Related papers: Dictionary Learning by Dynamical Neural Networks

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…

The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…

Associative networks theory is increasingly providing tools to interpret update rules of artificial neural networks. At the same time, deriving neural learning rules from a solid theory remains a fundamental challenge. We make some steps in…

We study a mathematical model of biological neuronal networks composed by any finite number $N \geq 2$ of non necessarily identical cells. The model is a deterministic dynamical system governed by finite-dimensional impulsive differential…

Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…

Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with artificial neural…

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…

Representation is a core issue in artificial intelligence. Humans use discrete language to communicate and learn from each other, while machines use continuous features (like vector, matrix, or tensor in deep neural networks) to represent…

Deep neural networks (DNNs) transform stimuli across multiple processing stages to produce representations that can be used to solve complex tasks, such as object recognition in images. However, a full understanding of how they achieve this…

We introduce an algorithm to do backpropagation on a spiking network. Our network is "spiking" in the sense that our neurons accumulate their activation into a potential over time, and only send out a signal (a "spike") when this potential…

Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In…

This paper presents a compact, matrix-based representation of neural networks in a self-contained tutorial fashion. Specifically, we develop neural networks as a composition of several vector-valued functions. Although neural networks are…

In this article we review computational aspects of Deep Learning (DL). Deep learning uses network architectures consisting of hierarchical layers of latent variables to construct predictors for high-dimensional input-output models. Training…

Spiking neural networks (SNNs) have closer dynamics to the brain than current deep neural networks. Their low power consumption and sample efficiency make these networks interesting. Recently, several deep convolutional spiking neural…

Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…

Artificial neural networks are algorithms which have been developed to tackle a range of computational problems. These range from modelling brain function to making predictions of time-dependent phenomena to solving hard (NP-complete)…

Neurons in the brain communicate with each other through discrete action spikes as opposed to continuous signal transmission in artificial neural networks. Therefore, the traditional techniques for optimization of parameters in neural…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…