Damien Querlioz

Nikhil Garg, Ismael Balafrej, Terrence C. Stewart et al.

This study proposes voltage-dependent-synaptic plasticity (VDSP), a novel brain-inspired unsupervised local learning rule for the online implementation of Hebb's plasticity mechanism on neuromorphic hardware. The proposed VDSP learning rule updates the synaptic conductance on the spike of the postsynaptic neuron only, which reduces by a factor of two the number of updates with respect to standard spike-timing-dependent plasticity (STDP). This update is dependent on the membrane potential of the presynaptic neuron, which is readily available as part of neuron implementation and hence does not require additional memory for storage. Moreover, the update is also regularized on synaptic weight and prevents explosion or vanishing of weights on repeated stimulation. Rigorous mathematical analysis is performed to draw an equivalence between VDSP and STDP. To validate the system-level performance of VDSP, we train a single-layer spiking neural network (SNN) for the recognition of handwritten digits. We report 85.01 $ \pm $ 0.76% (Mean $ \pm $ S.D.) accuracy for a network of 100 output neurons on the MNIST dataset. The performance improves when scaling the network size (89.93 $ \pm $ 0.41% for 400 output neurons, 90.56 $ \pm $ 0.27 for 500 neurons), which validates the applicability of the proposed learning rule for spatial pattern recognition tasks. Future work will consider more complicated tasks. Interestingly, the learning rule better adapts than STDP to the frequency of input signal and does not require hand-tuning of hyperparameters

Simone D'Agostino, Filippo Moro, Tifenn Hirtzlin et al.

Deep learning has made remarkable progress in various tasks, surpassing human performance in some cases. However, one drawback of neural networks is catastrophic forgetting, where a network trained on one task forgets the solution when learning a new one. To address this issue, recent works have proposed solutions based on Binarized Neural Networks (BNNs) incorporating metaplasticity. In this work, we extend this solution to quantized neural networks (QNNs) and present a memristor-based hardware solution for implementing metaplasticity during both inference and training. We propose a hardware architecture that integrates quantized weights in memristor devices programmed in an analog multi-level fashion with a digital processing unit for high-precision metaplastic storage. We validated our approach using a combined software framework and memristor based crossbar array for in-memory computing fabricated in 130 nm CMOS technology. Our experimental results show that a two-layer perceptron achieves 97% and 86% accuracy on consecutive training of MNIST and Fashion-MNIST, equal to software baseline. This result demonstrates immunity to catastrophic forgetting and the resilience to analog device imperfections of the proposed solution. Moreover, our architecture is compatible with the memristor limited endurance and has a 15x reduction in memory

Kellian Cottart, Théo Ballet, Djohan Bonnet et al.

Always-on edge systems must keep learning as conditions change under tight compute budgets and must detect unreliable predictions. Bayesian binary neural networks are attractive in this setting, but mean-field Bernoulli posteriors can saturate on long non-stationary streams, wiping out epistemic uncertainty and freezing plasticity. We propose BiMU, derived from a bounded-memory variational objective that balances stability, plasticity, and forgetting. BiMU combines a data term with controlled relaxation toward the prior and an uncertainty-dependent step size that prevents saturation and sustains informative uncertainty. This non-degenerate posterior enables fully online, buffer-free active querying via Monte Carlo disagreement, reducing label queries and backpropagation updates under imbalance. BiMU sustains learning and strong OOD detection on 1000-tasks Permuted-MNIST, and on OpenLORIS-Object achieves up to 32$\times$ label/update savings at matched accuracy under class imbalance and feature compression.

Théo Ballet, Aymen Romdhane, Bruno Lovison-Franco et al.

