Related papers: On Ternary Coding and Three-Valued Logic
Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let $\alpha $ be a generator of…
This paper introduces the Trinary decision tree, an algorithm designed to improve the handling of missing data in decision tree regressors and classifiers. Unlike other approaches, the Trinary decision tree does not assume that missing…
We present an algorithm, called the Offset Tree, for learning to make decisions in situations where the payoff of only one choice is observed, rather than all choices. The algorithm reduces this setting to binary classification, allowing…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
Since most machine learning (ML) algorithms are designed for numerical inputs, efficiently encoding categorical variables is a crucial aspect in data analysis. A common problem are high cardinality features, i.e. unordered categorical…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…
Consider a binary classification problem solved using a feed-forward artificial neural network (ANN). Let the ANN be composed of a ReLU layer and several linear layers (convolution, sum-pooling, or fully connected). We assume the network…
Why do neurons encode information the way they do? Normative answers to this question model neural activity as the solution to an optimisation problem; for example, the celebrated efficient coding hypothesis frames neural activity as the…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…
Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated the advantage over linear ones due to their…
The binary string matching problem consists in finding all the occurrences of a pattern in a text where both strings are built on a binary alphabet. This is an interesting problem in computer science, since binary data are omnipresent in…
An agent who lacks preferences and instead makes decisions using criteria that are costly to create should select efficient sets of criteria, where the cost of making a given number of choice distinctions is minimized. Under mild…
The Syndrome Decoding problem is at the core of many code-based cryptosystems. In this paper, we study ternary Syndrome Decoding in large weight. This problem has been introduced in the Wave signature scheme but has never been thoroughly…
We propose a new ternary spiking neuron model to improve the representation capacity of binary spiking neurons in deep Q-learning. Although a ternary neuron model has recently been introduced to overcome the limited representation capacity…
Some crucial decisions in AI design tend to be overlooked or factor choices are assumed implicitly. The question often answered first is what the AI will do, not how it will interact with the rest of the world. This reduces our…
We present an alternative layer to convolution layers in convolutional neural networks (CNNs). Our approach reduces the complexity of convolutions by replacing it with binary decisions. Those binary decisions are used as indexes to…
Search-based dialog models typically re-encode the dialog history at every turn, incurring high cost. Curved Contrastive Learning, a representation learning method that encodes relative distances between utterances into the embedding space…