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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.22669 |
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| _version_ | 1866910678274539520 |
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| author | Alam, Mohammad Mahmudul Oberle, Alexander Raff, Edward Biderman, Stella Oates, Tim Holt, James |
| author_facet | Alam, Mohammad Mahmudul Oberle, Alexander Raff, Edward Biderman, Stella Oates, Tim Holt, James |
| contents | Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Walsh Hadamard Derived Linear Vector Symbolic Architecture Alam, Mohammad Mahmudul Oberle, Alexander Raff, Edward Biderman, Stella Oates, Tim Holt, James Artificial Intelligence Machine Learning Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ 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 |
| title | A Walsh Hadamard Derived Linear Vector Symbolic Architecture |
| topic | Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2410.22669 |