mlsanityData to 7 Oct 2026

A Walsh Hadamard Derived Linear Vector Symbolic Architecture

arXiv 2410.22669 ↗First posted 30 Oct 2024cs.AI cs.LGcited by 4

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Abstract (arXiv)

Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in ℝd are `bound' together to produce a new vector in the same space. VSAs support the commutativity and associativity of this binding operation, along with an inverse operation, allowing one to construct symbolic-style manipulations over real-valued vectors. Most VSAs were developed before deep learning and automatic differentiation became popular and instead focused on efficacy in hand-designed systems. In this work, we introduce the Hadamard-derived linear Binding (HLB), which is designed to have favorable computational efficiency, and efficacy in classic VSA tasks, and perform well in differentiable systems. Code is available at https://github.com/FutureComputing4AI/Hadamard-derived-Linear-Binding

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 30 Oct 2024.

Builds on

22 of 45 references.

References · 22

  1. 2021Linear Transformers Are Secretly Fast Weight Programmerscited by 471
  2. 2020On the Binding Problem in Artificial Neural Networkscited by 230
  3. 2018AttentionXML: Label Tree-based Attention-Aware Deep Model for High-Performance Extreme Multi-Label Text Classificationcited by 101
  4. 2021A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part I: Models and Data Transformationscited by 98
  5. 2021A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challengescited by 68
  6. 2016Efficient softmax approximation for GPUscited by 67
  7. 2020A comparison of Vector Symbolic Architecturescited by 63
  8. 2019InteractE: Improving Convolution-based Knowledge Graph Embeddings by Increasing Feature Interactionscited by 58
  9. 2021Vector Symbolic Architectures as a Computing Framework for Emerging Hardwarecited by 35
  10. 2018Learning to Reason with Third-Order Tensor Productscited by 27
  11. 2021Learning with Holographic Reduced Representationscited by 25
  12. 2022Torchhd: An Open Source Python Library to Support Research on Hyperdimensional Computing and Vector Symbolic Architecturescited by 17
10 more
  1. 2017Learning to Attend via Word-Aspect Associative Fusion for Aspect-based Sentiment Analysiscited by 14
  2. 2023Recasting Self-Attention with Holographic Reduced Representationscited by 14
  3. 2023MIMONets: Multiple-Input-Multiple-Output Neural Networks Exploiting Computation in Superpositioncited by 14
  4. 2019CircConv: A Structured Convolution with Low Complexitycited by 8
  5. 2019Accelerating Extreme Classification via Adaptive Feature Agglomerationcited by 7
  6. 2022Deploying Convolutional Networks on Untrusted Platforms Using 2D Holographic Reduced Representationscited by 7
  7. 2024Holographic Global Convolutional Networks for Long-Range Prediction Tasks in Malware Detectioncited by 6
  8. 2023Towards Generalization in Subitizing with Neuro-Symbolic Loss using Holographic Reduced Representationscited by 4
  9. 2022Lempel-Ziv Networkscited by 3
  10. 2023WHYPE: A Scale-Out Architecture with Wireless Over-the-Air Majority for Scalable In-memory Hyperdimensional Computingcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025Linearithmic Clean-up for Vector-Symbolic Key-Value Memory with Kroneker Rotation Productscited by 2
  2. 2025Composing Linear Layers from Irreduciblescited by 1
  3. 2025A Vector Symbolic Approach to Multiple Instance Learningcited by 0
  4. 2026Recursive Binding on a Budget: Subspace Carving in Order-p Tensor Memoriescited by 0