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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>

 

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，e ^ { total } </math > 是神经网络的总能量函数，而 < math > varepsilon ^ { KN }{ knm } </math > 是生成模型前和后部随时间变化的预测误差

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.

比较两个模型的结果显示了显著的相似性，同时指出了一个显著的差异，即，在标准版本的 SAIM，模型的重点主要是在兴奋性联系，而在 pe-SAIM 的抑制性联系将被利用来作出推断。实验结果表明，该模型能较好地预测人体实验中的脑电信号和功能磁共振成像数据。

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>

 

=== Perceptual learning and memory 知觉学习与记忆===

=== Perceptual learning and memory 知觉学习与记忆===