Computing With Residue Numbers in High-Dimensional Representation.

We introduce residue hyperdimensional computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using resources that scale only logarithmically with the range, a vast improvement over previous methods.

Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps.

We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in distributed representation. Spatial position is encoded in a residue number system, with individual residues represented by high-dimensional, complex-valued vectors. These are composed into a single vector representing position by a similarity-preserving, conjunctive vector-binding operation.

Computing with Residue Numbers in High-Dimensional Representation.

We introduce , a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using vastly fewer resources than previous methods, and it exhibits impressive robustness to noise.

Vector Symbolic Architectures as a Computing Framework for Emerging Hardware.

This article reviews recent progress in the development of the computing framework (also known as Hyperdimensional Computing). This framework is well suited for implementation in stochastic, emerging hardware and it naturally expresses the types of cognitive operations required for Artificial Intelligence (AI). We demonstrate in this article that the field-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 to modern computing.

Efficient optimization with higher-order ising machines.

A prominent approach to solving combinatorial optimization problems on parallel hardware is Ising machines, i.e., hardware implementations of networks of interacting binary spin variables.

Efficient Decoding of Compositional Structure in Holistic Representations.

We investigate the task of retrieving information from compositional distributed representations formed by hyperdimensional computing/vector symbolic architectures and present novel techniques that achieve new information rate bounds. First, we provide an overview of the decoding techniques that can be used to approach the retrieval task. The techniques are categorized into four groups.

Perceptron Theory Can Predict the Accuracy of Neural Networks.

Multilayer neural networks set the current state of the art for many technical classification problems. But, these networks are still, essentially, black boxes in terms of analyzing them and predicting their performance. Here, we develop a statistical theory for the one-layer perceptron and show that it can predict performances of a surprisingly large variety of neural networks with different architectures.

On separating long- and short-term memories in hyperdimensional computing.

Operations on high-dimensional, fixed-width vectors can be used to distribute information from several vectors over a single vector of the same width. For example, a set of key-value pairs can be encoded into a single vector with multiplication and addition of the corresponding key and value vectors: the keys are bound to their values with component-wise multiplication, and the key-value pairs are combined into a single superposition vector with component-wise addition. The superposition vector is, thus, a memory which can then be queried for the value of any of the keys, but the result of the query is approximate.

Hyperseed: Unsupervised Learning With Vector Symbolic Architectures.

Motivated by recent innovations in biologically inspired neuromorphic hardware, this article presents a novel unsupervised machine learning algorithm named Hyperseed that draws on the principles of vector symbolic architectures (VSAs) for fast learning of a topology preserving feature map of unlabeled data. It relies on two major operations of VSA, binding and bundling. The algorithmic part of Hyperseed is expressed within the Fourier holographic reduced representations (FHRR) model, which is specifically suited for implementation on spiking neuromorphic hardware.

Generalized Key-Value Memory to Flexibly Adjust Redundancy in Memory-Augmented Networks.

Memory-augmented neural networks enhance a neural network with an external key-value (KV) memory whose complexity is typically dominated by the number of support vectors in the key memory. We propose a generalized KV memory that decouples its dimension from the number of support vectors by introducing a free parameter that can arbitrarily add or remove redundancy to the key memory representation. In effect, it provides an additional degree of freedom to flexibly control the tradeoff between robustness and the resources required to store and compute the generalized KV memory.

Cellular Automata Can Reduce Memory Requirements of Collective-State Computing.

Various nonclassical approaches of distributed information processing, such as neural networks, reservoir computing (RC), vector symbolic architectures (VSAs), and others, employ the principle of collective-state computing. In this type of computing, the variables relevant in computation are superimposed into a single high-dimensional state vector, the collective state. The variable encoding uses a fixed set of random patterns, which has to be stored and kept available during the computation.

Variable Binding for Sparse Distributed Representations: Theory and Applications.

Variable binding is a cornerstone of symbolic reasoning and cognition. But how binding can be implemented in connectionist models has puzzled neuroscientists, cognitive psychologists, and neural network researchers for many decades. One type of connectionist model that naturally includes a binding operation is vector symbolic architectures (VSAs).

A Comprehensive Study of Complexity and Performance of Automatic Detection of Atrial Fibrillation: Classification of Long ECG Recordings Based on the PhysioNet Computing in Cardiology Challenge 2017.

Objective: The 2017 PhysioNet/CinC Challenge focused on automatic classification of atrial fibrillation (AF) in short ECGs. This study aimed to evaluate the use of the data and results from the challenge for detection of AF in longer ECGs, taken from three other PhysioNet datasets.

Approach: The used data-driven models were based on features extracted from ECG recordings, calculated according to three solutions from the challenge.

Integer Echo State Networks: Efficient Reservoir Computing for Digital Hardware.

We propose an approximation of echo state networks (ESNs) that can be efficiently implemented on digital hardware based on the mathematics of hyperdimensional computing. The reservoir of the proposed integer ESN (intESN) is a vector containing only n -bits integers (where is normally sufficient for a satisfactory performance). The recurrent matrix multiplication is replaced with an efficient cyclic shift operation.

Density Encoding Enables Resource-Efficient Randomly Connected Neural Networks.

The deployment of machine learning algorithms on resource-constrained edge devices is an important challenge from both theoretical and applied points of view. In this brief, we focus on resource-efficient randomly connected neural networks known as random vector functional link (RVFL) networks since their simple design and extremely fast training time make them very attractive for solving many applied classification tasks. We propose to represent input features via the density-based encoding known in the area of stochastic computing and use the operations of binding and bundling from the area of hyperdimensional computing for obtaining the activations of the hidden neurons.

Classification and Recall With Binary Hyperdimensional Computing: Tradeoffs in Choice of Density and Mapping Characteristics.

Hyperdimensional (HD) computing is a promising paradigm for future intelligent electronic appliances operating at low power. This paper discusses tradeoffs of selecting parameters of binary HD representations when applied to pattern recognition tasks. Particular design choices include density of representations and strategies for mapping data from the original representation.

Robust Methods for Automated Selection of Cardiac Signals After Blind Source Separation.

Objective: Novel minimum-contact vital signs monitoring techniques like textile or capacitive electrocardiogram (ECG) provide new opportunities for health monitoring. These techniques are sensitive to artifacts and require handling of unstable signal quality. Spatio-temporal blind source separation (BSS) is capable of processing suchlike multichannel signals.

A Theory of Sequence Indexing and Working Memory in Recurrent Neural Networks.

To accommodate structured approaches of neural computation, we propose a class of recurrent neural networks for indexing and storing sequences of symbols or analog data vectors. These networks with randomized input weights and orthogonal recurrent weights implement coding principles previously described in vector symbolic architectures (VSA) and leverage properties of reservoir computing. In general, the storage in reservoir computing is lossy, and crosstalk noise limits the retrieval accuracy and information capacity.

Holographic Graph Neuron: A Bioinspired Architecture for Pattern Processing.

In this paper, we propose a new approach to implementing hierarchical graph neuron (HGN), an architecture for memorizing patterns of generic sensor stimuli, through the use of vector symbolic architectures. The adoption of a vector symbolic representation ensures a single-layer design while retaining the existing performance characteristics of HGN. This approach significantly improves the noise resistance of the HGN architecture, and enables a linear (with respect to the number of stored entries) time search for an arbitrary subpattern.