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Maxence Ernoult

Alumni

Publications

Towards Scaling Difference Target Propagation by Learning Backprop Targets
Maxence Ernoult
Fabrice Normandin
Abhinav Moudgil
Sean Spinney
Eugene Belilovsky
Irina Rish
Blake Richards
Yoshua Bengio
The development of biologically-plausible learning algorithms is important for understanding learning in the brain, but most of them fail to… (voir plus) scale-up to real-world tasks, limiting their potential as explanations for learning by real brains. As such, it is important to explore learning algorithms that come with strong theoretical guarantees and can match the performance of backpropagation (BP) on complex tasks. One such algorithm is Difference Target Propagation (DTP), a biologically-plausible learning algorithm whose close relation with Gauss-Newton (GN) optimization has been recently established. However, the conditions under which this connection rigorously holds preclude layer-wise training of the feedback pathway synaptic weights (which is more biologically plausible). Moreover, good alignment between DTP weight updates and loss gradients is only loosely guaranteed and under very specific conditions for the architecture being trained. In this paper, we propose a novel feedback weight training scheme that ensures both that DTP approximates BP and that layer-wise feedback weight training can be restored without sacrificing any theoretical guarantees. Our theory is corroborated by experimental results and we report the best performance ever achieved by DTP on CIFAR-10 and ImageNet 32
2022-06-28
Proceedings of the 39th International Conference on Machine Learning (publié)
proceedings.mlr.press
arxiv.org
Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing Its Gradient Estimator Bias
Axel Laborieux
Maxence Ernoult
Benjamin Scellier
Yoshua Bengio
Julie Grollier
Damien Querlioz
2021-02-18
Frontiers in Neuroscience (publié)
doi.org
arxiv.org
Continual Weight Updates and Convolutional Architectures for Equilibrium Propagation
Maxence Ernoult
Julie Grollier
Damien Querlioz
Yoshua Bengio
Benjamin Scellier
Equilibrium Propagation (EP) is a biologically inspired alternative algorithm to backpropagation (BP) for training neural networks. It appli… (voir plus)es to RNNs fed by a static input x that settle to a steady state, such as Hopfield networks. EP is similar to BP in that in the second phase of training, an error signal propagates backwards in the layers of the network, but contrary to BP, the learning rule of EP is spatially local. Nonetheless, EP suffers from two major limitations. On the one hand, due to its formulation in terms of real-time dynamics, EP entails long simulation times, which limits its applicability to practical tasks. On the other hand, the biological plausibility of EP is limited by the fact that its learning rule is not local in time: the synapse update is performed after the dynamics of the second phase have converged and requires information of the first phase that is no longer available physically. Our work addresses these two issues and aims at widening the spectrum of EP from standard machine learning models to more bio-realistic neural networks. First, we propose a discrete-time formulation of EP which enables to simplify equations, speed up training and extend EP to CNNs. Our CNN model achieves the best performance ever reported on MNIST with EP. Using the same discrete-time formulation, we introduce Continual Equilibrium Propagation (C-EP): the weights of the network are adjusted continually in the second phase of training using local information in space and time. We show that in the limit of slow changes of synaptic strengths and small nudging, C-EP is equivalent to BPTT (Theorem 1). We numerically demonstrate Theorem 1 and C-EP training on MNIST and generalize it to the bio-realistic situation of a neural network with asymmetric connections between neurons.
2020-04-29
ArXiv (prépublication)
arxiv.org
arxiv.org
Updates of Equilibrium Prop Match Gradients of Backprop Through Time in an RNN with Static Input
Maxence Ernoult
Julie Grollier
Damien Querlioz
Yoshua Bengio
Benjamin Scellier
Equilibrium Propagation (EP) is a biologically inspired learning algorithm for convergent recurrent neural networks, i.e. RNNs that are fed … (voir plus)by a static input x and settle to a steady state. Training convergent RNNs consists in adjusting the weights until the steady state of output neurons coincides with a target y. Convergent RNNs can also be trained with the more conventional Backpropagation Through Time (BPTT) algorithm. In its original formulation EP was described in the case of real-time neuronal dynamics, which is computationally costly. In this work, we introduce a discrete-time version of EP with simplified equations and with reduced simulation time, bringing EP closer to practical machine learning tasks. We first prove theoretically, as well as numerically that the neural and weight updates of EP, computed by forward-time dynamics, are step-by-step equal to the ones obtained by BPTT, with gradients computed backward in time. The equality is strict when the transition function of the dynamics derives from a primitive function and the steady state is maintained long enough. We then show for more standard discrete-time neural network dynamics that the same property is approximately respected and we subsequently demonstrate training with EP with equivalent performance to BPTT. In particular, we define the first convolutional architecture trained with EP achieving ~ 1% test error on MNIST, which is the lowest error reported with EP. These results can guide the development of deep neural networks trained with EP.
arxiv.org