Memristor computing offers a route to low-energy edge AI, but device variability, sensitivity to operating conditions, and system-integration challenges can hinder deployment. Here we show that these limitations can be mitigated by using memristor AI not as the final decision maker but as the ultra-low-power, always-on front end of a heterogeneous inference system. We implement this architecture by coupling a fabricated memristor Bayesian machine to a programmable CPU running a higher-power, higher-accuracy software neural network. The memristor front end acts as a probabilistic screener. When it predicts an abnormal event or produces an ambiguous or invalid output, a dedicated hardware wake-up path activates the CPU, which produces the final decision. We validate this architecture on a heartbeat-classification benchmark by interfacing the fabricated Bayesian machine with an FPGA-based wake-up platform and CPU back end. The resulting uncertainty-triggered wake-up system achieves high final classification accuracy under nominal operation and maintains this accuracy even when the memristor front end is degraded by voltage scaling or reduced programming margins, because unreliable outputs are converted into recoverable wake-up events instead of becoming silent errors. Post-layout analysis of an ASIC implementation shows that average energy is governed primarily by wake-up frequency, providing practical design rules for choosing front-end operating points. These results establish uncertainty-triggered wake-up as a strategy for energy-efficient, error-resilient edge AI.

Dongshu Liu, Jérémie Laydevant, Adrien Pontlevy et al.

Designing algorithms for versatile AI hardware that can learn on the edge using both labeled and unlabeled data is challenging. Deep end-to-end training methods incorporating phases of self-supervised and supervised learning are accurate and adaptable to input data but self-supervised learning requires even more computational and memory resources than supervised learning, too high for current embedded hardware. Conversely, unsupervised layer-by-layer training, such as Hebbian learning, is more compatible with existing hardware but does not integrate well with supervised learning. To address this, we propose a method enabling networks or hardware designed for end-to-end supervised learning to also perform high-performance unsupervised learning by adding two simple elements to the output layer: Winner-Take-All (WTA) selectivity and homeostasis regularization. These mechanisms introduce a "self-defined target" for unlabeled data, allowing purely unsupervised training for both fully-connected and convolutional layers using backpropagation or equilibrium propagation on datasets like MNIST (up to 99.2%), Fashion-MNIST (up to 90.3%), and SVHN (up to 81.5%). We extend this method to semi-supervised learning, adjusting targets based on data type, achieving 96.6% accuracy with only 600 labeled MNIST samples in a multi-layer perceptron. Our results show that this approach can effectively enable networks and hardware initially dedicated to supervised learning to also perform unsupervised learning, adapting to varying availability of labeled data.

Djohan Bonnet, Tifenn Hirtzlin, Tarcisius Januel et al.

Catastrophic forgetting remains a challenge for neural networks, especially in lifelong learning scenarios. In this study, we introduce MEtaplasticity from Synaptic Uncertainty (MESU), inspired by metaplasticity and Bayesian inference principles. MESU harnesses synaptic uncertainty to retain information over time, with its update rule closely approximating the diagonal Newton's method for synaptic updates. Through continual learning experiments on permuted MNIST tasks, we demonstrate MESU's remarkable capability to maintain learning performance across 100 tasks without the need of explicit task boundaries.

Walid A. Misba, Mark Lozano, Damien Querlioz et al.

We demonstrate that extremely low resolution quantized (nominally 5-state) synapses with large stochastic variations in Domain Wall (DW) position can be both energy efficient and achieve reasonably high testing accuracies compared to Deep Neural Networks (DNNs) of similar sizes using floating precision synaptic weights. Specifically, voltage controlled DW devices demonstrate stochastic behavior as modeled rigorously with micromagnetic simulations and can only encode limited states; however, they can be extremely energy efficient during both training and inference. We show that by implementing suitable modifications to the learning algorithms, we can address the stochastic behavior as well as mitigate the effect of their low-resolution to achieve high testing accuracies. In this study, we propose both in-situ and ex-situ training algorithms, based on modification of the algorithm proposed by Hubara et al. [1] which works well with quantization of synaptic weights. We train several 5-layer DNNs on MNIST dataset using 2-, 3- and 5-state DW device as synapse. For in-situ training, a separate high precision memory unit is adopted to preserve and accumulate the weight gradients, which are then quantized to program the low precision DW devices. Moreover, a sizeable noise tolerance margin is used during the training to address the intrinsic programming noise. For ex-situ training, a precursor DNN is first trained based on the characterized DW device model and a noise tolerance margin, which is similar to the in-situ training. Remarkably, for in-situ inference the energy dissipation to program the devices is only 13 pJ per inference given that the training is performed over the entire MNIST dataset for 10 epochs.

Xing Chen, Flavio Abreu Araujo, Mathieu Riou et al.

