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International audience; In recent years, deep learning has revolutionized the field of machine learning, for computer vision in particular. In this approach, a deep (multilayer) artificial neural network (ANN) is trained, most often in a supervised manner using backpropagation. Vast amounts of labeled training examples are required, but the resulting classification accuracy is truly impressive, sometimes outperforming humans.Neurons in an ANN are characterized by a single, static, continuous-valued activation. Yet biological neurons use discrete spikes to compute and transmit information, and the spike times, in addition to the spike rates, matter. Spiking neural networks (SNNs) are thus more biologically realistic than ANNs, and are arguably the only viable option if one wants to understand how the brain computes at the neuronal description level. The spikes of biological neurons are sparse in time and space, and event-driven. Combined with bio-plausible local learning rules, this makes it easier to build low-power, neuromorphic hardware for SNNs. However, training deep SNNs remains a challenge. Spiking neurons’ transfer function is usually non-differentiable, which prevents using backpropagation.Here we review recent supervised and unsupervised methods to train deep SNNs, and compare them in terms of accuracy and computational cost. The emerging picture is that SNNs still lag behind ANNs in terms of accuracy, but the gap is decreasing, and can even vanish on some tasks, while SNNs typically require many fewer operations and are the better candidates to process spatio-temporal data.

Error backpropagation is the most common approach for direct training of spiking neural networks. However, the non-differentiability of spiking neurons makes the backpropagation of error a challenge. In this paper, we introduce a new temporal learning algorithm, STiDi-BP, in which we ignore backward recursive gradient computation, and to avoid the non-differentiability of SNNs, we use a linear approximation to compute the derivative of latency with respect to the potential. We apply gradient descent to each layer independently based on an estimation of the temporal error in that layer. To do so, we calculate the desired firing time of each neuron and compare it to its actual firing time. In STiDi-BP, we employ the time-to-first-spike temporal coding, one spike per neuron, and use spiking neuron models with piecewise linear postsynaptic potential which provide large computational benefits. To evaluate the performance of the proposed learning rule, we run three experiments on the XOR problem, the face/motorbike categories of the Caltech 101 dataset, and the MNIST dataset. Experimental results show that the STiDi-BP outperforms traditional BP in terms of accuracy and/or computational cost.

We recently proposed the S4NN algorithm, essentially an adaptation of backpropagation to multilayer spiking neural networks that use simple non-leaky integrate-and-fire neurons and a form of temporal coding known as time-to-first-spike coding. With this coding scheme, neurons fire at most once per stimulus, but the firing order carries information. Here, we introduce BS4NN, a modification of S4NN in which the synaptic weights are constrained to be binary (+1 or -1), in order to decrease memory (ideally, one bit per synapse) and computation footprints. This was done using two sets of weights: firstly, real-valued weights, updated by gradient descent, and used in the backward pass of backpropagation, and secondly, their signs, used in the forward pass. Similar strategies have been used to train (non-spiking) binarized neural networks. The main difference is that BS4NN operates in the time domain: spikes are propagated sequentially, and different neurons may reach their threshold at different times, which increases computational power. We validated BS4NN on two popular benchmarks, MNIST and Fashion-MNIST, and obtained reasonable accuracies for this sort of network (97.0% and 87.3% respectively) with a negligible accuracy drop with respect to real-valued weights (0.4% and 0.7%, respectively). We also demonstrated that BS4NN outperforms a simple BNN with the same architectures on those two datasets (by 0.2% and 0.9% respectively), presumably because it leverages the temporal dimension. The source codes of the proposed BS4NN are publicly available at https://github.com/SRKH/BS4NN.

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, nonleaky 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 .

