Generative models drop backprop: equilibrium propagation hits FID 3.64 on CIFAR-10, close to backprop's 3.54
Synopsis
A backprop-free training path reaches FID 3.64 on unconditional CIFAR-10 against 3.54 for backpropagation, the first CIFAR-scale generative model trained with equilibrium propagation.
Interpretation
A generative model can be sampled entirely by physical relaxation instead of integrating a velocity field step by step. Diffusion and flow-matching models typically integrate a velocity field over hundreds of sequential steps, a computation that suits a GPU poorly but an analog neuromorphic substrate well. An Energy Matching model trained by backpropagation can be loaded into the network unchanged and sampled by relaxation alone, matching the original model's FID to within 0.04 at CIFAR-10 and ImageNet-32 scale.
Training can also proceed without backpropagation, with parameter updates nearly identical to backpropagation's. Backpropagation requires global gradient transport, which is hard to realise in analog hardware. Equilibrium Propagation reproduces backpropagation's parameter updates to a cosine similarity of 0.9998, and training end to end with those updates reaches FID 3.64 on unconditional CIFAR-10 against 3.54 for backpropagation.
Reaching this quality does not require group normalisation or attention. Common high-quality generative architectures often rely on group normalisation and attention modules. An architecture of only convolutions and pointwise nonlinearities, both native to an analog crossbar, reaches FID 3.51 when trained by backpropagation.
Perspective
The result concerns image generation at CIFAR-10 and ImageNet-32 scale, for readers interested in generative training rules and analog hardware fit. The material states that a trained Energy Matching model can be loaded into the network and sampled by relaxation alone, and that the network can be trained end to end with equilibrium propagation; it gives no next step toward larger scale or physical analog hardware.
The material is a summary and does not state training cost, hardware measurements, or behaviour on larger datasets. The reported FID and cosine similarity correspond to CIFAR-10 and ImageNet-32 scale, so they are results within that setting.