Random synaptic feedback weights support error backpropagation for deep learning

By Timothy P. Lillicrap, Daniel Cownden, Douglas B. Tweed, Colin J. Akerman. 2016

953 citations recorded by the source corpus.

The brain processes information through multiple layers of neurons. This deep architecture is representationally powerful, but complicates learning because it is difficult to identify the responsible neurons when a mistake is made. In machine learning, the backpropagation algorithm assigns blame by multiplying error signals with all the synaptic weights on each neuron’s axon and further downstream. However, this involves a precise, symmetric backward connectivity pattern, which is thought to be impossible in the brain. Here we demonstrate that this strong architectural constraint is not required for effective error propagation. We present a surprisingly simple mechanism that assigns blame by multiplying errors by even random synaptic weights. This mechanism can transmit teaching signals across multiple layers of neurons and performs as effectively as backpropagation on a variety of tasks. Our results help reopen questions about how the brain could use error signals and dispel long-held assumptions about algorithmic constraints on learning. Multi-layered neural architectures that implement learning require elaborate mechanisms for symmetric backpropagation of errors that are biologically implausible. Here the authors propose a simple resolution to this problem of blame assignment that works even with feedback using random synaptic weights.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Electrical and Electronic Engineering, Neuroscience

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Citations in the corpus

Why Should We Add Early Exits to Neural Networks? (2020, background): “Point (ii) has been explored in-depth in the literature on feedback alignment (and similar) [5, 39, 49], in which it is shown that the transpose of the weight matrix can be replaced by a (fixed) random matrix during the backward pass while still allowing for convergence of the algorithm.”
Decoupled Neural Interfaces using Synthetic Gradients (2016, methodology): “It is also possible to use other styles of critics or error approximation techniques such as Feedback Alignment (Lillicrap et al., 2016), Direct Feedback Alignment (Nøkland, 2016), and Kickback (Balduzzi et al., 2014b)) – interestingly (Czarnecki et al., 2017) shows that they can all be framed in…”
Learning Rapid-Temporal Adaptations (2017, methodology): “Direct feedback meta information Direct feedback (DF) meta information is inspired by feed-back alignment methods [21, 27] and on biologically plausible deep learning [4].”
Mean Field Residual Networks: On the Edge of Chaos (2017, neutral): “This is similar to the practice of feedback alignment [8].”
An Approximation of the Error Backpropagation Algorithm in a Predictive Coding Network with Local Hebbian Synaptic Plasticity (2017, methodology): “The models in the second class explicitly approximate the backpropagation algorithm (O’Reilly, 1998; Lillicrap, Cownden, Tweed, & Akerman, 2016; Balduzzi, Vanchinathan, & Buhmann, 2014; Bengio, 2014; Bengio, Lee, Bornschein, & Lin, 2015; Scellier & Bengio, 2016), and we will compare them in detail…”
Understanding Synthetic Gradients and Decoupled Neural Interfaces (2017, methodology): “We focus on three such approaches: Feedback Alignment (FA) (Lillicrap et al., 2016), Direct Feedback Alignment (DFA) (Nøkland, 2016), and Kickback (KB) (Balduzzi et al.”
Theories of Error Back-Propagation in the Brain (2019, background): “…(e.g., handwritten digit classi ﬁ cation) [12 – 14, The criticism of weight symmetry has been addressed by demonstrating that even if the errors in arti ﬁ cial neural networks are back-propagated by random connections, good performance in classi ﬁ cation tasks can still be achieved [21,23 – 27].”
Deep Supervised Learning Using Local Errors (2017, methodology): “It is important to note that in feedback alignment, the feedforward weights eventually ’align’ with the random weights used to backpropagate errors [15] enabling the network to learn.”
Greedy Layerwise Learning Can Scale to ImageNet (2018, background): “For example Feedback Alignment (Lillicrap et al., 2016) which is able to achieve 63% on CIFAR-10 compared to 68% with backprop, on the 1000 class ImageNet obtains only 6 .”
The Forward-Forward Algorithm: Some Preliminary Investigations (2022, methodology): “…pass instead of the transpose of the forward weights, and this yields fake derivatives that work surprisingly well on small-scale tasks like MNIST (Lillicrap et al., 2016), but it does not scale well to large networks and it is particularly bad at squeezing information through narrow bottlenecks.”
Deep physical neural networks trained with backpropagation (2021, methodology): “This technique is well known in neuromorphic computing 48–53 , appearing recently in direct feedback alignment 52 and quantization-aware training 48 , which inspired PAT.”
Synaptic Plasticity Dynamics for Deep Continuous Local Learning (DECOLLE) (2018, methodology): “Previous work demonstrated learning in multiple layers of SNN using feedback alignment (Lillicrap et al., 2016; Neftci et al., 2017), performing at about 2% classiﬁcation error on MNIST.”
Putting An End to End-to-End: Gradient-Isolated Learning of Representations (2019, methodology): “hod from end-to-end backpropagation. There are a number of optimization algorithms that eliminate the need for backpropagation altogether [Balduzzi et al., 2015, Kohan et al., 2018, Lee et al., 2015, Lillicrap et al., 2016, Scellier and Bengio, 2017]. In contrast to our method, these methods employ ”
DIET-SNN: A Low-Latency Spiking Neural Network With Direct Input Encoding and Leakage and Threshold Optimization (2021, background): “Some of these algorithms apply random weights [40] or fixed weights [41] as the feedback weight during backpropagation.”
Material for Decoupled Neural Interfaces using Synthetic Gradients (2017, methodology): “It is also possible to use other styles of critics or error approximation techniques such as Feedback Alignment (Lillicrap et al., 2016), Direct Feedback Alignment (Nøkland, 2016), and Kickback (Balduzzi et al.”
Neuroscience-Inspired Artificial Intelligence. (2017, background): “…backward connections, even when held ﬁxed throughout network training, are sufﬁcient to allow the backpropagation algorithm to function effectively through a process whereby adjustment of the forward weights allows backward projections to transmit useful teaching signals (Lillicrap et al., 2016).”