Systematic Abductive Reasoning via Diverse Relation Representations in Vector-symbolic Architecture

In abstract visual reasoning, monolithic deep learning models suffer from limited interpretability and generalization, while existing neuro-symbolic approaches fall short in capturing the diversity and systematicity of attributes and relation representations. To address these challenges, we propose a Systematic Abductive Reasoning model with diverse relation representations (Rel-SAR) in Vector-symbolic Architecture (VSA) to solve Raven's Progressive Matrices (RPM). To derive attribute representations with symbolic reasoning potential, we introduce not only various types of atomic vectors that represent numeric, periodic and logical semantics, but also the structured high-dimentional representation (SHDR) for the overall Grid component. For systematic reasoning, we propose novel numerical and logical relation functions and perform rule abduction and execution in a unified framework that integrates these relation representations. Experimental results demonstrate that Rel-SAR achieves significant improvement on RPM tasks and exhibits robust out-of-distribution generalization. Rel-SAR leverages the synergy between HD attribute representations and symbolic reasoning to achieve systematic abductive reasoning with both interpretable and computable semantics.

Vector-Symbolic Architecture for Event-Based Optical Flow

From a perspective of feature matching, optical flow estimation for event cameras involves identifying event correspondences by comparing feature similarity across accompanying event frames. In this work, we introduces an effective and robust high-dimensional (HD) feature descriptor for event frames, utilizing Vector Symbolic Architectures (VSA). The topological similarity among neighboring variables within VSA contributes to the enhanced representation similarity of feature descriptors for flow-matching points, while its structured symbolic representation capacity facilitates feature fusion from both event polarities and multiple spatial scales. Based on this HD feature descriptor, we propose a novel feature matching framework for event-based optical flow, encompassing both model-based (VSA-Flow) and self-supervised learning (VSA-SM) methods. In VSA-Flow, accurate optical flow estimation validates the effectiveness of HD feature descriptors. In VSA-SM, a novel similarity maximization method based on the HD feature descriptor is proposed to learn optical flow in a self-supervised way from events alone, eliminating the need for auxiliary grayscale images. Evaluation results demonstrate that our VSA-based method achieves superior accuracy in comparison to both model-based and self-supervised learning methods on the DSEC benchmark, while remains competitive among both methods on the MVSEC benchmark. This contribution marks a significant advancement in event-based optical flow within the feature matching methodology.