Related papers: What makes a neural code convex?
Convolutional codes are error-correcting linear codes that utilize shift registers to encode. These codes have an arbitrary block size and they can incorporate both past and current information bits. DNA codes represent DNA sequences and…
In the brain, information is encoded, transmitted and used to inform behaviour at the level of timing of action potentials distributed over population of neurons. To implement neural-like systems in silico, to emulate neural function, and…
Evolution and its intelligence element present thrill and challenges in its exploration. Yet, how species have memory, retrieve them and maintain continuity are the fundamental questions. Most of the phenomenon can only be hypothesised by…
The study of the visual system of the brain has attracted the attention and interest of many neuro-scientists, that derived computational models of some types of neuron that compose it. These findings inspired researchers in image…
A neural code on $ n $ neurons is a collection of subsets of the set $ [n]=\{1,2,\dots,n\} $. In this paper, we study some properties of graphs of neural codes. In particular, we study codeword containment graph (CCG) given by Chan et al.…
Understanding neural networks is challenging in part because of the dense, continuous nature of their hidden states. We explore whether we can train neural networks to have hidden states that are sparse, discrete, and more interpretable by…
Neural codes are binary codes in $\{0,1\}^n$; here we focus on the ones which represent the firing patterns of a type of neurons called place cells. There is much interest in determining which neural codes can be realized by a collection of…
We study the open, closed, and non-degenerate embedding dimensions of neural codes, which are the smallest respective dimensions in which one can find a realization of a code consisting of convex sets that are open, closed, or…
In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains. However, these neuron populations' precise encoding and operations have…
We describe the combinatorics of equilibria and steady states of neurons in threshold-linear networks that satisfy Dale's law. The combinatorial code of a Dale network is characterized in terms of two conditions: (i) a condition on the…
Understanding brain function, constructing computational models and engineering neural prosthetics require assessing two problems, namely encoding and decoding, but their relation remains controversial. For decades, the encoding problem has…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
It is a fundamental behavior that different individuals see the world in a largely similar manner. This is an essential basis for humans' ability to cooperate and communicate. However, what are the neuronal properties that underlie these…
Neuroscience is undergoing a period of rapid experimental progress and expansion. New mathematical tools, previously unknown in the neuroscience community, are now being used to tackle fundamental questions and analyze emerging data sets.…
This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration, in particular, led to the consideration…
The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used…
Neural network (connectionist) models are designed to encode image features and provide the building blocks for object and shape recognition. These models generally call for: a) initial diffuse connections from one neuron population to…
Neural coding is a field of study that concerns how sensory information is represented in the brain by networks of neurons. The link between external stimulus and neural response can be studied from two parallel points of view. The first,…
Learning to read places a strong challenge on the visual system. Years of expertise lead to a remarkable capacity to separate highly similar letters and encode their relative positions, thus distinguishing words such as FORM and FROM,…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…