Learning with Holographic Reduced Representations
- URL: http://arxiv.org/abs/2109.02157v1
- Date: Sun, 5 Sep 2021 19:37:34 GMT
- Title: Learning with Holographic Reduced Representations
- Authors: Ashwinkumar Ganesan, Hang Gao, Sunil Gandhi, Edward Raff, Tim Oates,
James Holt, Mark McLean
- Abstract summary: Holographic Reduced Representations (HRR) are a method for performing symbolic AI on top of real-valued vectors.
This paper revisits this approach to understand if it is viable for enabling a hybrid neural-symbolic approach to learning.
- Score: 28.462635977110413
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Holographic Reduced Representations (HRR) are a method for performing
symbolic AI on top of real-valued vectors \cite{Plate1995} 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.
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