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations (ODEs) to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Spin-Neural ODEs an acceleration factor over 200 compared to micromagnetic simulations for a complex problem -- the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Spin-Neural ODEs on five milliseconds of their measured response to different excitations. Spin-Neural ODE is a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Spin-Neural ODE can also be generalized to other electronic devices involving dynamics.

Jérémie Laydevant, Maxence Ernoult, Damien Querlioz et al.

Equilibrium Propagation (EP) is an algorithm intrinsically adapted to the training of physical networks, thanks to the local updates of weights given by the internal dynamics of the system. However, the construction of such a hardware requires to make the algorithm compatible with existing neuromorphic CMOS technologies, which generally exploit digital communication between neurons and offer a limited amount of local memory. In this work, we demonstrate that EP can train dynamical networks with binary activations and weights. We first train systems with binary weights and full-precision activations, achieving an accuracy equivalent to that of full-precision models trained by standard EP on MNIST, and losing only 1.9% accuracy on CIFAR-10 with equal architecture. We then extend our method to the training of models with binary activations and weights on MNIST, achieving an accuracy within 1% of the full-precision reference for fully connected architectures and reaching the full-precision accuracy for convolutional architectures. Our extension of EP to binary networks opens new solutions for on-chip learning and provides a compact framework for training BNNs end-to-end with the same circuitry as for inference.

Axel Laborieux, Maxence Ernoult, Benjamin Scellier et al.

Equilibrium Propagation (EP) is a biologically-inspired counterpart of Backpropagation Through Time (BPTT) which, owing to its strong theoretical guarantees and the locality in space of its learning rule, fosters the design of energy-efficient hardware dedicated to learning. In practice, however, EP does not scale to visual tasks harder than MNIST. In this work, we show that a bias in the gradient estimate of EP, inherent in the use of finite nudging, is responsible for this phenomenon and that cancelling it allows training deep ConvNets by EP, including architectures with distinct forward and backward connections. These results highlight EP as a scalable approach to compute error gradients in deep neural networks, thereby motivating its hardware implementation.

Erwann Martin, Maxence Ernoult, Jérémie Laydevant et al.

Finding spike-based learning algorithms that can be implemented within the local constraints of neuromorphic systems, while achieving high accuracy, remains a formidable challenge. Equilibrium Propagation is a promising alternative to backpropagation as it only involves local computations, but hardware-oriented studies have so far focused on rate-based networks. In this work, we develop a spiking neural network algorithm called EqSpike, compatible with neuromorphic systems, which learns by Equilibrium Propagation. Through simulations, we obtain a test recognition accuracy of 97.6% on MNIST, similar to rate-based Equilibrium Propagation, and comparing favourably to alternative learning techniques for spiking neural networks. We show that EqSpike implemented in silicon neuromorphic technology could reduce the energy consumption of inference and training respectively by three orders and two orders of magnitude compared to GPUs. Finally, we also show that during learning, EqSpike weight updates exhibit a form of Spike Timing Dependent Plasticity, highlighting a possible connection with biology.

G. Hocquet, O. Bichler, D. Querlioz

In the field of Continual Learning, the objective is to learn several tasks one after the other without access to the data from previous tasks. Several solutions have been proposed to tackle this problem but they usually assume that the user knows which of the tasks to perform at test time on a particular sample, or rely on small samples from previous data and most of them suffer of a substantial drop in accuracy when updated with batches of only one class at a time. In this article, we propose a new method, OvA-INN, which is able to learn one class at a time and without storing any of the previous data. To achieve this, for each class, we train a specific Invertible Neural Network to extract the relevant features to compute the likelihood on this class. At test time, we can predict the class of a sample by identifying the network which predicted the highest likelihood. With this method, we show that we can take advantage of pretrained models by stacking an Invertible Network on top of a feature extractor. This way, we are able to outperform state-of-the-art approaches that rely on features learning for the Continual Learning of MNIST and CIFAR-100 datasets. In our experiments, we reach 72% accuracy on CIFAR-100 after training our model one class at a time.

Axel Laborieux, Maxence Ernoult, Benjamin Scellier et al.

