The search for "biologically plausible" learning algorithms has converged on the idea of representing gradients as activity differences. However, most approaches require a high degree of synchronization (distinct phases during learning) and introduce substantial computational overhead, which raises doubts regarding their biological plausibility as well as their potential utility for neuromorphic computing. Furthermore, they commonly rely on applying infinitesimal perturbations (nudges) to output units, which is impractical in noisy environments. Recently it has been shown that by modelling artificial neurons as dyads with two oppositely nudged compartments, it is possible for a fully local learning algorithm named ``dual propagation'' to bridge the performance gap to backpropagation, without requiring separate learning phases or infinitesimal nudging. However, the algorithm has the drawback that its numerical stability relies on symmetric nudging, which may be restrictive in biological and analog implementations. In this work we first provide a solid foundation for the objective underlying the dual propagation method, which also reveals a surpising connection with adversarial robustness. Second, we demonstrate how dual propagation is related to a particular adjoint state method, which is stable regardless of asymmetric nudging.

Activity difference based learning algorithms—such as contrastive Hebbian learning and equilibrium propagation—have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.

We propose a new algorithm for training deep neural networks (DNNs) with binary weights. In particular, we first cast the problem of training binary neural networks (BiNNs) as a bilevel optimization instance and subsequently construct flexible relaxations of this bilevel program. The resulting training method shares its algorithmic simplicity with several existing approaches to train BiNNs, in particular with the straight-through gradient estimator successfully employed in BinaryConnect and subsequent methods. Infact, our proposed method can be interpreted as an adaptive variant of the original straight-through estimator that conditionally (but not always) acts like a linear mapping in the backward pass of error propagation. Experimental results demonstrate that our new algorithm offers favorable performance compared to existing approaches.11This work was partially supported by theWallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.