The error-backpropagation (backprop) algorithm remains the most common solution to the credit assignment problem in artificial neural networks.

Stochastic gradient descent with backpropagation is the workhorse of artificial neural networks. It has long been recognized that backpropagation fails to be a biologically plausible algorithm. Fundamentally, it is a non-local procedure-- updating one neuron's synaptic weights requires knowledge of synaptic weights or receptive fields of downstream neurons. This limits the use of artificial neural networks as a tool for understanding the biological principles of information processing in the brain. Lillicrap et al. (2016) propose a more biologically plausible "feedback alignment" algorithm that uses random and fixed backpropagation weights, and show promising simulations. In this paper we study the mathematical properties of the feedback alignment procedure by analyzing convergence and alignment for two-layer networks under squared error loss. In the overparameter-ized setting, we prove that the error converges to zero exponentially fast, and also that regularization is necessary in order for the parameters to become aligned with the random backpropagation weights. Simulations are given that are consistent with this analysis and suggest further generalizations. These results contribute to our understanding of how biologically plausible algorithms might carry out weight learning in a manner different from Hebbian learning, with performance that is comparable with the full non-local backpropagation algorithm.

We describe the nonlinearities we employed in appendix H.

Here, we propose that extra-synaptic diffusion of local neuromodulators such as neuropeptides may afford an effective mode of back-propagation lying within the bounds of biological plausibility.

The spike-based operational principles of SNNs not only allow information coding based on efficient temporal codes and give rise to promising spatiotemporal computing power but also render energy-efficient VLSI neuromorphic chips such as IBM's TrueNorth [

Solving real world problems with embedded neural networks requires both training algorithms that achieve high performance and compatible hardware that runs in real time while remaining energy efficient. For the former, deep learning using backpropagation has recently achieved a string of successes across many domains and datasets. For the latter, neuromorphic chips that run spiking neural networks have recently achieved unprecedented energy efficiency. To bring these two advances together, we must first resolve the incompatibility between backpropagation, which uses continuous-output neurons and synaptic weights, and neuromorphic designs, which employ spiking neurons and discrete synapses. Our approach is to treat spikes and discrete synapses as continuous probabilities, which allows training the network using standard backpropagation. The trained network naturally maps to neuromorphic hardware by sampling the probabilities to create one or more networks, which are merged using ensemble averaging. To demonstrate, we trained a sparsely connected network that runs on the TrueNorth chip using the MNIST dataset. With a high performance network (ensemble of $64$), we achieve $99.42\%$ accuracy at $121 \mu$J per image, and with a high efficiency network (ensemble of $1$) we achieve $92.7\%$ accuracy at $0.408 \mu$J per image.

Terahertz single-pixel imaging (THz SPI) has garnered widespread attention for its potential to overcome challenges associated with THz focal plane arrays. However, the inherently long wavelength of THz waves limits imaging resolution, while achieving subwavelength resolution requires harsh experimental conditions and time-consuming processes. Here, we propose a sub-diffraction THz backpropagation SPI technique. We illuminate the object with continuous-wave 0.36-THz radiation (λ0 = 833.3 μm). The transmitted THz wave is modulated by prearranged patterns generated on a 500-μm-thick silicon wafer and subsequently recorded by a far-field single-pixel detector. An untrained neural network constrained with the physical SPI process iteratively reconstructs the THz images with an ultralow sampling ratio of 1.5625%, significantly reducing the long sampling times. To further suppress the THz diffraction-field effects, a backpropagation SPI from near field to far field is implemented by integrating with a THz physical propagation model into the output layer of the network. Notably, using the thick wafer where THz evanescent field cannot be fully recorded, we achieve a spatial resolution of 118 μm (~λ0/7) through backpropagation SPI, thus eliminating the need for ultrathin photomodulators. This approach provides an efficient solution for advancing THz microscopic imaging and addressing other inverse imaging challenges.

Training neural networks with reinforcement learning (RL) typically relies on backpropagation (BP), necessitating storage of activations from the forward pass for subsequent backward updates. Furthermore, backpropagating error signals through multiple layers often leads to vanishing or exploding gradients, which can degrade learning performance and stability. We propose a novel approach that trains each layer of the neural network using local signals during the forward pass in RL settings. Our approach introduces local, layer-wise losses leveraging the principle of matching pairwise distances from multi-dimensional scaling, enhanced with optional reward-driven guidance. This method allows each hidden layer to be trained using local signals computed during forward propagation, thus eliminating the need for backward passes and storing intermediate activations. Our experiments, conducted with policy gradient methods across common RL benchmarks, demonstrate that this backpropagation-free method achieves competitive performance compared to their classical BP-based counterpart. Additionally, the proposed method enhances stability and consistency within and across runs, and improves performance especially in challenging environments.