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Timothée Masquelier

Timothée Masquelier contributes to research discovery and scholarly infrastructure.

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Published work

7 published item(s)

preprint2026arXiv

Binary Spiking Neural Networks as Causal Models

We provide a causal analysis of Binary Spiking Neural Networks (BSNNs) to explain their behavior. We formally define a BSNN and represent its spiking activity as a binary causal model. Thanks to this causal representation, we are able to explain the output of the network by leveraging logic-based methods. In particular, we show that we can successfully use a SAT as well as a SMT solver to compute abductive explanations from this binary causal model. To illustrate our approach, we trained the BSNN on the standard MNIST dataset and applied our SAT-based and SMT-based methods to finding abductive explanations of the network's classifications based on pixel-level features. We also compared the found explanations against SHAP, a popular method used in the area of explainable AI. We show that, unlike SHAP, our approach guarantees that a found explanation does not contain completely irrelevant features.

preprint2024arXiv

Parallel Spiking Neurons with High Efficiency and Ability to Learn Long-term Dependencies

Vanilla spiking neurons in Spiking Neural Networks (SNNs) use charge-fire-reset neuronal dynamics, which can only be simulated serially and can hardly learn long-time dependencies. We find that when removing reset, the neuronal dynamics can be reformulated in a non-iterative form and parallelized. By rewriting neuronal dynamics without reset to a general formulation, we propose the Parallel Spiking Neuron (PSN), which generates hidden states that are independent of their predecessors, resulting in parallelizable neuronal dynamics and extremely high simulation speed. The weights of inputs in the PSN are fully connected, which maximizes the utilization of temporal information. To avoid the use of future inputs for step-by-step inference, the weights of the PSN can be masked, resulting in the masked PSN. By sharing weights across time-steps based on the masked PSN, the sliding PSN is proposed to handle sequences of varying lengths. We evaluate the PSN family on simulation speed and temporal/static data classification, and the results show the overwhelming advantage of the PSN family in efficiency and accuracy. To the best of our knowledge, this is the first study about parallelizing spiking neurons and can be a cornerstone for the spiking deep learning research. Our codes are available at \url{https://github.com/fangwei123456/Parallel-Spiking-Neuron}.

preprint2022arXiv

Deep Residual Learning in Spiking Neural Networks

Deep Spiking Neural Networks (SNNs) present optimization difficulties for gradient-based approaches due to discrete binary activation and complex spatial-temporal dynamics. Considering the huge success of ResNet in deep learning, it would be natural to train deep SNNs with residual learning. Previous Spiking ResNet mimics the standard residual block in ANNs and simply replaces ReLU activation layers with spiking neurons, which suffers the degradation problem and can hardly implement residual learning. In this paper, we propose the spike-element-wise (SEW) ResNet to realize residual learning in deep SNNs. We prove that the SEW ResNet can easily implement identity mapping and overcome the vanishing/exploding gradient problems of Spiking ResNet. We evaluate our SEW ResNet on ImageNet, DVS Gesture, and CIFAR10-DVS datasets, and show that SEW ResNet outperforms the state-of-the-art directly trained SNNs in both accuracy and time-steps. Moreover, SEW ResNet can achieve higher performance by simply adding more layers, providing a simple method to train deep SNNs. To our best knowledge, this is the first time that directly training deep SNNs with more than 100 layers becomes possible. Our codes are available at https://github.com/fangwei123456/Spike-Element-Wise-ResNet.

preprint2022arXiv

Encrypted Internet traffic classification using a supervised Spiking Neural Network

