Related papers: On Ternary Coding and Three-Valued Logic
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
The binary neural network, largely saving the storage and computation, serves as a promising technique for deploying deep models on resource-limited devices. However, the binarization inevitably causes severe information loss, and even…
Inference time, model size, and accuracy are critical for deploying deep neural network models. Numerous research efforts have been made to compress neural network models with faster inference and higher accuracy. Pruning and quantization…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
Recent research (arXiv:2310.11453, arXiv:2402.17764) has proposed binary and ternary transformer networks as a way to significantly reduce memory and improve inference speed in Large Language Models (LLMs) while maintaining accuracy. In…
In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…
Unary coding is useful but it is redundant in its standard form. Unary coding can also be seen as spatial coding where the value of the number is determined by its place in an array. Motivated by biological finding that several neurons in…
Recently, it has been observed that {0,1,-1}-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform {-1,1}-binary codes in image retrieval. To obtain better ternary codes, we for the first time…
As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight…
Classification with a large number of classes is a key problem in machine learning and corresponds to many real-world applications like tagging of images or textual documents in social networks. If one-vs-all methods usually reach top…
Ordinary binary multiplication of natural numbers can be generalized in a non-trivial way to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of `3-primality' -- primality with…
This paper considers the enumeration of ternary trees (i.e. rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…
This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…
Embedding models have become essential tools in both natural language processing and computer vision, enabling efficient semantic search, recommendation, clustering, and more. However, the high memory and computational demands of…
Binary codes are widely used to represent the data due to their small storage and efficient computation. However, there exists an ambiguity problem that lots of binary codes share the same Hamming distance to a query. To alleviate the…
The growing amount of data available in modern-day datasets makes the need to efficiently search and retrieve information. To make large-scale search feasible, Distance Estimation and Subset Indexing are the main approaches. Although binary…