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1. Resonator Networks, 1: An Efficient Solution for Factoring High-Dimensional, Distributed Representations of Data Structures

   https://doi.org/https://doi.org/10.1162/neco_a_01331  

   Frady, E. Paxon; Kent, Spencer J.; Olshausen, Bruno A.; Sommer, Friedrich (December 2020, Neural computation)

   null (Ed.)

   The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of cognition. Here we show how this may be accomplished within the framework of Vector Symbolic Architectures (VSAs) (Plate, 1991; Gayler, 1998; Kanerva, 1996), whereby data structures are encoded by combining high-dimensional vectors with operations that together form an algebra on the space of distributed representations. In particular, we propose an efficient solution to a hard combinatorial search problem that arises when decoding elements of a VSA data structure: the factorization of products of multiple codevectors. Our proposed algorithm, called a resonator network, is a new type of recurrent neural network that interleaves VSA multiplication operations and pattern completion. We show in two examples—parsing of a tree-like data structure and parsing of a visual scene—how the factorization problem arises and how the resonator network can solve it. More broadly, resonator networks open the possibility of applying VSAs to myriad artificial intelligence problems in real-world domains. The companion article in this issue (Kent, Frady, Sommer, & Olshausen, 2020) presents a rigorous analysis and evaluation of the performance of resonator networks, showing it outperforms alternative approaches. 

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2. Computing on Functions Using Randomized Vector Representations

   Frady, E. Paxon; Kleyko, Denis; Kymn, Christopher J.; Olshausen, Bruno A.; Sommer, Friedrich T. (September 2021, ArXivorg)

   null (Ed.)

   Vector space models for symbolic processing that encode symbols by random vectors have been proposed in cognitive science and connectionist communities under the names Vector Symbolic Architecture (VSA), and, synonymously, Hyperdimensional (HD) computing. In this paper, we generalize VSAs to function spaces by mapping continuous-valued data into a vector space such that the inner product between the representations of any two data points represents a similarity kernel. By analogy to VSA, we call this new function encoding and computing framework Vector Function Architecture (VFA). In VFAs, vectors can represent individual data points as well as elements of a function space (a reproducing kernel Hilbert space). The algebraic vector operations, inherited from VSA, correspond to well-defined operations in function space. Furthermore, we study a previously proposed method for encoding continuous data, fractional power encoding (FPE), which uses exponentiation of a random base vector to produce randomized representations of data points and fulfills the kernel properties for inducing a VFA. We show that the distribution from which elements of the base vector are sampled determines the shape of the FPE kernel, which in turn induces a VFA for computing with band-limited functions. In particular, VFAs provide an algebraic framework for implementing large-scale kernel machines with random features, extending Rahimi and Recht, 2007. Finally, we demonstrate several applications of VFA models to problems in image recognition, density estimation and nonlinear regression. Our analyses and results suggest that VFAs constitute a powerful new framework for representing and manipulating functions in distributed neural systems, with myriad applications in artificial intelligence. 

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3. Efficient Decoding of Compositional Structure in Holistic Representations

   Kleyko, Denis; Bybee, Connor; Huang, Ping-Chen; Kymn, Christopher J.; Olshausen, Bruno A.; Frady, E. Paxon; Sommer, Friedrich T. (June 2023, Neural computation)

   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. We then evaluate the considered techniques in several settings that involve, for example, inclusion of external noise and storage elements with reduced precision. In particular, we find that the decoding techniques from the sparse coding and compressed sensing literature (rarely used for hyperdimensional computing/vector symbolic architectures) are also well suited for decoding information from the compositional distributed representations.Combining these decoding techniqueswith interference cancellation ideas from communications improves previously reported bounds (Hersche et al., 2021) of the information rate of the distributed representations from 1.20 to 1.40 bits per dimension for smaller codebooks and from 0.60 to 1.26 bits per dimension for larger codebooks. 

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4. Holographic Declarative Memory: Distributional Semantics as the Architecture of Memory

   https://doi.org/10.1111/cogs.12904  

   Kelly, Mary Alexandria; Arora, Nipun; West, Robert L.; Reitter, David (November 2020, Cognitive Science)

   Abstract We demonstrate that the key components of cognitive architectures (declarative and procedural memory) and their key capabilities (learning, memory retrieval, probability judgment, and utility estimation) can be implemented as algebraic operations on vectors and tensors in a high‐dimensional space using a distributional semantics model. High‐dimensional vector spaces underlie the success of modern machine learning techniques based on deep learning. However, while neural networks have an impressive ability to process data to find patterns, they do not typically model high‐level cognition, and it is often unclear how they work. Symbolic cognitive architectures can capture the complexities of high‐level cognition and provide human‐readable, explainable models, but scale poorly to naturalistic, non‐symbolic, or big data. Vector‐symbolic architectures, where symbols are represented as vectors, bridge the gap between the two approaches. We posit that cognitive architectures, if implemented in a vector‐space model, represent a useful, explanatory model of the internal representations of otherwise opaque neural architectures. Our proposed model, Holographic Declarative Memory (HDM), is a vector‐space model based on distributional semantics. HDM accounts for primacy and recency effects in free recall, the fan effect in recognition, probability judgments, and human performance on an iterated decision task. HDM provides a flexible, scalable alternative to symbolic cognitive architectures at a level of description that bridges symbolic, quantum, and neural models of cognition. 

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5. Neuromorphic visual scene understanding with resonator networks

   https://doi.org/10.1038/s42256-024-00848-0  

   Renner, Alpha; Supic, Lazar; Danielescu, Andreea; Indiveri, Giacomo; Olshausen, Bruno A; Sandamirskaya, Yulia; Sommer, Friedrich T; Frady, E Paxon (June 2024, Nature Machine Intelligence)

   Analysing a visual scene by inferring the configuration of a generative model is widely considered the most flexible and generalizable approach to scene understanding. Yet, one major problem is the computational challenge of the inference procedure, involving a combinatorial search across object identities and poses. Here we propose a neuromorphic solution exploiting three key concepts: (1) a computational framework based on vector symbolic architectures (VSAs) with complex-valued vectors, (2) the design of hierarchical resonator networks to factorize the non-commutative transforms translation and rotation in visual scenes and (3) the design of a multi-compartment spiking phasor neuron model for implementing complex-valued resonator networks on neuromorphic hardware. The VSA framework uses vector binding operations to form a generative image model in which binding acts as the equivariant operation for g eo me tric t ra nsformations. A scene can therefore be described as a sum of vector products, which can then be efficiently factorized by a resonator network to infer objects and their poses. The hierarchical resonator network features a partitioned architecture in which vector binding is equivariant for horizontal and vertical translation within one partition and for rotation and scaling within the other partition. The spiking neuron model allows mapping the resonator network onto efficient and low-power neuromorphic hardware. Our approach is demonstrated on synthetic scenes composed of simple two-dimensional shapes undergoing rigid geometric transformations and colour changes. A companion paper demonstrates the same approach in real-world application scenarios for machine vision and robotics. 

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