Equilibrium Propagation (EP) is a biologically inspired local learning rule first proposed for convergent recurrent neural networks (CRNNs), in which synaptic updates depend only on neuron states from two distinct phases. EP estimates gradients that closely align with those computed by Backpropaga-tion Through Time (BPTT) while significantly reducing computational demands, positioning it as a potential candidate for on-chip training in neuromorphic architectures. However, prior studies on EP have been constrained to shallow architectures, as deeper networks suffer from the vanishing gradient problem, leading to convergence difficulties in both energy minimization and gradient computation. To address the vanishing gradient problem in deep EP networks, we propose a novel EP framework that incorporates intermediate error signals to enhance information flow and convergence of neuron dynamics. This is the first work to integrate knowledge distillation and local error signals into EP, enabling the training of significantly deeper architectures. Our proposed approach achieves state-of-the-art performance on the CIFAR-10 and CIFAR-100 datasets, showcasing its scalability on deep VGG architectures. These results represent a significant advancement in the scalability of EP, paving the way for its application in real-world systems.

Spiking neural networks (SNNs) for event-based optical flow are claimed to be computationally more efficient than their artificial neural networks (ANNs) counterparts, but a fair comparison is missing in the literature. In this work, we propose an event-based optical flow solution based on activation sparsification and a neuromorphic processor, SENECA. SENECA has an event-driven processing mechanism that can exploit the sparsity in ANN activations and SNN spikes to accelerate the inference of both types of neural networks. The ANN and the SNN for comparison have similar low activation/spike density (~5%) thanks to our novel sparsification-aware training. In the hardware-in-loop experiments designed to deduce the average time and energy consumption, the SNN consumes 44.9ms and 927.0 microjoules, which are 62.5% and 75.2% of the ANN's consumption, respectively. We find that SNN's higher efficiency attributes to its lower pixel-wise spike density (43.5% vs. 66.5%) that requires fewer memory access operations for neuron states.

The out-of-distribution (OOD) problem generally arises when neural networks encounter data that significantly deviates from the training data distribution, i.e., in-distribution (InD). In this paper, we study the OOD problem from a neuron activation view. We first formulate neuron activation states by considering both the neuron output and its influence on model decisions. Then, to characterize the relationship between neurons and OOD issues, we introduce the \textit{neuron activation coverage} (NAC) -- a simple measure for neuron behaviors under InD data. Leveraging our NAC, we show that 1) InD and OOD inputs can be largely separated based on the neuron behavior, which significantly eases the OOD detection problem and beats the 21 previous methods over three benchmarks (CIFAR-10, CIFAR-100, and ImageNet-1K). 2) a positive correlation between NAC and model generalization ability consistently holds across architectures and datasets, which enables a NAC-based criterion for evaluating model robustness. Compared to prevalent InD validation criteria, we show that NAC not only can select more robust models, but also has a stronger correlation with OOD test performance.