Equilibrium Propagation (EP) is a biologically-inspired algorithm for convergent RNNs with a local learning rule that comes with strong theoretical guarantees. The parameter updates of the neural network during the credit assignment phase have been shown mathematically to approach the gradients provided by Backpropagation Through Time (BPTT) when the network is infinitesimally nudged toward its target. In practice, however, training a network with the gradient estimates provided by EP does not scale to visual tasks harder than MNIST. In this work, we show that a bias in the gradient estimate of EP, inherent in the use of finite nudging, is responsible for this phenomenon and that cancelling it allows training deep ConvNets by EP. We show that this bias can be greatly reduced by using symmetric nudging (a positive nudging and a negative one). We also generalize previous EP equations to the case of cross-entropy loss (by opposition to squared error). As a result of these advances, we are able to achieve a test error of 11.7% on CIFAR-10 by EP, which approaches the one achieved by BPTT and provides a major improvement with respect to the standard EP approach with same-sign nudging that gives 86% test error. We also apply these techniques to train an architecture with asymmetric forward and backward connections, yielding a 13.2% test error. These results highlight EP as a compelling biologically-plausible approach to compute error gradients in deep neural networks.

Maxence Ernoult, Julie Grollier, Damien Querlioz et al.

Equilibrium Propagation (EP) is a learning algorithm that bridges Machine Learning and Neuroscience, by computing gradients closely matching those of Backpropagation Through Time (BPTT), but with a learning rule local in space. Given an input $x$ and associated target $y$, EP proceeds in two phases: in the first phase neurons evolve freely towards a first steady state; in the second phase output neurons are nudged towards $y$ until they reach a second steady state. However, in existing implementations of EP, the learning rule is not local in time: the weight 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. In this work, we propose a version of EP named Continual Equilibrium Propagation (C-EP) where neuron and synapse dynamics occur simultaneously throughout the second phase, so that the weight update becomes local in time. Such a learning rule local both in space and time opens the possibility of an extremely energy efficient hardware implementation of EP. We prove theoretically that, provided the learning rates are sufficiently small, at each time step of the second phase the dynamics of neurons and synapses follow the gradients of the loss given by BPTT (Theorem 1). We demonstrate training with C-EP on MNIST and generalize C-EP to neural networks where neurons are connected by asymmetric connections. We show through experiments that the more the network updates follows the gradients of BPTT, the best it performs in terms of training. These results bring EP a step closer to biology by better complying with hardware constraints while maintaining its intimate link with backpropagation.

Maxence Ernoult, Julie Grollier, Damien Querlioz et al.

Equilibrium Propagation (EP) is a biologically inspired alternative algorithm to backpropagation (BP) for training neural networks. It applies 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.

Axel Laborieux, Maxence Ernoult, Tifenn Hirtzlin et al.

While deep neural networks have surpassed human performance in multiple situations, they are prone to catastrophic forgetting: upon training a new task, they rapidly forget previously learned ones. Neuroscience studies, based on idealized tasks, suggest that in the brain, synapses overcome this issue by adjusting their plasticity depending on their past history. However, such "metaplastic" behaviours do not transfer directly to mitigate catastrophic forgetting in deep neural networks. In this work, we interpret the hidden weights used by binarized neural networks, a low-precision version of deep neural networks, as metaplastic variables, and modify their training technique to alleviate forgetting. Building on this idea, we propose and demonstrate experimentally, in situations of multitask and stream learning, a training technique that reduces catastrophic forgetting without needing previously presented data, nor formal boundaries between datasets and with performance approaching more mainstream techniques with task boundaries. We support our approach with a theoretical analysis on a tractable task. This work bridges computational neuroscience and deep learning, and presents significant assets for future embedded and neuromorphic systems, especially when using novel nanodevices featuring physics analogous to metaplasticity.

Tifenn Hirtzlin, Bogdan Penkovsky, Jacques-Olivier Klein et al.

