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A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformations

arXiv.org Artificial Intelligence

This two-part comprehensive survey is devoted to a computing framework most commonly known under the names Hyperdimensional Computing and Vector Symbolic Architectures (HDC/VSA). Both names refer to a family of computational models that use high-dimensional distributed representations and rely on the algebraic properties of their key operations to incorporate the advantages of structured symbolic representations and vector distributed representations. Notable models in the HDC/VSA family are Tensor Product Representations, Holographic Reduced Representations, Multiply-Add-Permute, Binary Spatter Codes, and Sparse Binary Distributed Representations but there are other models too. HDC/VSA is a highly interdisciplinary area with connections to computer science, electrical engineering, artificial intelligence, mathematics, and cognitive science. This fact makes it challenging to create a thorough overview of the area. However, due to a surge of new researchers joining the area in recent years, the necessity for a comprehensive survey of the area has become extremely important. Therefore, amongst other aspects of the area, this Part I surveys important aspects such as: known computational models of HDC/VSA and transformations of various input data types to high-dimensional distributed representations. Part II of this survey is devoted to applications, cognitive computing and architectures, as well as directions for future work. The survey is written to be useful for both newcomers and practitioners.


Vector Symbolic Architectures as a Computing Framework for Nanoscale Hardware

arXiv.org Artificial Intelligence

This article reviews recent progress in the development of the computing framework Vector Symbolic Architectures (also known as Hyperdimensional Computing). This framework is well suited for implementation in stochastic, nanoscale hardware and it naturally expresses the types of cognitive operations required for Artificial Intelligence (AI). We demonstrate in this article that the ring-like algebraic structure of Vector Symbolic Architectures offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant in modern computing. In addition, we illustrate the distinguishing feature of Vector Symbolic Architectures, "computing in superposition," which sets it apart from conventional computing. This latter property opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. Vector Symbolic Architectures are Turing complete, as we show, and we see them acting as a framework for computing with distributed representations in myriad AI settings. This paper serves as a reference for computer architects by illustrating techniques and philosophy of VSAs for distributed computing and relevance to emerging computing hardware, such as neuromorphic computing.


Recursive Binding for Similarity-Preserving Hypervector Representations of Sequences

arXiv.org Artificial Intelligence

Hyperdimensional computing (HDC), also known as vector symbolic architectures (VSA), is a computing framework used within artificial intelligence and cognitive computing that operates with distributed vector representations of large fixed dimensionality. A critical step for designing the HDC/VSA solutions is to obtain such representations from the input data. Here, we focus on sequences and propose their transformation to distributed representations that both preserve the similarity of identical sequence elements at nearby positions and are equivariant to the sequence shift. These properties are enabled by forming representations of sequence positions using recursive binding and superposition operations. The proposed transformation was experimentally investigated with symbolic strings used for modeling human perception of word similarity. The obtained results are on a par with more sophisticated approaches from the literature. The proposed transformation was designed for the HDC/VSA model known as Fourier Holographic Reduced Representations. However, it can be adapted to some other HDC/VSA models.


Commentaries on "Learning Sensorimotor Control with Neuromorphic Sensors: Toward Hyperdimensional Active Perception" [Science Robotics Vol. 4 Issue 30 (2019) 1-10

arXiv.org Artificial Intelligence

This correspondence comments on the findings reported in a recent Science Robotics article by Mitrokhin et al. [1]. The main goal of this commentary is to expand on some of the issues touched on in that article. Our experience is that hyperdimensional computing is very different from other approaches to computation and that it can take considerable exposure to its concepts before attaining practically useful understanding. Therefore, in order to provide an overview of the area to the first time reader of [1], the commentary includes a brief historic overview as well as connects the findings of the article to a larger body of literature existing in the area. I. INTRODUCTION The recent article by A. Mitrokhin, P. Sutor, C. Ferm├╝ller, and Y. Aloimonos, "Learning Sensorimotor Control with Neuromorphic Sensors: Toward Hyperdimensional Active Perception", which appeared in Science Robotics vol. 4 issue 30 (2019), presents a case for using a computation framework called hyperdimensional computing also known as Vector Symbolic Architectures (VSAs) for fusing motoric abilities of a robot with its perception system. The idea of computing with random vectors as basic objects is also known as Holographic Reduced Representation [2], Multiply-Add-Permute [3], Binary Spatter Codes [4], Binary Sparse Distributed Codes [5], Matrix Binding of Additive Terms [6], and Semantic Pointer Architecture [7]. All these frameworks are essentially equivalent. In the light of the present very high level of attention to the area of autonomous AIempowered systems from the industry and the society, we hope and believe that the application of VSAs in robotics will get an appropriately increasing attention from the community of AI/robotics researchers and practitioners. Our own experience with VSAs has shown that due to its considerable difference from the conventional computing paradigms the development of intuition and understanding required for practical applications needs to be supported by extended exposure to the details and interpretation of VSAs.


Classification using Hyperdimensional Computing: A Review

arXiv.org Artificial Intelligence

Hyperdimensional (HD) computing is built upon its unique data type referred to as hypervectors. The dimension of these hypervectors is typically in the range of tens of thousands. Proposed to solve cognitive tasks, HD computing aims at calculating similarity among its data. Data transformation is realized by three operations, including addition, multiplication and permutation. Its ultra-wide data representation introduces redundancy against noise. Since information is evenly distributed over every bit of the hypervectors, HD computing is inherently robust. Additionally, due to the nature of those three operations, HD computing leads to fast learning ability, high energy efficiency and acceptable accuracy in learning and classification tasks. This paper introduces the background of HD computing, and reviews the data representation, data transformation, and similarity measurement. The orthogonality in high dimensions presents opportunities for flexible computing. To balance the tradeoff between accuracy and efficiency, strategies include but are not limited to encoding, retraining, binarization and hardware acceleration. Evaluations indicate that HD computing shows great potential in addressing problems using data in the form of letters, signals and images. HD computing especially shows significant promise to replace machine learning algorithms as a light-weight classifier in the field of internet of things (IoTs).