Reinforcement learning (RL) has recently regained popularity, with major achievements such as beating the European game of Go champion. Here, for the first time, we show that RL can be used efficiently to train a spiking neural network (SNN) to perform object recognition in natural images without using an external classifier. We used a feedforward convolutional SNN and a temporal coding scheme where the most strongly activated neurons fire first, while less activated ones fire later, or not at all. In the highest layers, each neuron was assigned to an object category, and it was assumed that the stimulus category was the category of the first neuron to fire. If this assumption was correct, the neuron was rewarded, i.e. spike-timing-dependent plasticity (STDP) was applied, which reinforced the neuron's selectivity. Otherwise, anti-STDP was applied, which encouraged the neuron to learn something else. As demonstrated on various image datasets (Caltech, ETH-80, and NORB), this reward modulated STDP (R-STDP) approach extracted particularly discriminative visual features, whereas classic unsupervised STDP extracts any feature that consistently repeats. As a result, R-STDP outperformed STDP on these datasets. Furthermore, R-STDP is suitable for online learning, and can adapt to drastic changes such as label permutations. Finally, it is worth mentioning that both feature extraction and classification were done with spikes, using at most one spike per neuron. Thus the network is hardware friendly and energy efficient., Comment: supplementary materials are added, Caltech face/motorbike demonstration figure is updated, some parts of the main manuscript are moved to the supplementary materials, additional network analysis and performance comparison with deep nets are added

Previous studies have shown that spike-timing-dependent plasticity (STDP) can be used in spiking neural networks (SNN) to extract visual features of low or intermediate complexity in an unsupervised manner. These studies, however, used relatively shallow architectures, and only one layer was trainable. Another line of research has demonstrated - using rate-based neural networks trained with back-propagation - that having many layers increases the recognition robustness, an approach known as deep learning. We thus designed a deep SNN, comprising several convolutional (trainable with STDP) and pooling layers. We used a temporal coding scheme where the most strongly activated neurons fire first, and less activated neurons fire later or not at all. The network was exposed to natural images. Thanks to STDP, neurons progressively learned features corresponding to prototypical patterns that were both salient and frequent. Only a few tens of examples per category were required and no label was needed. After learning, the complexity of the extracted features increased along the hierarchy, from edge detectors in the first layer to object prototypes in the last layer. Coding was very sparse, with only a few thousands spikes per image, and in some cases the object category could be reasonably well inferred from the activity of a single higher-order neuron. More generally, the activity of a few hundreds of such neurons contained robust category information, as demonstrated using a classifier on Caltech 101, ETH-80, and MNIST databases. We also demonstrate the superiority of STDP over other unsupervised techniques such as random crops (HMAX) or auto-encoders. Taken together, our results suggest that the combination of STDP with latency coding may be a key to understanding the way that the primate visual system learns, its remarkable processing speed and its low energy consumption. These mechanisms are also interesting for artificial vision systems, particularly for hardware solutions.

The human visual system contains a hierarchical sequence of modules that take part in visual perception at different levels of abstraction, i.e., superordinate, basic, and subordinate levels. One important question is to identify the “entry” level at which the visual representation is commenced in the process of object recognition. For a long time, it was believed that the basic level had a temporal advantage over two others. This claim has been challenged recently. Here we used a series of psychophysics experiments, based on a rapid presentation paradigm, as well as two computational models, with bandpass filtered images of five object classes to study the processing order of the categorization levels. In these experiments, we investigated the type of visual information required for categorizing objects in each level by varying the spatial frequency bands of the input image. The results of our psychophysics experiments and computational models are consistent. They indicate that the different spatial frequency information had different effects on object categorization in each level. In the absence of high frequency information, subordinate and basic level categorization are performed less accurately, while the superordinate level is performed well. This means that low frequency information is sufficient for superordinate level, but not for the basic and subordinate levels. These finer levels rely more on high frequency information, which appears to take longer to be processed, leading to longer reaction times. Finally, to avoid the ceiling effect, we evaluated the robustness of the results by adding different amounts of noise to the input images and repeating the experiments. As expected, the categorization accuracy decreased and the reaction time increased significantly, but the trends were the same. This shows that our results are not due to a ceiling effect. The compatibility between our psychophysical and computational results suggests that the temporal advantage of the superordinate (resp. basic) level to basic (resp. subordinate) level is mainly due to the computational constraints (the visual system processes higher spatial frequencies more slowly, and categorization in finer levels depends more on these higher spatial frequencies).

Mixture of Experts is one of the most popular ensemble methods in pattern recognition systems. Although, diversity between the experts is one of the necessary conditions for the success of combining methods, ensemble systems based on Mixture of Experts suffer from the lack of enough diversity among the experts caused by unfavorable initial parameters. In the conventional Mixture of Experts, each expert receives the whole feature space. To increase diversity among the experts, solve the structural issues of Mixture of Experts such as zero coefficient problem, and improve efficiency in the system, we intend to propose a model, entitled Mixture of Feature Specified Experts, in which each expert gets a different subset of the original feature set. To this end, we first select a set of feature subsets which lead to a set of diverse and efficient classifiers. Then the initial parameters are infused to the system with training classifiers on the selected feature subsets. Finally, we train the expert and the gating networks using the learning rule of classical Mixture of Experts to organize collaboration between the members of system and aiding the gating network to find the best partitioning of the problem space. To evaluate our proposed method, we have used six datasets from the UCI repository. In addition the generalization capability of our proposed method is considered on real-world database of EEG based Brain-Computer Interface. The performance of our method is evaluated with various appraisal criteria and significant improvement in recognition rate of our proposed method is indicated in all practical tests.

Behavioral studies in humans indicate that peripheral vision can do object recognition to some extent. Moreover, recent studies have shown that some information from brain regions retinotopic to visual periphery is somehow fed back to regions retinotopic to the fovea and disrupting this feedback impairs object recognition in human. However, it is unclear to what extent the information in visual periphery contributes to human object categorization. Here, we designed two series of rapid object categorization tasks to first investigate the performance of human peripheral vision in categorizing natural object images at different eccentricities and abstraction levels (superordinate, basic, and subordinate). Then, using a delayed foveal noise mask, we studied how modulating the foveal representation impacts peripheral object categorization at any of the abstraction levels. We found that peripheral vision can quickly and accurately accomplish superordinate categorization, while its performance in finer categorization levels dramatically drops as the object presents further in the periphery. Also, we found that a 300-ms delayed foveal noise mask can significantly disturb categorization performance in basic and subordinate levels, while it has no effect on the superordinate level. Our results suggest that human peripheral vision can easily process objects at high abstraction levels, and the information is fed back to foveal vision to prime foveal cortex for finer categorizations when a saccade is made toward the target object.

We present a new classifier fusion method to combine soft-level classifiers with a new approach, which can be considered as a generalized decision templates method. Previous combining methods based on decision templates employ a single prototype for each class, but this global point of view mostly fails to properly represent the decision space. This drawback extremely affects the classification rate in such cases: insufficient number of training samples, island-shaped decision space distribution, and classes with highly overlapped decision spaces. To better represent the decision space, we utilize a prototype selection method to obtain a set of local decision prototypes for each class. Afterward, to determine the class of a test pattern, its decision profile is computed and then compared to all decision prototypes. In other words, for each class, the larger the numbers of decision prototypes near to the decision profile of a given pattern, the higher the chance for that class. The efficiency of our proposed method is evaluated over some well-known classification datasets suggesting superiority of our method in comparison with other proposed techniques.

Retinal image of surrounding objects varies tremendously due to the changes in position, size, pose, illumination condition, background context, occlusion, noise, and non-rigid deformations. But despite these huge variations, our visual system is able to invariantly recognize any object in just a fraction of a second. To date, various computational models have been proposed to mimic the hierarchical processing of the ventral visual pathway, with limited success. Here, we show that the association of both biologically inspired network architecture and learning rule significantly improves the models' performance when facing challenging invariant object recognition problems. Our model is an asynchronous feedforward spiking neural network. When the network is presented with natural images, the neurons in the entry layers detect edges, and the most activated ones fire first, while neurons in higher layers are equipped with spike timing-dependent plasticity. These neurons progressively become selective to intermediate complexity visual features appropriate for object categorization. The model is evaluated on 3D-Object and ETH-80 datasets which are two benchmarks for invariant object recognition, and is shown to outperform state-of-the-art models, including DeepConvNet and HMAX. This demonstrates its ability to accurately recognize different instances of multiple object classes even under various appearance conditions (different views, scales, tilts, and backgrounds). Several statistical analysis techniques are used to show that our model extracts class specific and highly informative features.

