Related papers: Neural Codes With Three Maximal Codewords: Convexi…
We study the parameterized complexity of training two-layer neural networks with respect to the dimension of the input data and the number of hidden neurons, considering ReLU and linear threshold activation functions. Albeit the…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Speech coding facilitates the transmission of speech over low-bandwidth networks with minimal distortion. Neural-network based speech codecs have recently demonstrated significant improvements in quality over traditional approaches. While…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
A basic problem for constant dimension codes is to determine the maximum possible size $A_q(n,d;k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$, called codewords, such that the subspace distance satisfies…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…
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…
Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…
The high computational complexity and increasing parameter counts of deep neural networks pose significant challenges for deployment in resource-constrained environments, such as edge devices or real-time systems. To address this, we…
The Nearest Neighbor (NN) Representation is an emerging computational model that is inspired by the brain. We study the complexity of representing a neuron (threshold function) using the NN representations. It is known that two anchors (the…
Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…
In general, approximating classes of functions defined over high-dimensional input spaces by linear combinations of a fixed set of basis functions or ``features'' is known to be hard. Typically, the worst-case error of the best basis set…
A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the…
In this work we consider a generalization of the well-studied problem of coding for ``stuck-at'' errors, which we refer to as ``strong stuck-at'' codes. In the traditional framework of stuck-at codes, the task involves encoding a message…
Convolutional neural networks have achieved astonishing results in different application areas. Various methods which allow us to use these models on mobile and embedded devices have been proposed. Especially binary neural networks seem to…
In this paper we give a compact presentation of the theory of abstract spaces for convolutional codes and convolutional encoders, and show a connection between them that seems to be missing in the literature. We use it for a short proof of…
Neural networks are typically represented as data structures that are traversed either through iteration or by manual chaining of method calls. However, a deeper analysis reveals that structured recursion can be used instead, so that…
Semantic code search is the task of retrieving relevant code snippet given a natural language query. Different from typical information retrieval tasks, code search requires to bridge the semantic gap between the programming language and…
Small neural networks (NNs) used for error correction were shown to improve on classic channel codes and to address channel model changes. We extend the code dimension of any such structure by using the same NN under one-hot encoding…
Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…