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Yuhan Helena Liu, Arna Ghosh, Blake A. Richards, Eric Shea-Brown, Guillaume Lajoie

To unveil how the brain learns, ongoing work seeks biologically-plausible approximations of gradient descent algorithms for training recurrent neural networks (RNNs). Yet, beyond task accuracy, it is unclear if such learning rules converge to solutions that exhibit different levels of generalization than their nonbiologically-plausible counterparts. Leveraging results from deep learning theory based on loss landscape curvature, we ask: how do biologically-plausible gradient approximations affect generalization? We first demonstrate that state-of-the-art biologically-plausible learning rules for training RNNs exhibit worse and more variable generalization performance compared to their machine learning counterparts that follow the true gradient more closely. Next, we verify that such generalization performance is correlated significantly with loss landscape curvature, and we show that biologically-plausible learning rules tend to approach high-curvature regions in synaptic weight space. Using tools from dynamical systems, we derive theoretical arguments and present a theorem explaining this phenomenon. This predicts our numerical results, and explains why biologically-plausible rules lead to worse and more variable generalization properties. Finally, we suggest potential remedies that could be used by the brain to mitigate this effect. To our knowledge, our analysis is the first to identify the reason for this generalization gap between artificial and biologically-plausible learning rules, which can help guide future investigations into how the brain learns solutions that generalize.

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Anthony GX-Chen, Veronica Chelu, Blake A. Richards, Joelle Pineau

Estimating value functions is a core component of reinforcement learning algorithms. Temporal difference (TD) learning algorithms use bootstrapping, i.e. they update the value function toward a learning target using value estimates at subsequent time-steps. Alternatively, the value function can be updated toward a learning target constructed by separately predicting successor features (SF)--a policy-dependent model--and linearly combining them with instantaneous rewards. We focus on bootstrapping targets used when estimating value functions, and propose a new backup target, the $\eta$-return mixture, which implicitly combines value-predictive knowledge (used by TD methods) with (successor) feature-predictive knowledge--with a parameter $\eta$ capturing how much to rely on each. We illustrate that incorporating predictive knowledge through an $\eta\gamma$-discounted SF model makes more efficient use of sampled experience, compared to either extreme, i.e. bootstrapping entirely on the value function estimate, or bootstrapping on the product of separately estimated successor features and instantaneous reward models. We empirically show this approach leads to faster policy evaluation and better control performance, for tabular and nonlinear function approximations, indicating scalability and generality.

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Luke Y. Prince, Ellen Boven, Roy Henha Eyono, Arna Ghosh, Joe Pemberton, Franz Scherr, Claudia Clopath, Rui Ponte Costa, Wolfgang Maass, Blake A. Richards, Cristina Savin, Katharina Anna Wilmes

This perspective piece came about through the Generative Adversarial Collaboration (GAC) series of workshops organized by the Computational Cognitive Neuroscience (CCN) conference in 2020. We brought together a number of experts from the field of theoretical neuroscience to debate emerging issues in our understanding of how learning is implemented in biological recurrent neural networks. Here, we will give a brief review of the common assumptions about biological learning and the corresponding findings from experimental neuroscience and contrast them with the efficiency of gradient-based learning in recurrent neural networks commonly used in artificial intelligence. We will then outline the key issues discussed in the workshop: synaptic plasticity, neural circuits, theory-experiment divide, and objective functions. Finally, we conclude with recommendations for both theoretical and experimental neuroscientists when designing new studies that could help to bring clarity to these issues.

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Jordan Guerguiev, Konrad P. Kording, Blake A. Richards

In artificial neural networks trained with gradient descent, the weights used for processing stimuli are also used during backward passes to calculate gradients. For the real brain to approximate gradients, gradient information would have to be propagated separately, such that one set of synaptic weights is used for processing and another set is used for backward passes. This produces the so-called "weight transport problem" for biological models of learning, where the backward weights used to calculate gradients need to mirror the forward weights used to process stimuli. This weight transport problem has been considered so hard that popular proposals for biological learning assume that the backward weights are simply random, as in the feedback alignment algorithm. However, such random weights do not appear to work well for large networks. Here we show how the discontinuity introduced in a spiking system can lead to a solution to this problem. The resulting algorithm is a special case of an estimator used for causal inference in econometrics, regression discontinuity design. We show empirically that this algorithm rapidly makes the backward weights approximate the forward weights. As the backward weights become correct, this improves learning performance over feedback alignment on tasks such as Fashion-MNIST and CIFAR-10. Our results demonstrate that a simple learning rule in a spiking network can allow neurons to produce the right backward connections and thus solve the weight transport problem.

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Sergey Bartunov, Adam Santoro, Blake A. Richards, Geoffrey E. Hinton, Timothy Lillicrap

The backpropagation of error algorithm (BP) is often said to be impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired proposals for understanding how the brain might learn across multiple layers, and hence how it might implement or approximate BP. As of yet, none of these proposals have been rigorously evaluated on tasks where BP-guided deep learning has proved critical, or in architectures more structured than simple fully-connected networks. Here we present the first results on scaling up biologically motivated models of deep learning on datasets which need deep networks with appropriate architectures to achieve good performance. We present results on the MNIST, CIFAR-10, and ImageNet datasets and explore variants of target-propagation (TP) and feedback alignment (FA) algorithms, and explore performance in both fully- and locally-connected architectures. We also introduce weight-transport-free variants of difference target propagation (DTP) modified to remove backpropagation from the penultimate layer. Many of these algorithms perform well for MNIST, but for CIFAR and ImageNet we find that TP and FA variants perform significantly worse than BP, especially for networks composed of locally connected units, opening questions about whether new architectures and algorithms are required to scale these approaches. Our results and implementation details help establish baselines for biologically motivated deep learning schemes going forward.

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