Learning with Holographic Reduced Representations
This work addresses the challenge of integrating symbolic AI with deep learning for researchers in neuro-symbolic AI, though it is incremental as it builds on existing HRR methods.
The paper tackled the problem of making Holographic Reduced Representations (HRR) viable for hybrid neural-symbolic learning by addressing numerical instability, improving concept retrieval efficacy by over 100×, and demonstrating its application in multi-label classification with a differentiable output layer and loss function.
Holographic Reduced Representations (HRR) are a method for performing symbolic AI on top of real-valued vectors by associating each vector with an abstract concept, and providing mathematical operations to manipulate vectors as if they were classic symbolic objects. This method has seen little use outside of older symbolic AI work and cognitive science. Our goal is to revisit this approach to understand if it is viable for enabling a hybrid neural-symbolic approach to learning as a differentiable component of a deep learning architecture. HRRs today are not effective in a differentiable solution due to numerical instability, a problem we solve by introducing a projection step that forces the vectors to exist in a well behaved point in space. In doing so we improve the concept retrieval efficacy of HRRs by over $100\times$. Using multi-label classification we demonstrate how to leverage the symbolic HRR properties to develop an output layer and loss function that is able to learn effectively, and allows us to investigate some of the pros and cons of an HRR neuro-symbolic learning approach. Our code can be found at https://github.com/NeuromorphicComputationResearchProgram/Learning-with-Holographic-Reduced-Representations