Sokoloski Sacha
Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany, and Albert Einstein College of Medicine, New York, NY 10461, U.S.A.
Neural Comput. 2017 Sep;29(9):2450-2490. doi: 10.1162/NECO_a_00991. Epub 2017 Jun 9.
In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.
为了与现实世界中的物体进行智能交互，动物必须首先将神经群体反应转化为对引起这些反应的动态、未知刺激的估计。解决这个问题的贝叶斯方法称为贝叶斯滤波器，它应用贝叶斯规则将群体反应与内部模型的预测相结合。贝叶斯滤波器的内部模型基于真实的刺激动态，在本笔记中，我们提出了一种训练理论神经回路的方法，当刺激动态未知时，该回路可近似实现贝叶斯滤波器。为此，我们利用线性概率群体编码的推理特性来计算贝叶斯规则，并训练神经网络通过最大似然法计算近似预测。特别是，我们对神经网络参数的负对数似然进行随机梯度下降，梯度采用一种新颖的近似方法。我们在有限状态、线性和非线性滤波问题上展示了我们的方法，并展示了神经网络的隐藏层如何发展出与实验神经科学研究结果一致的调谐曲线。
