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In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…
Neural networks based on metric recognition methods have a strictly determined architecture. Number of neurons, connections, as well as weights and thresholds values are calculated analytically, based on the initial conditions of tasks:…
Dynamic imaging is essential for analyzing various biological systems and behaviors but faces two main challenges: data incompleteness and computational burden. For many imaging systems, high frame rates and short acquisition times require…
We describe a first step towards learning general-purpose visual representations of physical scenes using only image prediction as a training criterion. To do so, we first define "physical scene" and show that, even though different agents…
We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…
Convolutional networks are ubiquitous in deep learning. They are particularly useful for images, as they reduce the number of parameters, reduce training time, and increase accuracy. However, as a model of the brain they are seriously…
There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…
Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to…
Neural development represents not only an exciting and complex field of study, with ongoing progress, but it also became the epicentre of neuroscience and developmental biology, as it strives to describe the underlying cellular and…
This paper proposes a hypothesis for the aesthetic appreciation that aesthetic images make a neural network strengthen salient concepts and discard inessential concepts. In order to verify this hypothesis, we use multi-variate interactions…
Recently, diffusion model have demonstrated impressive image generation performances, and have been extensively studied in various computer vision tasks. Unfortunately, training and evaluating diffusion models consume a lot of time and…
Recent progress in deep learning-based models has improved photo-realistic (or perceptual) single-image super-resolution significantly. However, despite their powerful performance, many methods are difficult to apply to real-world…
We introduce Neural Radiosity, an algorithm to solve the rendering equation by minimizing the norm of its residual similar as in traditional radiosity techniques. Traditional basis functions used in radiosity techniques, such as piecewise…
For the last decade, there has been a push to use multi-dimensional (latent) spaces to represent concepts; and yet how to manipulate these concepts or reason with them remains largely unclear. Some recent methods exploit multiple latent…
Neural networks have enabled applications in artificial intelligence through machine learning, and neuromorphic computing. Software implementations of neural networks on conventional computers that have separate memory and processor (and…
Sequential neuronal activity underlies a wide range of processes in the brain. Neuroscientific evidence for neuronal sequences has been reported in domains as diverse as perception, motor control, speech, spatial navigation and memory.…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
Considering the retina as a high dimensional, non autonomous, dynamical system, layered and structured, with non stationary and spatially inhomogeneous entries (visual scenes), we present several examples where dynamical systems-,…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
Recent models for image processing are using the Convolutional neural network (CNN) which requires a pixel per pixel analysis of the input image. This method works well. However, it is time-consuming if we have large images. To increase the…