Large language models (LLMs) have significantly transformed the landscape of artificial intelligence, demonstrating exceptional capabilities in natural language understanding and generation. Recently, the integration of LLMs with neurosymbolic architectures has gained traction to enhance contextual awareness and planning capabilities. However, this integration faces computational challenges that hinder scalability and efficiency, especially in edge computing environments. This paper provides an in-depth analysis of these challenges and explores state-of-the-art solutions, focusing on memory-centric computing principles at both algorithmic and hardware levels. Our exploration is centered around the key computational elements of the Transformer, the foundation of all LLMs, and vector-symbolic architecture, the leading neuro-symbolic model for edge applications. Additionally, we propose potential research directions for further investigation. By examining these aspects, this paper aims to bridge critical gaps in the path toward effective artificial general intelligence at the edge.

, 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. We demonstrate the potential for this framework to solve computationally difficult problems in visual perception and combinatorial optimization, showing improvement over baseline methods. More broadly, the framework provides a possible account for the computational operations of grid cells in the brain, and it suggests new machine learning architectures for representing and manipulating numerical data.

(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. In addition, we illustrate the distinguishing feature of Vector Symbolic Architectures, "computing in superposition," which sets it apart from conventional computing. It also opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. We sketch ways of demonstrating that Vector Symbolic Architectures are computationally universal. We see them acting as a framework for computing with distributed representations that can play a role of an abstraction layer for emerging computing hardware. This article serves as a reference for computer architects by illustrating the philosophy behind Vector Symbolic Architectures, techniques of distributed computing with them, and their relevance to emerging computing hardware, such as neuromorphic computing.

Abstract High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory and lexical information for many tasks related to human-generated data. Human language makes use of a large and varying number of features, lexical and constructional items as well as contextual and discourse-specific data of various types, which all interact to represent various aspects of communicative information. Some of these features are mostly local and useful for the organisation of, for example, argument structure of a predication; others are persistent over the course of a discourse and necessary for achieving a reasonable level of understanding of the content. This paper describes a model for high-dimensional representation for utterance and text-level data including features such as constructions or contextual data, based on a mathematically principled and behaviourally plausible approach to representing linguistic information. The implementation of the representation is a straightforward extension of Random Indexing models previously used for lexical linguistic items. The paper shows how the implementedmodel is able to represent a broad range of linguistic features in a common integral framework of fixed dimensionality, which is computationally habitable, and which is suitable as a bridge between symbolic representations such as dependency analysis and continuous representations used, for example, in classifiers or further machine-learning approaches. This is achieved with operations on vectors that constitute a powerful computational algebra, accompanied with an associative memory for the vectors. The paper provides a technical overview of the framework and a worked through implemented example of how it can be applied to various types of linguistic features.

Recognizing the very size of the brain's circuits, hyperdimensional (HD) computing can model neural activity patterns with points in a HD space, that is, with HD vectors. Key examined properties of HD computing include: a versatile set of arithmetic operations on HD vectors, generality, scalability, analyzability, one-shot learning, and energy efficiency. These make it a prime candidate for efficient biosignal processing where signals are noisy and nonstationary, training data sets are not huge, individual variability is significant, and energy-efficiency constraints are tight. Purely based on native HD computing operators, we describe a combined method for multiclass learning and classification of various ExG biosignals such as electromyography (EMG), electroencephalography (EEG), and electrocorticography (ECoG). We develop a full set of HD network templates that comprehensively encode body potentials and brain neural activity recorded from different electrodes into a single HD vector without requiring domain expert knowledge or ad hoc electrode selection process. Such encoded HD vector is processed as a single unit for fast one-shot learning, and robust classification. It can be interpreted to identify the most useful features as well. Compared to state-of-the-art counterparts, HD computing enables online, incremental, and fast learning as it demands less than a third as much training data as well as less preprocessing.

Distributed associative memory architectures store data in multiple locations redundantly, and are thus robust to circuit irregularities and noise. In this paper we explain ways to store the occurrence statistics of vectors in a distributed memory. Sparse data vectors are used to maximize vector capacity, and binding of sparse vectors is used to combine elementary symbols into symbols that represent larger entities. The use of such statistics is demonstrated with an on-line learning example that uses redundancy reduction. We show that occurrence statistics can be represented with distributed Willshaw-type associative memories sing hardware counters, as well as symbolically using two-bit memory cells.

The mathematical properties of high-dimensional (HD) spaces show remarkable agreement with behaviors controlled by the brain. Computing with HD vectors, referred to as "hypervectors," is a brain-inspired alternative to computing with numbers. Hypervectors are high-dimensional, holographic, and (pseudo)random with independent and identically distributed (i.i.d.) components. They provide for energy-efficient computing while tolerating hardware variation typical of nanoscale fabrics. We describe a hardware architecture for a hypervector-based classifier and demonstrate it with language identification from letter trigrams. The HD classifier is 96.7% accurate, 1.2% lower than a conventional machine learning method, operating with half the energy. Moreover, the HD classifier is able to tolerate 8.8-fold probability of failure of memory cells while maintaining 94% accuracy. This robust behavior with erroneous memory cells can significantly improve energy efficiency.

In this paper we present a CMOS implementation of a 512×512-cell Associative Content Addressable Memory (ACAM) in 180 nm CMOS. The memory can be operated either as an associative CAM or it can be configured into a Willshaw memory for operating with sparse data. The vector matching operation can use a tunable hit threshold or the strongest hit can be selected with a winner-take-all (WTA) network. Built-in row and column circuitry can perform logic operations on the contents of the row and column memories. The operation of the circuit is verified experimentally with an example on computing with random vectors.

Associative memories, in contrast to conventional address-based memories, are inherently fault-tolerant and allow retrieval of data based on partial search information. This paper considers the possibility of implementing large-scale associative memories through memristive devices jointly with CMOS circuitry. An advantage of a memristive associative memory is that the memory elements are located physically above the CMOS layer, which yields more die area for the processing elements realized in CMOS. This allows for high-capacity memories even while using an older CMOS technology, as the capacity of the memory depends more on the feature size of the memristive crossbar than on that of the CMOS components. In this paper, we propose the memristive implementations, and present simulations and error analysis of the autoassociative content-addressable memory, the Willshaw memory, and the sparse distributed memory. Furthermore, we present a CMOS cell that can be used to implement the proposed memory architectures.