A Neuro-vector-symbolic Architecture for Solving Raven's Progressive Matrices

Abstract

Neither deep neural networks nor symbolic AI alone have approached the kind of intelligence expressed in humans. This is mainly because neural networks are not able to decompose distinct objects from their joint representation (the so-called binding problem), while symbolic AI suffers from exhaustive rule searches, among other problems. These two problems are still pronounced in neuro-symbolic AI which aims to combine the best of the two paradigms.Here, we show that the two problems can be addressed with our proposed neuro-vector-symbolic architecture (NVSA) by exploiting its powerful operators on fixed-width holographic vectorized representations that serve as a common language between neural networks and symbolic logical reasoning. The efficacy of NVSA is demonstrated by solving the Raven's progressive matrices. NVSA achieves a new record of 97.7% average accuracy in RAVEN, and 98.8% in I-RAVEN datasets, with two orders of magnitude faster execution than the symbolic logical reasoning on CPUs.Human fluid intelligence is the ability to think and reason abstractly, and make inferences in a novel domain. The Raven's progressive matrices (RPM) 1 test has been a widely-used assessment of fluid intelligence and abstract reasoning 2,3 . The RPM is a non-verbal test which involves perceiving pattern continuation, element abstraction, and finding relations between abstract elements based on underlying rules. Each RPM test is an analogy problem presented as a 3×3 pictorial matrix of context panels. Every panel in the matrix is filled with several geometric objects based on a certain rule, except the last panel which is left blank. The participants are asked to complete the missing panel in the matrix by picking the correct answer from a set of candidate answer panels that matches the implicit rule (see Methods and Supplementary Fig. 1). Solving this test mainly involves two aspects of intelligence: visual perception and abstract reasoning.As opposed to deep learning methods that blend perception and reasoning in a monolithic model [4][5][6] , the reasoning capability is not necessarily interwoven with the visual perception in humans. For instance, one can close one's eyes and build a scene representation through touch, followed by reasoning that remains effortless without the vision 7 . This decoupling is at the core of hybrid systems that advocate combining subsymbolic (e.g., neural networks) with symbolic artificial intelligence, aiming to reach human-level generalization [8][9][10][11] . Among the hybrid systems, neuro-symbolic architectures separately handle the perception and reasoning aspects by using a combination of neural networks and symbolic approaches. Considerable effort has been devoted to integrate these two paradigms that led to the state-of-the-art performance of neuro-symbolic architectures in various tasks, e.g., visual question answering 7,12,13 , causal video reasoning 14 , and solving RPM 15 . However, the resulting neuro-symbolic architectures are not immune to the potential problems of their indiv...

A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges

“…All of the previously described studies have two limitations: First, they assume the perception system provides the symbolic representations that support the reasoning for solving Raven's Progressive Matrices test, and, second, they only support the progression rule. [144] addressed these limitations by positioning VSA/HDC as a common language between a neural network (to solve the perception issue) and a symbolic logical reasoning engine (to support more rules). Specifically, it exploited the superposition of multiplicative bindings in a neural network to describe raw sensory visual objects in a panel and used Fourier Holographic Reduced Representations (FHRR) to efficiently emulate a symbolic logical reasoning with a rich set of rules [144].…”

Deep Non-Monotonic Reasoning for Visual Abstract Reasoning Tasks

“…Neuro-symbolic approach and the next approach are data-driven approach, whereas the first two approaches are knowledge-based approaches. Examples of neuro-symbolic models for solving RPM-like tasks include ALANS2, PrAE, VAE-GPP, TRIVR, LoGe, and NVSA (Zhang et al, 2020(Zhang et al, , 2021Shi et al, 2021;He et al, 2021;Yu et al, 2021;Hersche et al, 2022).…”

Achieving software-equivalent accuracy for hyperdimensional computing with ferroelectric-based in-memory computing

“…5.5 7.1 7.9 9.5 9.5 9.5 6. 5 www.nature.com/scientificreports/ implementation on average achieves 1.24x and 1.31x energy improvement compared to 2-bit and 3-bit implementations, respectively. These improvements are associated with the higher ML and DL voltages (see Supplementary Fig.…”