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Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…
To evaluate the nature of the neural code in the cerebral cortex, we have used a combination of theory and experiment to assess how information is represented in a realistic cortical population response. We have shown how a sensory stimulus…
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…
When a neural network (NN) is used to decode a polar code, its training complexity scales exponentially as the code block size (or to be precise, as a number of message bits) increases. Therefore, existing solutions that use a neural…
A combinatorial code $\mathcal{C}$ is a collection of subsets of $[n]$, or equivalently a set of points in $\{0,1\}^n$. A morphism of codes is a map from one combinatorial code to another such that the coordinates of points in the image can…
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…
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 article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
Convolutional neural network (CNN) is a neural network that can make use of the internal structure of data such as the 2D structure of image data. This paper studies CNN on text categorization to exploit the 1D structure (namely, word…
We provide a comparative study between neural word representations and traditional vector spaces based on co-occurrence counts, in a number of compositional tasks. We use three different semantic spaces and implement seven tensor-based…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…
In this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a {\it junta}; i.e. a subspace code in which all codewords…
The neural coding is yet to be discovered. The neuronal operational modes that arise with fixed inputs but with varying degrees of stimulation help to elucidate their coding properties. In neurons receiving {\it in vivo} stimulation, we…
Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal…
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…
Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly…