Sparse coding holds the idea that signals can be concisely described as a linear mixture of few components (called atoms) picked from a bigger set of primary kernels (called dictionary). This framework has long been used to model the strategy employed by mammals´ primary visual cortex (V1) to detect low-level features, in particular, oriented edges in natural scenes. Differently, predictive coding is a prominent tool used to model hierarchical neural dynamics: high-level cortical layers predict at best the activity of lower-level ones and this prediction is sent back through of a feedback connection between the layers. This defines a recursive loop in which prediction error is integrated to the sensory input and fed forward to refine the quality of the prediction. We propose a Sparse Deep Predictive Coding algorithm (SDPC) that exploits convolutional dictionaries and a feedback information flow for meaningful, hierarchical feature learning in static images. The proposed architecture allows us to add arbitrary non-linear spatial transformation stages between each layer of the hierarchical sparse representations, such as Max-Pooling or Spatial Transformer layers. SPDC consists of a dynamical system in the form of a convolutional neural network, analogous to the model proposed by Rao and Ballard, 1999. The state variables are sparse feature maps encoding the input and the feedback signals while the parameters of the system are convolutional dictionaries optimized through Hebbian learning. We observed that varying the strength of the feedback modulates the overall sparsity of low-level representations (lower feedback scales correspond to a less sparse activity), but without changing the exponential shape of the distribution of the sparse prior. This model could shed light on the role of sparsity and feedback modulation in hierarchical feature learning with important applications in signal processing (data compression), computer vision (by extending it to dynamic scenes) and computational neuroscience, notably by using more complex priors like group sparsity to model topological organization in the brain cortex.

The brain has to solve inverse problems to correctly interpret sensory data and infer the set of causes that generated the sensory inputs. Such a problem is typically ill-posed, and thus requires constraint the narrow down the number of solutions. Predictive coding (PC)is a computational neuroscience framework that finds the most likely causes for the sensory input by minimizing the mismatch between the sensory data and the predicted input. Such a framework could be used to build sparse hierarchical internal representations of a given input.

It is still not fully understood how visual system integrates motion energy across different spatial and temporal frequencies to build a coherent percept of the global motion under the complex, noisy naturalistic conditions. We addressed this question by manipulating local speed variability distribution (i. e. speed bandwidth) using a well-controlled class of broadband random-texture stimuli called Motion Clouds (MCs) with continuous naturalistic spatiotemporal frequency spectra (Sanz-Leon et al., 2012, ; Simoncini et al., 2012). In a first 2AFC experiment on speed discrimination, participants had to compare the speed of a broad speed bandwidth MC (range: 0.05-8$,^∘$/s) moving at 1 of 5 possible mean speeds (ranging from 5 to 13 $,^∘$/s) to that of another MC with a small speed bandwidth (SD: 0.05 $,^∘$/s), always moving at a mean speed of 10$,^∘$/s . We found that MCs with larger speed bandwidth (between 0.05-0.5$,^∘$/s) were perceived moving faster. Within this range, speed uncertainty results in over-estimating stimulus velocity. However, beyond a critical bandwidth (SD: 0.5 $,^∘$/s), perception of a coherent speed was lost. In a second 2AFC experiment on direction discrimination, participants had to estimate the motion direction of moving MCs with different speed bandwidths. We found that for large band MCs participant could no longer discriminate motion direction. These results suggest that when increasing speed bandwidth from small to large range, the observer experiences different perceptual regimes. We then decided to run a Maximum Likelihood Difference Scaling (Knoblauch & Maloney, 2008) experiment with our speed bandwidth stimuli to investigate these different possible perceptual regimes. We identified three regimes within this space that correspond to motion coherency, motion transparency and motion incoherency. These results allow to further characterize the shape of the interactions kernel observed between different speed tuned channels and different spatiotemporal scales (Gekas et al ., 2017) that underlies global velocity estimation.

The selectivity of the visual system to oriented patterns is very well documented in a wide range of species, especially in mammals. In particular, neurons of the primary visual cortex are anatomically grouped by their preference to a given oriented visual stimulus. Interactions between such groups of neurons have been successfully modeled using recurrently-connected network of spiking neurons, so called "ring models". Nonetheless, this selectivity is most often studied with crystal-like patterns such as gratings. Here, we studied the ability of human observers to discriminate texture-like patterns for which we could quantitatively tune the precision of their oriented content and we propose a generic model to explain such results. The first contribution shows that the discrimination threshold as a function of the precision did not vary smoothly as would be expected, but more in a binary, "all or none" fashion. Our second contribution is to propose a novel model of orientation selectivity that is based on deep-learning techniques, which performance we evaluated in the same task. This model has human-like performance in term of accuracy and exhibits qualitatively similar psychophysical curves. One hypothesis that such a structure allows for the system to be robust to noise in its visual inputs.

It is widely assumed that visual processing follows a forward sequence of processing steps along a hierarchy of laminar sub-populations of the neural system. Taking the example of the early visual system of mammals, most models are consequently organized in layers from the retina to visual cortical areas, until a decision is taken using the representation that is formed in the highest layer. Typically, features of higher complexity (position, orientation, size, curvature, …) are successively extracted in distinct layers (Carandini, 2012). This is prevalent in most deep learning algorithms and stems from a long history of feed-forward architectures. Though this proved to be highly successful, the origin of such architectures is not known i̧teSerre07. Using a generic unsupervised learning algorithm, we first trained a simple one-layer convolutional neural network on a seta of natural images with a growing number of neurons. By doing this, we could quantitatively manipulate the complexity of the representation that emerges from such learning and analyze if sub-populations within the layer could be grouped by their similarity, hence justifying the emergence of a hierarchical processing. As shown in previous studies (Olshausen, 1996), such an algorithm converges to a weight matrix that has strong analogies with the receptive fields of simple cells located in the Primary Visual Cortex of mammals (V1). This result extends naturally to a cortical representation of the input image that encodes second-order features (edges) as neural responses arranged in a three-dimensional space, where the third dimension can be seen as a model of hyper-columns of the Primary Visual Cortex. From this bio-inspired encoding, we were able to define contours in images as simple smooth trajectories in a cortical representation space. This simple model shows that hierarchical processing may originate from the neural encoding of different visual transformations within natural images: respectively translation, rotations and zooms, which correspond to rigid translation in the cortical space. The model can be further extended to reproduce the effect of complex cells in V1 (max pooling) and feedback signals from higher cortical areas. We predict that invariance to more complex transformation like shearing (perspective) and viewpoint changes (looming) will emerge as these additional steps in sensory processing are taken into account. Indeed, a higher level of complexity can be introduced as the cortical representation is extended from smooth trajectories (space domain) to smooth surfaces (space-time domain). As such, this justifies the extension of a simple sparse network formalism to translation invariant neural networks (such as the convolutional neural networks used in deep learning) that is able to generalize geometrical transformations, such as translation, rotations, and zooms, in an invariant bio-inspired representation (Perrinet, 2015). This should provide some key insights into higher-order features such as co-occurrences, but also to novel categorization architectures. Indeed, such features were recently found to be sufficient to allow the categorization of images containing an animal (Perrinet and Bednar, 2015). Crucially, as the geometrical transformations develop in time, we expect that the detection of these features is made robust by dynamical processes.

This paper presents for the first time the embedded stand-alone version of the bio-inspired M2APix (Michaelis-Menten auto-adaptive pixels) sensor as a ventral optic flow sensor to endow glider-type unmanned aerial vehicles with autonomous landing ability. Assuming the aircraft is equipped with any reliable speed measurement system such as a global positioning system or an inertial measurement unit, we can use the velocity of the glider to determine with high precision its height while landing. This information is robust to different outdoor lighting conditions and over different kinds of textured ground, a crucial property to control the landing phase of the aircraft.

The formation of connections between neural cells is essentially emerging from an unsupervised learning process. During the development of primary visual cortex (V1) of mammals, for example, one may observe the emergence of cells selective to localized and oriented features. This leads to the development of a rough contour-based representation of the retinal image in area V1. We modeled the formation of this representation along the thalamo-cortical pathway using a sparse unsupervised learning algorithm in a hierarchical network. This algorithm alternates (i) a coding phase to encode the information and (ii) a learning phase to find the proper encoder (also called dictionary). We replicated and adapted the Multi-Layer Convolutional Sparse Coding (ML-CSC) model from Michael Elad’s group. As an application, we have trained our implementation on a database containing images from faces. The extracted features show similarities with some of the neuron’s receptive field found in V1 and beyond. Furthermore, our results demonstrate the potential application of such a strategy to the fast classification of images, for example in hierarchical and dynamical architectures.

Humans are able to accurately track a moving object with a combination of saccades and smooth eye movements. These movements allow us to align and stabilize the object on the fovea, thus enabling high-resolution visual analysis. When predictive information is available about target motion, anticipatory smooth pursuit eye movements (aSPEM) are efficiently generated before target appearance, which reduce the typical sensorimotor delay between target motion onset and foveation. It is generally assumed that the role of anticipatory eye movements is to limit the behavioral impairment due to eyetotarget position and velocity mismatch. By manipulating the probability for target motion direction we were able to bias the direction and mean velocity of aSPEM, as measured during a fixed duration gap before target rampmotion onset. This suggests that probabilistic information may be used to inform the internal representation of motion prediction for the initiation of anticipatory movements. However, such estimate may become particularly challenging in a dynamic context, where the probabilistic contingencies vary in time in an unpredictable way. In addition, whether and how the information processing underlying the buildup of aSPEM is linked to an explicit estimate of probabilities is unknown. We developed a new paired task paradigm in order to address these two questions. In a first session, participants observe a target moving horizontally with constant speed from the center either to the right or left across trials. The probability of either motion direction changes randomly in time. Participants are asked to estimate "how much they are confident that the target will move to the right or left in the next trial" and to adjust the cursor’s position on the screen accordingly. In a second session the participants eye movements are recorded during the observation of the same sequence of random direction trials. In parallel, we are developing new automatic routines for the advanced analysis of oculomotor traces. In order to extract the relevant parameters of the oculomotor responses (latency, gain, initial acceleration, catchup saccades), we developed new tools based on bestfitting procedure of predefined patterns (i.e. the typical smooth pursuit velocity profile).

Humans are able to accurately track a moving object with a combination of saccades and smooth eye movements. These movements allow us to align and stabilize the object on the fovea, thus enabling highresolution visual analysis. When predictive information is available about target motion, anticipatory smooth pursuit eye movements (aSPEM) are efficiently generated before target appearance, which reduce the typical sensorimotor delay between target motion onset and foveation. It is generally assumed that the role of anticipatory eye movements is to limit the behavioral impairment due to eyetotarget position and velocity mismatch. By manipulating the probability for target motion direction we were able to bias the direction and mean velocity of aSPEM, as measured during a fixed duration gap before target rampmotion onset. This suggests that probabilistic information may be used to inform the internal representation of motion prediction for the initiation of anticipatory movements. However, such estimate may become particularly challenging in a dynamic context, where the probabilistic contingencies vary in time in an unpredictable way. In addition, whether and how the information processing underlying the buildup of aSPEM is linked to an explicit estimate of probabilities is unknown. We developed a new paired* task paradigm in order to address these two questions. In a first session, participants observe a target moving horizontally with constant speed from the center either to the right or left across trials. The probability of either motion direction changes randomly in time. Participants are asked to estimate "how much they are confident that the target will move to the right or left in the next trial" and to adjust the cursor’s position on the screen accordingly. In a second session the participants eye movements are recorded during the observation of the same sequence of randomdirection trials. In parallel, we are developing new automatic routines for the advanced analysis of oculomotor traces. In order to extract the relevant parameters of the oculomotor responses (latency, gain, initial acceleration, catchup saccades), we developed new tools based on best*fitting procedure of predefined patterns (i.e. the typical smooth pursuit velocity profile).

Recording eye movements is a technique that attracts an increasing number of scientists, but also in the general public. Indeed, this allows to quantitatively measure a number of useful dimensions of perception and behavior in general. However, most existing trackers rely on expensive or technically complex solutions. Here, we propose a simple framework to record eye movements using any camera, such as a webcam. As a proof of concept, the recorded image is processed in real-time to detect from a simple sub-set of eye movements : left, center, right or blink. The processing is based on two stages. First, we use a pre-trained computer vision algorithm to extract the image of the face. Second, we used a classical deep-learning architecture to learn to classify these sub-images. This network is a 3 layered convolutional neural network, for which we optimized performance as measured by the accuracy with cross-validation on a wide range of the network’s hyper-parameters. Over a dataset of more than 1000 images, this network achieves an average accuracy of approximately 97 percent. We also provide with an integration with the psychopy library which shows that frames can be processed on a standard laptop at a rate of approximately 25 Hz.

The properties of motion processing for driving smooth eye movements have bee investigated using simple, artificial stimuli such as gratings, small dots or random dot patterns. Motion processing in the context of complex, natural images is less known. We have previously investigated the human ocular following responses to a novel class of random texture stimuli of parameterized naturalistic statistics: the Motion Clouds. In Fourier space, these dynamical textures are designed with a log normal distribution of spatial frequencies power multiplied by a pink noise power spectral density that reduces the high frequency contents of the stimulus (Sanz-Leon et al. 2011). We have previously shown that the precision of reflexive tracking increases with the spatial frequency bandwidth of large (> 30 deg diameter) patterns (i.e. the width of the spatial frequency distribution around a given mean spatial frequency; Simoncini et al. 2012). Now, we extend this approach to voluntary tracking and focused on the effects of spatial frequency bandwidth upon the initial phase of smooth pursuit eye movements. Participants were instructed to pursue a large patch of moving clouds (mean speeds: 5, 10 or 20 deg/s) embedded within a smoothing Gaussian window of standard deviation 5 deg. The motion stimuli were presented with four different spatial frequency bandwidths and two different mean spatial frequencies (0.3 and 1 cpd). We observed that smaller bandwidth textures exhibit a stronger spectral energy within the low spatial frequency range (below 1cpd), yielding to shorter latency of smooth pursuit eye movements. A weak and less consistent effect was found on initial eye acceleration, contrary what was previously observed with OFR. After 400ms, the steady-state tracking velocity matched the mean visual motion speed and pursuit performance was comparable with that observed with a control, small dot motion. Motion Clouds offer an efficient tool to probe the optimal window of visibility for human smooth pursuit through the manipulation of both the mean and the variability of spatial frequency.

One core advantage of sparse representations is the efficient coding of complex signals using compact codes. For instance, it allows for the representation of any image as a combination of few elements drawn from a large dictionary of basis functions. In the context of the efficient processing of natural images, we propose here that such codes can be optimized by designing proper homeostatic rules between the elements of the dictionary. Indeed, a common design for unsupervised learning rules relies on a gradient descent over a cost measuring representation quality with respect to sparseness. The sparseness constraint introduces a competition which can be optimized by ensuring that each item in the dictionary is selected as often as others. We implemented this rule by introducing a gain normalization similar to what is observed in a balanced neural network. We validated this theoretical insight by challenging different sparse coding algorithms with the same learning rule but with or without homeostasis. The different sparse coding algorithms were chosen for their efficiency and generality. They include least-angle regression, orthogonal matching pursuit and basis pursuit. Simulations show that for a given homeostasis rule, gradient descent performed similarly the learning of a dataset of image patches. While the coding algorithm did not matter much, including homeostasis changed qualitatively the learned features. In particular, homeostasis results in a more homogeneous set of orientation selective filters, which is closer to what is found in the visual cortex of mammals. To further validate these results, we applied this algorithm to the optimization of a visual system embedded in an aerial robot. As a consequence, this biologically-inspired learning rule demonstrates that principles observed in neural computations can help improve real-life machine learning algorithms.

One core advantage of sparse representations is the efficient coding of complex signals using compact codes. For instance, it allows for the representation of any image as a combination of few elements drawn from a large dictionary of basis functions. In the context of the efficient processing of natural images, we propose here that such codes can be optimized by designing proper homeostatic rules between the elements of the dictionary. Indeed, a common design for unsupervised learning rules relies on a gradient descent over a cost measuring representation quality with respect to sparseness. The sparseness constraint introduces a competition which can be optimized by ensuring that each item in the dictionary is selected as often as others. We implemented this rule by introducing a gain normalization similar to what is observed in a balanced neural network. We validated this theoretical insight by challenging different sparse coding algorithms with the same learning rule but with or without homeostasis. The different sparse coding algorithms were chosen for their efficiency and generality. They include least-angle regression, orthogonal matching pursuit and basis pursuit. Simulations show that for a given homeostasis rule, gradient descent performed similarly the learning of a dataset of image patches. While the coding algorithm did not matter much, including homeostasis changed qualitatively the learned features. In particular, homeostasis results in a more homogeneous set of orientation selective filters, which is closer to what is found in the visual cortex of mammals. To further validate these results, we applied this algorithm to the optimization of a visual system embedded in an aerial robot. As a consequence, this biologically-inspired learning rule demonstrates that principles observed in neural computations can help improve real-life machine learning algorithms.

Improve performances of existing recognition computer vision algorithms with biological concepts. The gain are expected in the following: Recognition latency and accuracy (faster and better), less data needed to train algorithms and of decreased power consumption.)

Natural images follow statistics inherited by the structure of our physical (visual) environment. In particular, a prominent facet of this structure is that images can be described by a relatively sparse number of features. We designed a sparse coding algorithm biologically-inspired by the architecture of the primary visual cortex. We show here that coefficients of this representation exhibit a power-law distribution. For each image, the exponent of this distribution characterizes sparseness and varies from image to image. To investigate the role of this sparseness, we designed a new class of random textured stimuli with a controlled sparseness value inspired by measurements of natural images. Then, we provide with a method to synthesize random textures images with a given sparseness statistics that match that of some class of natural images and provide perspectives for their use in neurophysiology.

We consider the problem of sensorimotor delays in the optimal control of movement under uncertainty. Specifically, we consider axonal conduction delays in the visuo-oculomotor loop and their implications for active inference. Active inference uses a generalisation of Kalman filtering to provide Bayes optimal estimates of hidden states and action in generalised coordinates of motion. Representing hidden states in generalised coordinates provides a simple means of compensating for both sensory and oculomotor delays. This compensation is illustrated using neuronal simulations of oculomotor following responses with and without compensation. We then consider an extension of the generative model that produces ocular following to simulate smooth pursuit eye movements in which the system believes both the target and its centre of gaze are attracted by a (fictive) point moving in the visual field. Finally, the generative model is equipped with a hierarchical structure, so that it can register and remember unseen (occluded) trajectories and emit anticipatory responses. These simulations speak to a straightforward and neurobiologically plausible solution to the generic problem of integrating information from different sources with different temporal delays and the particular difficulties encountered when a system, like the oculomotor system, tries to control its environment with delayed signals.