Internet traffic recognition is an essential tool for access providers since recognizing traffic categories related to different data packets transmitted on a network help them define adapted priorities. That means, for instance, high priority requirements for an audio conference and low ones for a file transfer, to enhance user experience. As internet traffic becomes increasingly encrypted, the mainstream classic traffic recognition technique, payload inspection, is rendered ineffective. This paper uses machine learning techniques for encrypted traffic classification, looking only at packet size and time of arrival. Spiking neural networks (SNN), largely inspired by how biological neurons operate, were used for two reasons. Firstly, they are able to recognize time-related data packet features. Secondly, they can be implemented efficiently on neuromorphic hardware with a low energy footprint. Here we used a very simple feedforward SNN, with only one fully-connected hidden layer, and trained in a supervised manner using the newly introduced method known as Surrogate Gradient Learning. Surprisingly, such a simple SNN reached an accuracy of 95.9% on ISCX datasets, outperforming previous approaches. Besides better accuracy, there is also a very significant improvement on simplicity: input size, number of neurons, trainable parameters are all reduced by one to four orders of magnitude. Next, we analyzed the reasons for this good accuracy. It turns out that, beyond spatial (i.e. packet size) features, the SNN also exploits temporal ones, mostly the nearly synchronous (within a 200ms range) arrival times of packets with certain sizes. Taken together, these results show that SNNs are an excellent fit for encrypted internet traffic classification: they can be more accurate than conventional artificial neural networks (ANN), and they could be implemented efficiently on low power embedded systems.

preprint2022arXiv

Spiking neural networks trained via proxy

We propose a new learning algorithm to train spiking neural networks (SNN) using conventional artificial neural networks (ANN) as proxy. We couple two SNN and ANN networks, respectively, made of integrate-and-fire (IF) and ReLU neurons with the same network architectures and shared synaptic weights. The forward passes of the two networks are totally independent. By assuming IF neuron with rate-coding as an approximation of ReLU, we backpropagate the error of the SNN in the proxy ANN to update the shared weights, simply by replacing the ANN final output with that of the SNN. We applied the proposed proxy learning to deep convolutional SNNs and evaluated it on two benchmarked datasets of Fashion-MNIST and Cifar10 with 94.56% and 93.11% classification accuracy, respectively. The proposed networks could outperform other deep SNNs trained with tandem learning, surrogate gradient learning, or converted from deep ANNs. Converted SNNs require long simulation times to reach reasonable accuracies while our proxy learning leads to efficient SNNs with much smaller simulation times. The source codes of the proposed method are publicly available at https://github.com/SRKH/ProxyLearning.

preprint2021arXiv

Fast threshold optimization for multi-label audio tagging using Surrogate gradient learning

Multi-label audio tagging consists of assigning sets of tags to audio recordings. At inference time, thresholds are applied on the confidence scores outputted by a probabilistic classifier, in order to decide which classes are detected active. In this work, we consider having at disposal a trained classifier and we seek to automatically optimize the decision thresholds according to a performance metric of interest, in our case F-measure (micro-F1). We propose a new method, called SGL-Thresh for Surrogate Gradient Learning of Thresholds, that makes use of gradient descent. Since F1 is not differentiable, we propose to approximate the thresholding operation gradients with the gradients of a sigmoid function. We report experiments on three datasets, using state-of-the-art pre-trained deep neural networks. In all cases, SGL-Thresh outperformed three other approaches: a default threshold value (defThresh), an heuristic search algorithm and a method estimating F1 gradients numerically. It reached 54.9\% F1 on AudioSet eval, compared to 50.7% with defThresh. SGL-Thresh is very fast and scalable to a large number of tags. To facilitate reproducibility, data and source code in Pytorch are available online: https://github.com/topel/SGL-Thresh

preprint2020arXiv

S4NN: temporal backpropagation for spiking neural networks with one spike per neuron

We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with any number of layers. This approach reaches state-of-the-art performance with supervised multi fully-connected layer SNNs: test accuracy of 97.4% for the MNIST dataset, and 99.2% for the Caltech Face/Motorbike dataset. Yet, the neuron model that we use, non-leaky integrate-and-fire, is much simpler than the one used in all previous works. The source codes of the proposed S4NN are publicly available at https://github.com/SRKH/S4NN.