Scellier Benjamin, Bengio Yoshua
Département d'Informatique et de Recherche Opérationnelle, Montreal Institute for Learning Algorithms, Université de MontréalMontreal, QC, Canada.
Front Comput Neurosci. 2017 May 4;11:24. doi: 10.3389/fncom.2017.00024. eCollection 2017.
We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal "back-propagated" during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task.
我们引入了平衡传播，这是一种基于能量模型的学习框架。它只涉及一种神经计算，在训练的第一阶段（进行预测时）和第二阶段（目标或预测误差被揭示后）都要执行。尽管此算法像反向传播一样计算目标函数的梯度，但在第二阶段不需要特殊的计算或电路，误差在该阶段是隐式传播的。平衡传播与对比赫布学习和对比散度有相似之处，同时解决了这两种算法的理论问题：我们的算法计算一个定义明确的目标函数的梯度。由于目标函数是根据局部扰动定义的，平衡传播的第二阶段仅对应于将预测（不动点或平稳分布）朝着减少预测误差的配置微调。在递归多层监督网络的情况下，输出单元在第二阶段会朝着其目标轻微微调，并且在输出层引入的扰动会在隐藏层中向后传播。我们表明，当突触更新对应于标准形式的脉冲时间依赖可塑性时，在第二阶段“反向传播”的信号对应于误差导数的传播，并编码目标函数的梯度。这项工作使得大脑有可能实现类似于反向传播的机制，因为在我们的模型中，泄漏积分器神经计算同时执行推理和误差反向传播。两个阶段之间唯一的局部差异在于是否允许突触变化。我们还通过实验表明，可以使用平衡传播在排列不变的MNIST任务上训练具有1个、2个和3个隐藏层的多层递归连接网络。
