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MissionHD: Hyperdimensional Refinement of Distribution-Deficient Reasoning Graphs for Video Anomaly Detection

Sanggeon Yun, Raheeb Hassan, Ryozo Masukawa, Nathaniel D. Bastian, Mohsen Imani

TL;DR

MissionHD is introduced, an HDC framework that encodes graphs with constrained graph-neural operations, aligns them directly with downstream task loss, and decodes refined structures, establishing HDC-GSR as an effective pre-processing step for structured reasoning in video anomaly tasks.

Abstract

LLM-generated reasoning graphs, referred to as mission-specific graphs (MSGs), are increasingly used for video anomaly detection (VAD) and recognition (VAR). These MSGs are novel artifacts: they often exhibit skewed connectivity and lack large-scale datasets for pre-training, which makes existing graph structure refinement (GSR) methods ineffective. To address this challenge, we propose HDC-constrained Graph Structure Refinement (HDC-GSR), a paradigm that leverages hyperdimensional computing (HDC) to optimize decodable graph representations without relying on structural-distribution learning. Building on this paradigm, we introduce MissionHD, an HDC framework that encodes graphs with constrained graph-neural operations, aligns them directly with downstream task loss, and decodes refined structures. Experiments on VAD/VAR benchmarks demonstrate that MissionHD-refined graphs consistently improve performance, establishing HDC-GSR as an effective pre-processing step for structured reasoning in video anomaly tasks.

MissionHD: Hyperdimensional Refinement of Distribution-Deficient Reasoning Graphs for Video Anomaly Detection

TL;DR

MissionHD is introduced, an HDC framework that encodes graphs with constrained graph-neural operations, aligns them directly with downstream task loss, and decodes refined structures, establishing HDC-GSR as an effective pre-processing step for structured reasoning in video anomaly tasks.

Abstract

LLM-generated reasoning graphs, referred to as mission-specific graphs (MSGs), are increasingly used for video anomaly detection (VAD) and recognition (VAR). These MSGs are novel artifacts: they often exhibit skewed connectivity and lack large-scale datasets for pre-training, which makes existing graph structure refinement (GSR) methods ineffective. To address this challenge, we propose HDC-constrained Graph Structure Refinement (HDC-GSR), a paradigm that leverages hyperdimensional computing (HDC) to optimize decodable graph representations without relying on structural-distribution learning. Building on this paradigm, we introduce MissionHD, an HDC framework that encodes graphs with constrained graph-neural operations, aligns them directly with downstream task loss, and decodes refined structures. Experiments on VAD/VAR benchmarks demonstrate that MissionHD-refined graphs consistently improve performance, establishing HDC-GSR as an effective pre-processing step for structured reasoning in video anomaly tasks.

Paper Structure

This paper contains 34 sections, 4 theorems, 18 equations, 8 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries & Related Works
  3. Hyperdimensional Computing
  4. Graph encoding/decoding in HDC
  5. Visual Representation Learning Using Graphs
  6. Methodology
  7. Setup and Notation
  8. Hyperdimensional Graph Encoding and Optimization
  9. MSG Encoding.
  10. Task-Driven Structure Optimization.
  11. Graph Structure Refinement via Hyperdimensional Decoding
  12. Theoretical Analysis
  13. HDC-Constrained GNN Equivalence.
  14. Edge score consistency.
  15. Decoding guarantees.
  16. ...and 19 more sections

Key Result

Theorem 4.1

An HDC layer operation, $z \mapsto L^{(i)}\otimes z$, is mathematically equivalent to a linear layer with a diagonal weight matrix $D_{L^{(i)}}:=\mathrm{diag}(L^{(i)})$.

Figures (8)

  • Figure 1: The proposed MissionHD framework refines LLM-generated mission-specific graphs (MSGs) through the HDC-GSR paradigm. By leveraging hyperdimensional encoding and decoding, it aligns graph structures with downstream tasks without relying on direct structural-distribution learning.
  • Figure 2: Overview of the MissionHD pipeline. We propose a hyperdimensional encoding and refinement framework for mission-specific reasoning graphs, enabling efficient symbolic representation and task-driven structure updates via edge contribution scoring.
  • Figure 3: Overview of the MissionHD encoding pipeline. A layered DAG has its node features projected into high-dimensional space. A DP approach then efficiently computes the global graph hypervector. The final hypervector is augmented with learnable structural edits and fused with sensor features for downstream decision-making.
  • Figure 4: Illustration of the hyperdimensional graph structure refinement in MissionHD. (a) Forward path encodings are computed assuming full connectivity. (b) Backward path encodings are computed in reverse. (c) A hypothetical hypervector for a candidate edge is constructed and compared against the trained graph vector to compute an edge contribution score.
  • Figure 5: Ablation on two dimensionalities: hyperspace (left) and latent space (right) on UCF-Crime dataset. Increasing latent dimensionality yields larger performance gains than increasing hyperspace dimensionality.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Theorem 4.1: HDC layer $\equiv$ diagonal linear map
  • Theorem 4.2: MissionHD as a path-sum GNN
  • Proposition 4.3: Edge score consistency
  • Proposition 4.4: Decoding accuracy bound
  • proof
  • proof
  • proof