Equilibrium Propagation (EP) is a physics-based training framework that has primarily been employed in energy-based models, including continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators. However, EP's practical applications have so far remained limited to relatively small-scale problems. Predictive coding networks (PCNs), another class of energy-based models rooted in computational neuroscience, are typically trained with a specialized algorithm and have likewise not yet been demonstrated at large scale. In this work, we develop an EP-based training method for PCNs which combines the centered variant of EP with a novel equilibration scheme for PCNs. Using this approach, we train a 10-layer convolutional PCN (VGG10) on full-size ImageNet, achieving 13.23\% test error rate on the top-5 classification task, close to the 12.2\% backpropagation baseline. To our knowledge, this is the first demonstration of both PCNs and EP-based training at ImageNet scale. These results significantly extend the scalability of both approaches and suggest that the primary challenges in scaling EP in other physical systems may come more from the computational properties of these systems than from inherent limitations of the EP framework.

翻译：均衡传播（EP）是一种基于物理的训练框架，主要应用于能量基模型，包括连续型Hopfield网络、非线性电阻网络和耦合相位振荡器。然而，EP的实际应用至今仍局限于相对小规模的问题。预测编码网络（PCN）作为另一类源于计算神经科学的能量基模型，通常采用专门算法进行训练，同样尚未在大规模任务中得到验证。本研究提出了一种基于EP的PCN训练方法，将EP的中心化变体与一种新型PCN均衡方案相结合。通过该方法，我们在全尺寸ImageNet上训练了10层卷积PCN（VGG10），在top-5分类任务上实现了13.23%的测试错误率，接近12.2%的反向传播基线。据我们所知，这是首次在ImageNet规模上对PCN和基于EP的训练方法进行验证。这些结果显著拓展了两种方法的可扩展性，并表明在其他物理系统中扩展EP的主要挑战可能更多源于这些系统的计算特性，而非EP框架本身的固有局限性。