Learning Without Feedback: Fixed Random Learning Signals Allow for Feedforward Training of Deep Neural Networks

Abstract

While the backpropagation of error algorithm enables deep neural network training, it implies (i) bidirectional synaptic weight transport and (ii) update locking until the forward and backward passes are completed. Not only do these constraints preclude biological plausibility, but they also hinder the development of low-cost adaptive smart sensors at the edge, as they severely constrain memory accesses and entail buffering overhead. In this work, we show that the one-hot-encoded labels provided in supervised classification problems, denoted as targets, can be viewed as a proxy for the error sign. Therefore, their fixed random projections enable a layerwise feedforward training of the hidden layers, thus solving the weight transport and update locking problems while relaxing the computational and memory requirements. Based on these observations, we propose the direct random target projection (DRTP) algorithm and demonstrate that it provides a tradeoff between accuracy and computational cost that is suitable for adaptive edge computing devices.

Neuronal-Plasticity and Reward-Propagation Improved Recurrent Spiking Neural Networks

“…The propagation of synaptic plasticity is closely related to the credit assignment of error signals in SNNs. Zhang et al have given an overview introduction of several target propagation methods, such as error propagation, symbol propagation, and label propagation (Frenkel et al, 2019), where the reward propagation can propagate the reward (instead of the traditional error signals) directly to all hidden layers (instead of the traditional layer-to-layer backpropagation). This plasticity is biologically-plausible and will also be used as the main credit assignment of SNNs in our NRR-SNN algorithm.…”

“…This study aims modify all synaptic weights parallelly without worrying about the gradient vanishing problem, especially for dynamic LIF neurons. Hence, we will pay more attention to the target propagation (Frenkel et al, 2019), as shown in Figure 1A, where the error or other reward-like signals are directly propagated from the output layer to all hidden layers parallelly without losing accuracy.…”

Eigenvalues of Autoencoders in Training and at Initialization

“…Random matrices are used in certain backpropagation techniques, such as feedback alignment [19], [22], random backpropagation [7], and related algorithms [11], [16]. In this work, the transpose of the forward weight matrices in the back propagation process is replaced with a random matrix, increasing training speed, generalizability and mimicking biological processes.…”

A Sparsity-Driven Backpropagation-Less Learning Framework Using Populations of Spiking Growth Transform Neurons

“…The data point is assigned to the class that produces the lowest firing across all layers of the network. This architecture is similar to Direct Random Target Projection (Frenkel et al, 2021) which projects the one-hot encoded targets onto the hidden layers for training multi-layer networks. The notable difference, aside from the neuromorphic aspect, is that we use the input and target information in each layer to train the lateral connections within the layer, and not the feed-forward weights from the preceding layer.…”

“…One well-known method is feedback alignment—also known as random backpropagation—which eradicates the weight transport problem by using fixed random weights in the feedback path for propagating error gradient information (Liao et al, 2016 ; Lillicrap et al, 2016 ). Subsequent research showed that directly propagating the output error (Nøkland and Eidnes, 2019 ) or even the raw one-hot encoded targets (Frenkel et al, 2021 ) is sufficient to maintain feedback alignment, and in case of the latter, also eradicates update locking by allowing simultaneous and independent weight updates at each layer. Equilibrium propagation (Scellier and Bengio, 2017 ) is another biologically relevant algorithm for training energy-based models, where the network initially relaxes to a fixed-point of its energy function in response to an external input.…”