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→Perceptual inference and categorisation 感性推理与分类
Free energy minimisation formalises the notion of [[unconscious inference]] in perception<ref name="Helmholtz" /><ref name="Dayan" /> and provides a normative (Bayesian) theory of neuronal processing. The associated process theory of neuronal dynamics is based on minimising free energy through gradient descent. This corresponds to [[Generalized filtering|generalised Bayesian filtering]] (where ~ denotes a variable in generalised coordinates of motion and <math>D</math> is a derivative matrix operator):<ref>Friston, K., Stephan, K., Li, B., & Daunizeau, J. (2010). [http://www.fil.ion.ucl.ac.uk/~karl/Generalised%20Filtering.pdf Generalised Filtering]. Mathematical Problems in Engineering, vol., 2010, 621670</ref>
Free energy minimisation formalises the notion of [[unconscious inference]] in perception<ref name="Helmholtz" /><ref name="Dayan" /> and provides a normative (Bayesian) theory of neuronal processing. The associated process theory of neuronal dynamics is based on minimising free energy through gradient descent. This corresponds to [[Generalized filtering|generalised Bayesian filtering]] (where ~ denotes a variable in generalised coordinates of motion and <math>D</math> is a derivative matrix operator):<ref>Friston, K., Stephan, K., Li, B., & Daunizeau, J. (2010). [http://www.fil.ion.ucl.ac.uk/~karl/Generalised%20Filtering.pdf Generalised Filtering]. Mathematical Problems in Engineering, vol., 2010, 621670</ref>
自由能最小化使知觉中的[[无意识推理]]概念正式化<ref name="Helmholtz" /><ref name="Dayan" />并提供了神经元处理的规范（贝叶斯）理论。神经元动力学的相关过程理论是基于通过梯度下降最小化自由能。这对应于[[广义滤波|广义贝叶斯滤波]]（其中~表示广义运动坐标中的变量，<math>D</math>是一个导数矩阵运算符）：<ref>Friston, K., Stephan, K., Li, B., & Daunizeau, J. (2010). [http://www.fil.ion.ucl.ac.uk/~karl/Generalised%20Filtering.pdf Generalised Filtering]. Mathematical Problems in Engineering, vol., 2010, 621670</ref>
where, <math>E^{total}</math> is the total energy function of the neural networks entail, and <math>\varepsilon^{KN}_{knm}</math> is the prediction error between the generative model (prior) and posterior changing over time.)
where, <math>E^{total}</math> is the total energy function of the neural networks entail, and <math>\varepsilon^{KN}_{knm}</math> is the prediction error between the generative model (prior) and posterior changing over time.)
其中，<math>E^{total}</math>是神经网络的总能量函数，而 <math>\varepsilon^{KN}_{knm}</math>是生成模型前和后随时间变化的预测误差。
: <math>\dot{\tilde{\mu}} = D \tilde{\mu} - \partial_{\mu}F(s,\mu)\Big|_{\mu = \tilde{\mu}}</math>
: <math>\dot{\tilde{\mu}} = D \tilde{\mu} - \partial_{\mu}F(s,\mu)\Big|_{\mu = \tilde{\mu}}</math>
Comparing the two models reveals a notable similarity between their results while pointing out to a remarkable discrepancy, in that, in the standard version of the SAIM, the model's focus is mainly upon the excitatory connections whereas in the PE-SAIM the inhibitory connections will be leveraged to make an inference. The model has also proved to be fit to predict the EEG and fMRI data drawn from human experiments with a high precision.
Comparing the two models reveals a notable similarity between their results while pointing out to a remarkable discrepancy, in that, in the standard version of the SAIM, the model's focus is mainly upon the excitatory connections whereas in the PE-SAIM the inhibitory connections will be leveraged to make an inference. The model has also proved to be fit to predict the EEG and fMRI data drawn from human experiments with a high precision.
