Related papers: Neural codes, decidability, and a new local obstru…

This paper proposes a neuronal circuitry layout and synaptic plasticity principles that allow the (pyramidal) neuron to act as a "combinatorial switch". Namely, the neuron learns to be more prone to generate spikes given those combinations…

In this paper, we shall give an explicit proof that constacyclic codes over finite commutative rings can be realized as ideals in some twisted group rings. Also, we shall study isometries between those codes and, finally, we shall study…

A pressing scientific challenge is to understand how brains work. Of particular interest is the neocortex,the part of the brain that is especially large in humans, capable of handling a wide variety of tasks including visual, auditory,…

Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…

Convex optimization is a vibrant and successful area due to the existence of a variety of efficient algorithms that leverage the rich structure provided by convexity. Convexity of a smooth set or a function in a Euclidean space is defined…

Although deep learning has shown its powerful performance in many applications, the mathematical principles behind neural networks are still mysterious. In this paper, we consider the problem of learning a one-hidden-layer neural network…

Synaptic plasticity is widely accepted to be the mechanism behind learning in the brain's neural networks. A central question is how synapses, with access to only local information about the network, can still organize collectively and…

We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide…

Cortical circuits are characterized by exquisitely complex connectivity patterns that emerge during development from undifferentiated networks. The development of these circuits is governed by a combination of precise molecular cues that…

In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy…

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…

The central problem with understanding brain and mind is the neural code issue: understanding the matter of our brain as basis for the phenomena of our mind. The richness with which our mind represents our environment, the parsimony of…

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…

Scalar variables, e.g., the orientation of a shape in an image, are commonly predicted using a single output neuron in a neural network. In contrast, the mammalian cortex represents variables with a population of neurons. In this population…

Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…

Convolutional neural networks (CNNs), in a few decades, have outperformed the existing state of the art methods in classification context. However, in the way they were formalised, CNNs are bound to operate on euclidean spaces. Indeed,…

We take the testing perspective to understand what the minimal discrimination time between two stimuli is for different types of rate coding neurons. Our main goal is to describe the testing abilities of two different encoding systems:…

Neural theories of consciousness face three difficulties: (1) The selection problem: how are those neurons which cause consciousness selected, from all the other neurons which do not? (2) the precision problem: how do neurons hold a…

Neural network models comprising elements which have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamic behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the…

The Nerve Theorem relates the topological type of a suitably nice space with the nerve of a good cover of that space. It has many variants, such as to consider acyclic covers and numerous applications in topology including applied and…