One of the most exciting applications of Spin Torque Magnetoresistive Random Access Memory (ST-MRAM) is the in-memory implementation of deep neural networks, which could allow improving the energy efficiency of Artificial Intelligence by orders of magnitude with regards to its implementation on computers and graphics cards. In particular, ST-MRAM could be ideal for implementing Binarized Neural Networks (BNNs), a type of deep neural networks discovered in 2016, which can achieve state-of-the-art performance with a highly reduced memory footprint with regards to conventional artificial intelligence approaches. The challenge of ST-MRAM, however, is that it is prone to write errors and usually requires the use of error correction. In this work, we show that these bit errors can be tolerated by BNNs to an outstanding level, based on examples of image recognition tasks (MNIST, CIFAR-10 and ImageNet): bit error rates of ST-MRAM up to 0.1% have little impact on recognition accuracy. The requirements for ST-MRAM are therefore considerably relaxed for BNNs with regards to traditional applications. By consequence, we show that for BNNs, ST-MRAMs can be programmed with weak (low-energy) programming conditions, without error correcting codes. We show that this result can allow the use of low energy and low area ST-MRAM cells, and show that the energy savings at the system level can reach a factor two.

Maxence Ernoult, Julie Grollier, Damien Querlioz et al.

Equilibrium Propagation (EP) is a biologically inspired learning algorithm for convergent recurrent neural networks, i.e. RNNs that are fed 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.

Flavio Abreu Araujo, Mathieu Riou, Jacob Torrejon et al.

The reservoir computing neural network architecture is widely used to test hardware systems for neuromorphic computing. One of the preferred tasks for bench-marking such devices is automatic speech recognition. However, this task requires acoustic transformations from sound waveforms with varying amplitudes to frequency domain maps that can be seen as feature extraction techniques. Depending on the conversion method, these may obscure the contribution of the neuromorphic hardware to the overall speech recognition performance. Here, we quantify and separate the contributions of the acoustic transformations and the neuromorphic hardware to the speech recognition success rate. We show that the non-linearity in the acoustic transformation plays a critical role in feature extraction. We compute the gain in word success rate provided by a reservoir computing device compared to the acoustic transformation only, and show that it is an appropriate benchmark for comparing different hardware. Finally, we experimentally and numerically quantify the impact of the different acoustic transformations for neuromorphic hardware based on magnetic nano-oscillators.

Christopher H. Bennett, Damien Querlioz, Jacques-Olivier Klein

Emerging nanodevices such as resistive memories are being considered for hardware realizations of a variety of artificial neural networks (ANNs), including highly promising online variants of the learning approaches known as reservoir computing (RC) and the extreme learning machine (ELM). We propose an RC/ELM inspired learning system built with nanosynapses that performs both on-chip projection and regression operations. To address time-dynamic tasks, the hidden neurons of our system perform spatio-temporal integration and can be further enhanced with variable sampling or multiple activation windows. We detail the system and show its use in conjunction with a highly analog nanosynapse device on a standard task with intrinsic timing dynamics- the TI-46 battery of spoken digits. The system achieves nearly perfect (99%) accuracy at sufficient hidden layer size, which compares favorably with software results. In addition, the model is extended to a larger dataset, the MNIST database of handwritten digits. By translating the database into the time domain and using variable integration windows, up to 95% classification accuracy is achieved. In addition to an intrinsically low-power programming style, the proposed architecture learns very quickly and can easily be converted into a spiking system with negligible loss in performance- all features that confer significant energy efficiency.

Christopher H. Bennett, Selina La Barbera, Adrien F. Vincent et al.

Memristive nanodevices offer new frontiers for computing systems that unite arithmetic and memory operations on-chip. Here, we explore the integration of electrochemical metallization cell (ECM) nanodevices with tunable filamentary switching in nanoscale learning systems. Such devices offer a natural transition between short-term plasticity (STP) and long-term plasticity (LTP). In this work, we show that this property can be exploited to efficiently solve noisy classification tasks. A single crossbar learning scheme is first introduced and evaluated. Perfect classification is possible only for simple input patterns, within critical timing parameters, and when device variability is weak. To overcome these limitations, a dual-crossbar learning system partly inspired by the extreme learning machine (ELM) approach is then introduced. This approach outperforms a conventional ELM-inspired system when the first layer is imprinted before training and testing, and especially so when variability in device timing evolution is considered: variability is therefore transformed from an issue to a feature. In attempting to classify the MNIST database under the same conditions, conventional ELM obtains 84% classification, the imprinted, uniform device system obtains 88% classification, and the imprinted, variable device system reaches 92% classification. We discuss benefits and drawbacks of both systems in terms of energy, complexity, area imprint, and speed. All these results highlight that tuning and exploiting intrinsic device timing parameters may be of central interest to future bio-inspired approximate computing systems.