Related papers: Strengthening Relationships between Neural Ideals …
A neural code $\mathcal{C}$ is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from place cells, neurons that respond to geographic stimulus. In…
Neural codes, represented as collections of binary strings, encode neural activity and show relationships among stimuli. Certain neurons, called place cells, have been shown experimentally to fire in convex regions in space. A natural…
A major area in neuroscience research is the study of how the brain processes spatial information. Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps,…
The neural ideal of a binary code $\mathbb{C} \subseteq \mathbb{F}_2^n$ is an ideal in $\mathbb{F}_2[x_1,\ldots, x_n]$ closely related to the vanishing ideal of $\mathbb{C}$. The neural ideal, first introduced by Curto et al, provides an…
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer…
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties…
Neural codes are binary codes that are used for information processing and representation in the brain. In previous work, we have shown how an algebraic structure, called the {\it neural ring}, can be used to efficiently encode geometric…
Neural codes form an algebraic framework to study the nervous system, and understanding neural codes is a key goal of mathematical neuroscience. Neural rings and ideals are the tools connecting neuroscience and commutative algebra. In this…
Neural codes, represented as collections of binary strings called codewords, are used to encode neural activity. A code is called convex if its codewords are represented as an arrangement of convex open sets in Euclidean space. Previous…
A combinatorial neural code is a subset of the power set $2^{[n]}$ on $[n]=\{1,\dots, n\}$, in which each $1\leq i\leq n$ represents a neuron and each element (codeword) represents the co-firing event of some neurons. Consider a space…
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…
The "neural code" is the way the brain characterizes, stores, and processes information. Unraveling the neural code is a key goal of mathematical neuroscience. Topology, coding theory, and, recently, commutative algebra are some the…
In this paper, we propose convolutional neural networks for learning an optimal representation of question and answer sentences. Their main aspect is the use of relational information given by the matches between words from the two members…
The brain processes information about the environment via neural codes. The neural ideal was introduced recently as an algebraic object that can be used to better understand the combinatorial structure of neural codes. Every neural ideal…
In this work, we explain in detail how receptive fields, effective receptive fields, and projective fields of neurons in different layers, convolution or pooling, of a Convolutional Neural Network (CNN) are calculated. While our focus here…
Although neural machine translation with the encoder-decoder framework has achieved great success recently, it still suffers drawbacks of forgetting distant information, which is an inherent disadvantage of recurrent neural network…
Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still…
We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly…
We describe how hierarchical concepts can be represented in three types of layered neural networks. The aim is to support recognition of the concepts when partial information about the concepts is presented, and also when some of the…
In many scenarios, human decisions are explained based on some high-level concepts. In this work, we take a step in the interpretability of neural networks by examining their internal representation or neuron's activations against concepts.…