论文标题
全体形态平衡传播通过有限尺寸振荡来计算精确的梯度
Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillations
论文作者
论文摘要
均衡传播（EP）是反向传播（BP）的替代方法，它允许使用本地学习规则训练深层神经网络。因此，它为训练神经形态系统并了解神经生物学中的学习提供了一个令人信服的框架。但是，EP需要无限的教学信号，从而限制了其在嘈杂的物理系统中的适用性。此外，该算法需要单独的时间阶段，并且尚未应用于大规模问题。在这里，我们通过将EP扩展到全体形态网络来解决这些问题。我们分析表明，即使对于有限的振幅教学信号，这种扩展也会自然导致精确的梯度。重要的是，可以将梯度计算为在连续时间内有限神经元活性振荡的第一个傅立叶系数，而无需单独的阶段。此外，我们在数值模拟中证明了我们的方法允许在存在噪声的情况下对梯度的强大估计，并且更深的模型受益于有限的教学信号。最后，我们在ImageNet 32x32数据集上建立了EP的第一个基准，并表明它与接受BP训练的等效网络的性能相匹配。我们的工作提供了分析见解，使EP可以扩展到大规模问题，并为振荡如何支持生物学和神经形态系统学习的正式框架建立了正式框架。
Equilibrium propagation (EP) is an alternative to backpropagation (BP) that allows the training of deep neural networks with local learning rules. It thus provides a compelling framework for training neuromorphic systems and understanding learning in neurobiology. However, EP requires infinitesimal teaching signals, thereby limiting its applicability in noisy physical systems. Moreover, the algorithm requires separate temporal phases and has not been applied to large-scale problems. Here we address these issues by extending EP to holomorphic networks. We show analytically that this extension naturally leads to exact gradients even for finite-amplitude teaching signals. Importantly, the gradient can be computed as the first Fourier coefficient from finite neuronal activity oscillations in continuous time without requiring separate phases. Further, we demonstrate in numerical simulations that our approach permits robust estimation of gradients in the presence of noise and that deeper models benefit from the finite teaching signals. Finally, we establish the first benchmark for EP on the ImageNet 32x32 dataset and show that it matches the performance of an equivalent network trained with BP. Our work provides analytical insights that enable scaling EP to large-scale problems and establishes a formal framework for how oscillations could support learning in biological and neuromorphic systems.
