Artificial Intelligence (AI) supported by Deep Artificial Neural Networks (ANNs) is booming and already used in many applications, with impressive results, and we are still its infancy. For many sensing applications it would be advantageous if we could move AI from cloud to Edge. However this requires huge improvements in energy-efficiency. The CONVOLVE project (convolve.eu) aims at enabling smart edge devices through a concerted effort at all layers of the design stack. This ranges from using much more efficient models and mappings, like exploiting Spiking Neural Networks (SNNs), to new processing architectures, like compute-in-memory (CIM), use of approximation, and using new device technology, like memristors. However these latter changes make HW more susceptible to noise and other disturbances. Online continuous learning (i.e. adapting weights) may alleviate these problems. This paper shows several CONVOLVE developments in the crucial areas of CIM architectures, SNN accelerators and online learning.

Equilibrium propagation (EP) is a compelling alternative to the back propagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to yield unbiased gradient estimates. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry contributes to bias is unknown because, in practice, its contribution may be masked by a finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that bias due to finite nudge can be avoided by estimating exact derivatives via a Cauchy integral. In contrast, weight asymmetry induces residual bias through poor alignment of EP's neuronal error vectors compared to BP resulting in low task performance. To mitigate the latter issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32$\times$32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

Non-contrastive SSL methods like BYOL and SimSiam rely on asymmetric predictor networks to avoid representational collapse without negative samples. Yet, how predictor networks facilitate stable learning is not fully understood. While previous theoretical analyses assumed Euclidean losses, most practical implementations rely on cosine similarity. To gain further theoretical insight into non-contrastive SSL, we analytically study learning dynamics in conjunction with Euclidean and cosine similarity in the eigenspace of closed-form linear predictor networks. We show that both avoid collapse through implicit variance regularization albeit through different dynamical mechanisms. Moreover, we find that the eigenvalues act as effective learning rate multipliers and propose a family of isotropic loss functions (IsoLoss) that equalize convergence rates across eigenmodes. Empirically, IsoLoss speeds up the initial learning dynamics and increases robustness, thereby allowing us to dispense with the EMA target network typically used with non-contrastive methods. Our analysis sheds light on the variance regularization mechanisms of non-contrastive SSL and lays the theoretical grounds for crafting novel loss functions that shape the learning dynamics of the predictor's spectrum.

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 to 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 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 $32 \times 32$ 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.

The design of systems implementing low precision neural networks with emerging memories such as resistive random access memory (RRAM) is a significant lead for reducing the energy consumption of artificial intelligence. To achieve maximum energy efficiency in such systems, logic and memory should be integrated as tightly as possible. In this work, we focus on the case of ternary neural networks, where synaptic weights assume ternary values. We propose a two-transistor/two-resistor memory architecture employing a precharge sense amplifier, where the weight value can be extracted in a single sense operation. Based on experimental measurements on a hybrid 130 nm CMOS/RRAM chip featuring this sense amplifier, we show that this technique is particularly appropriate at low supply voltage, and that it is resilient to process, voltage, and temperature variations. We characterize the bit error rate in our scheme. We show based on neural network simulation on the CIFAR-10 image recognition task that the use of ternary neural networks significantly increases neural network performance, with regards to binary ones, which are often preferred for inference hardware. We finally evidence that the neural network is immune to the type of bit errors observed in our scheme, which can therefore be used without error correction.