View-invariant object recognition is a challenging problem that has attracted much attention among the psychology, neuroscience, and computer vision communities. Humans are notoriously good at it, even if some variations are presumably more difficult to handle than others (e.g., 3D rotations). Humans are thought to solve the problem through hierarchical processing along the ventral stream, which progressively extracts more and more invariant visual features. This feed-forward architecture has inspired a new generation of bio-inspired computer vision systems called deep convolutional neural networks (DCNN), which are currently the best models for object recognition in natural images. Here, for the first time, we systematically compared human feed-forward vision and DCNNs at view-invariant object recognition task using the same set of images and controlling the kinds of transformation (position, scale, rotation in plane, and rotation in depth) as well as their magnitude, which we call "variation level." We used four object categories: car, ship, motorcycle, and animal. In total, 89 human subjects participated in 10 experiments in which they had to discriminate between two or four categories after rapid presentation with backward masking. We also tested two recent DCNNs (proposed respectively by Hinton's group and Zisserman's group) on the same tasks. We found that humans and DCNNs largely agreed on the relative difficulties of each kind of variation: rotation in depth is by far the hardest transformation to handle, followed by scale, then rotation in plane, and finally position (much easier). This suggests that DCNNs would be reasonable models of human feed-forward vision. In addition, our results show that the variation levels in rotation in depth and scale strongly modulate both humans' and DCNNs' recognition performances. We thus argue that these variations should be controlled in the image datasets used in vision research.

Deep convolutional neural networks (DCNNs) have attracted much attention recently, and have shown to be able to recognize thousands of object categories in natural image databases. Their architecture is somewhat similar to that of the human visual system: both use restricted receptive fields, and a hierarchy of layers which progressively extract more and more abstracted features. Yet it is unknown whether DCNNs match human performance at the task of view-invariant object recognition, whether they make similar errors and use similar representations for this task, and whether the answers depend on the magnitude of the viewpoint variations. To investigate these issues, we benchmarked eight state-of-the-art DCNNs, the HMAX model, and a baseline shallow model and compared their results to those of humans with backward masking. Unlike in all previous DCNN studies, we carefully controlled the magnitude of the viewpoint variations to demonstrate that shallow nets can outperform deep nets and humans when variations are weak. When facing larger variations, however, more layers were needed to match human performance and error distributions, and to have representations that are consistent with human behavior. A very deep net with 18 layers even outperformed humans at the highest variation level, using the most human-like representations.

Nowadays, brain signals are employed in various scientific and practical fields such as Medical Science, Cognitive Science, Neuroscience, and Brain Computer Interfaces. Hence, the need for robust signal analysis methods with adequate accuracy and generalizability is inevitable. The brain signal analysis is faced with complex challenges including small sample size, high dimensionality and noisy signals. Moreover, because of the non-stationarity of brain signals and the impacts of mental states on brain function, the brain signals are associated with an inherent uncertainty. In this paper, an evidence-based combining classifiers method is proposed for brain signal analysis. This method exploits the power of combining classifiers for solving complex problems and the ability of evidence theory to model as well as to reduce the existing uncertainty. The proposed method models the uncertainty in the labels of training samples in each feature space by assigning soft and crisp labels to them. Then, some classifiers are employed to approximate the belief function corresponding to each feature space. By combining the evidence raised from each classifier through the evidence theory, more confident decisions about testing samples can be made. The obtained results by the proposed method compared to some other evidence-based and fixed rule combining methods on artificial and real datasets exhibit the ability of the proposed method in dealing with complex and uncertain classification problems.