IEEE Circuits and Systems Magazine - Q2 2020 - 31

classification, etc.-by representing different types of
data using hypervectors, whose dimensionality is in the
thousands, e.g., 10,000-d, where d refers to dimensionality. The human brain contains about 100 billion neurons
and 1000 trillion synapses; therefore all possible states of
a human brain can be described by a high-dimensional
vector. In that sense, HD computing is a form of braininspired computing. Randomly or pseudo-randomly defined, these hypervectors are composed of independent
and identically distributed (i.i.d.) components, which can
be binary, integer, real or complex [8]. As a brain-inspired
computing model, HD computing is robust, scalable, energy efficient and requires less time for training and inference [9]. These features are a result of its ultra-wide data
representation and underlying mathematical operations.
One thing that should be emphasized is the concept of
orthogonality of the hypervectors.
The remainder of this paper is organized as follows.
Section II presents the background on HD computing,
including the data representation, data transformation
and similarity measurement. Section III illustrates the
general methodology in HD computing and its applicability in learning and inference tasks. Then two common
encoding methods to form hypervectors from the input
data are presented, and strategies to improve accuracy
and/or efficiency are pointed out. Some classical applications as well as several sophisticated designs are
reviewed in Section IV. Possible future directions of HD
computing are also pointed out in this section. Finally,
Section V concludes the paper.
II. Background on HD Computing
In this section, we review HD computing and present a
comparison between HD and classical computing. We

also describe the similarity metrics for hypervectors and
typical mathematical operations used in HD computing.
A. Classical Computing vs HD Computing
Data representation, data transformation and data retrieval play an important role in any computing system.
To be more specific, classical computing deals with bits.
Each bit is 0 or 1. This can be realized by the absence or
presence of electric charge. In terms of computation, data
transformation is inevitable. The arithmetic/logic unit
(ALU) computes new data using logical operation and four
arithmetic operations, including addition, subtraction,
multiplication and division [10]. The main memory allows
the data to be written and read. C
- ompared to classical
computing, HD computing employs hypervectors as its
data type, whose dimensionality is typically in the thousands. These ultra-wide words introduce redundancy
against noise, and are, therefore, inherently robust.
To transform data, HD computing performs three operations: multiplication, addition and permutation. HD
computing transforms the input hypervectors, which are
pre-stored in the item memory to form associations or
connections. In a classification problem, the hypervectors associated with classes are trained during training
process. During the testing process, the test hypervectors are compared with the class hypervectors. The hypervectors generated from training data are referred to
as class hypervectors and are stored in the associative
memory, while those generated from the test data are referred to as query hypervectors. An associative search
is performed to make a prediction as to which class a
given query hypervector most likely belongs. A comparison -between the classical and HD computing paradigms is summarized in Table 1. -Traditional -classification

Table 1.
Comparisons between classical computing and HD computing for classification.
Computing Paradigm

Classical Computing

HD Computing

Data Type

Bit

Hypervector

Data Transformation

Addition, Multiplication, Logic

Add-Multiply-Permute

Storage

Memory

Item Memory, Associative Memory

Training

Weights

Class Hypervectors

Testing

Run Pre-trained Classifier

Associate Query Hypervectors with Class Hypervectors

Model Complexity

High

Low

Accuracy

Very High

Acceptable

Feature Extraction

Easy

Difficult

Number of Features

Many

One

Lulu Ge and Keshab K. Parhi are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA
(e-mail: ge000567@umn.edu, parhi@umn.edu)
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