Related papers: Strengthening Relationships between Neural Ideals …
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
In this paper we introduce Neural Network Coding(NNC), a data-driven approach to joint source and network coding. In NNC, the encoders at each source and intermediate node, as well as the decoder at each destination node, are neural…
Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case.…
Inference of correspondences between images from different modalities is an extremely important perceptual ability that enables humans to understand and recognize cross-modal concepts. In this paper, we consider an instance of this problem…
The brain encodes spacial structure through a combinatorial code of neural activity. Experiments suggest such codes correspond to convex areas of the subject's environment. We present an intrinsic condition that implies a neural code may…
We investigated the relationship among neural representations of vocalized, mimed, and imagined speech recorded using publicly available stereotactic EEG recordings. Most prior studies have focused on decoding speech responses within each…
Neural codes are lists of subsets of neurons that fire together. Of particular interest are neurons called place cells, which fire when an animal is in specific, usually convex regions in space. A fundamental question, therefore, is to…
A neural code on $ n $ neurons is a collection of subsets of the set $ [n]=\{1,2,\dots,n\} $. Curto et al. \cite{curto2013neural} associated a ring $\mathcal{R}_{\mathcal{C}}$ (neural ring) to a neural code $\mathcal{C}$. A special class of…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Capsule networks are a type of neural network that have recently gained increased popularity. They consist of groups of neurons, called capsules, which encode properties of objects or object parts. The connections between capsules encrypt…
Mechanistic interpretability aims to understand how models store representations by breaking down neural networks into interpretable units. However, the occurrence of polysemantic neurons, or neurons that respond to multiple unrelated…
Predictive coding is a unifying framework for understanding perception, action and neocortical organization. In predictive coding, different areas of the neocortex implement a hierarchical generative model of the world that is learned from…
In this paper, we present a new neural network model based on attribute-specific representations (e.g., color, shape, size), a classic example of associative memory. The proposed model is based on a previous study on memory and recall of…
In the past few years, the study of receptive field codes has been of large interest to mathematicians. Here we give a complete characterization of receptive field codes realizable by connected receptive fields and we give the minimal…
We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…
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…
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…
Place cells are neurons that act as biological position sensors, associated with and firing in response to regions of an environment to situate an organism in space. These associations are recorded in (combinatorial) neural codes,…
Color Appearance Models are biological networks that consist of a cascade of linear+nonlinear layers that modify the linear measurements at the retinal photo-receptors leading to an internal (nonlinear) representation of color that…
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,…