让模拟电路块像数字电路一样训练，实现能效突破。

Power efficiency is plateauing in the standard digital electronics realm such that novel hardware, models, and algorithms are needed to reduce the costs of AI training. The combination of energy-based analog circuits and the Equilibrium Propagation (EP) algorithm constitutes one compelling alternative compute paradigm for gradient-based optimization of neural nets. Existing analog hardware accelerators, however, typically incorporate digital circuitry to sustain auxiliary non-weight-stationary operations, mitigate analog device imperfections, and leverage existing digital accelerators.This heterogeneous hardware approach calls for a new theoretical model building block. In this work, we introduce Feedforward-tied Energy-based Models (ff-EBMs), a hybrid model comprising feedforward and energy-based blocks accounting for digital and analog circuits. We derive a novel algorithm to compute gradients end-to-end in ff-EBMs by backpropagating and "eq-propagating" through feedforward and energy-based parts respectively, enabling EP to be applied to much more flexible and realistic architectures. We experimentally demonstrate the effectiveness of the proposed approach on ff-EBMs where Deep Hopfield Networks (DHNs) are used as energy-based blocks. We first show that a standard DHN can be arbitrarily split into any uniform size while maintaining performance. We then train ff-EBMs on ImageNet32 where we establish new SOTA performance in the EP literature (46 top-1 %). Our approach offers a principled, scalable, and incremental roadmap to gradually integrate self-trainable analog computational primitives into existing digital accelerators.