processes, such as the P300 and mismatch negativity (MMN), emerge naturally in simulations of different experimental paradigms, which supports the face validity of both the model structure and the neural process theory
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更多精彩：
how we learn 第二章 人脑比机器强在哪？（长文）
新概率书 Structured Probabilistic Reasoning
A Theory of Learning to Infer ：有限资源下不合理的合理性
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