比较这两个模型的结果发现他们之间有显著的相似性，同时指出了一个显著的差异，即在SAIM的标准版本中，模型的重点主要是兴奋性连接，而在PE-SAIM中，抑制性连接将被用来进行推断。该模型对人体实验的脑电和功能磁共振数据具有较高的预测精度。
Usually, the generative models that define free energy are non-linear and hierarchical (like cortical hierarchies in the brain). Special cases of generalised filtering include [[Kalman filter]]ing, which is formally equivalent to [[predictive coding]]<ref>Rao, R. P., & Ballard, D. H. (1999). [https://www.cs.utexas.edu/users/dana/nn.pdf Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects]. Nat Neurosci. , 2 (1), 79–87.</ref> – a popular metaphor for message passing in the brain. Under hierarchical models, predictive coding involves the recurrent exchange of ascending (bottom-up) prediction errors and descending (top-down) predictions<ref name="Mumford">Mumford, D. (1992). [http://cs.brown.edu/people/tld/projects/cortex/course/suggested_reading_list/supplements/documents/MumfordBC-92.pdf On the computational architecture of the neocortex]. II. Biol. Cybern. , 66, 241–51.</ref> that is consistent with the anatomy and physiology of sensory<ref>Bastos, A. M., Usrey, W. M., Adams, R. A., Mangun, G. R., Fries, P., & Friston, K. J. (2012). [http://www.fil.ion.ucl.ac.uk/~karl/Canonical%20Microcircuits%20for%20Predictive%20Coding.pdf Canonical microcircuits for predictive coding]. Neuron , 76 (4), 695–711.</ref> and motor systems.<ref>Adams, R. A., Shipp, S., & Friston, K. J. (2013). [http://www.fil.ion.ucl.ac.uk/~karl/Predictions%20not%20commands%20-%20active%20inference%20in%20the%20motor%20system.pdf Predictions not commands: active inference in the motor system]. Brain Struct Funct. , 218 (3), 611–43</ref>
Usually, the generative models that define free energy are non-linear and hierarchical (like cortical hierarchies in the brain). Special cases of generalised filtering include [[Kalman filter]]ing, which is formally equivalent to [[predictive coding]]<ref>Rao, R. P., & Ballard, D. H. (1999). [https://www.cs.utexas.edu/users/dana/nn.pdf Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects]. Nat Neurosci. , 2 (1), 79–87.</ref> – a popular metaphor for message passing in the brain. Under hierarchical models, predictive coding involves the recurrent exchange of ascending (bottom-up) prediction errors and descending (top-down) predictions<ref name="Mumford">Mumford, D. (1992). [http://cs.brown.edu/people/tld/projects/cortex/course/suggested_reading_list/supplements/documents/MumfordBC-92.pdf On the computational architecture of the neocortex]. II. Biol. Cybern. , 66, 241–51.</ref> that is consistent with the anatomy and physiology of sensory<ref>Bastos, A. M., Usrey, W. M., Adams, R. A., Mangun, G. R., Fries, P., & Friston, K. J. (2012). [http://www.fil.ion.ucl.ac.uk/~karl/Canonical%20Microcircuits%20for%20Predictive%20Coding.pdf Canonical microcircuits for predictive coding]. Neuron , 76 (4), 695–711.</ref> and motor systems.<ref>Adams, R. A., Shipp, S., & Friston, K. J. (2013). [http://www.fil.ion.ucl.ac.uk/~karl/Predictions%20not%20commands%20-%20active%20inference%20in%20the%20motor%20system.pdf Predictions not commands: active inference in the motor system]. Brain Struct Funct. , 218 (3), 611–43</ref>
通常，定义自由能的生成模型是非线性和层次结构的（就像大脑中的皮层层次结构）。广义滤波的特殊情况包括[[Kalman filter]]ing，它在形式上等价于[预测编码]]<ref>Rao, R. P., & Ballard, D. H. (1999). [https://www.cs.utexas.edu/users/dana/nn.pdf Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects]. Nat Neurosci. , 2 (1), 79–87.</ref> 一种关于大脑中信息传递的流行隐喻。在分层模型下，预测编码涉及到上升（自下而上）预测错误和下降（自上而下）预测的循环交换<ref name="Mumford">Mumford, D. (1992). [http://cs.brown.edu/people/tld/projects/cortex/course/suggested_reading_list/supplements/documents/MumfordBC-92.pdf On the computational architecture of the neocortex]. II. Biol. Cybern. , 66, 241–51.</ref>这与感觉器官的解剖学和生理学<ref>Bastos, A. M., Usrey, W. M., Adams, R. A., Mangun, G. R., Fries, P., & Friston, K. J. (2012). [http://www.fil.ion.ucl.ac.uk/~karl/Canonical%20Microcircuits%20for%20Predictive%20Coding.pdf Canonical microcircuits for predictive coding]. Neuron , 76 (4), 695–711.</ref>以及动力系统<ref>Adams, R. A., Shipp, S., & Friston, K. J. (2013). [http://www.fil.ion.ucl.ac.uk/~karl/Predictions%20not%20commands%20-%20active%20inference%20in%20the%20motor%20system.pdf Predictions not commands: active inference in the motor system]. Brain Struct Funct. , 218 (3), 611–43</ref>是一致的。
=== Perceptual learning and memory 知觉学习与记忆===
=== Perceptual learning and memory 知觉学习与记忆===