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Register a new userCategorical Representation Learning: Morphism is All You Need
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We provide a construction for categorical representation learning and introduce the foundations of $textit{categorifier}$. The central theme in representation learning is the idea of $textbf{everything to vector}$. Every object in a dataset $mathcal{S}$ can be represented as a vector in $mathbb{R}^n$ by an $textit{encoding map}$ $E: mathcal{O}bj(mathcal{S})tomathbb{R}^n$. More importantly, every morphism can be represented as a matrix $E: mathcal{H}om(mathcal{S})tomathbb{R}^{n}_{n}$. The encoding map $E$ is generally modeled by a $textit{deep neural network}$. The goal of representation learning is to design appropriate tasks on the dataset to train the encoding map (assuming that an encoding is optimal if it universally optimizes the performance on various tasks). However, the latter is still a $textit{set-theoretic}$ approach. The goal of the current article is to promote the representation learning to a new level via a $textit{category-theoretic}$ approach. As a proof of concept, we provide an example of a text translator equipped with our technology, showing that our categorical learning model outperforms the current deep learning models by 17 times. The content of the current article is part of the recent US patent proposal (patent application number: 63110906).
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Gradient-based meta-learning has proven to be highly effective at learning model initializations, representations, and update rules that allow fast adaptation from a few samples. The core idea behind these approaches is to use fast adaptation and generalization -- two second-order metrics -- as training signals on a meta-training dataset. However, little attention has been given to other possible second-order metrics. In this paper, we investigate a different training signal -- robustness to catastrophic interference -- and demonstrate that representations learned by directing minimizing interference are more conducive to incremental learning than those learned by just maximizing fast adaptation.
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