Position: Categorical Deep Learning is an Algebraic Theory of All Architectures
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914826492575744 |
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| author | Gavranović, Bruno Lessard, Paul Dudzik, Andrew von Glehn, Tamara Araújo, João G. M. Veličković, Petar |
| author_facet | Gavranović, Bruno Lessard, Paul Dudzik, Andrew von Glehn, Tamara Araújo, João G. M. Veličković, Petar |
| contents | We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Position: Categorical Deep Learning is an Algebraic Theory of All Architectures Gavranović, Bruno Lessard, Paul Dudzik, Andrew von Glehn, Tamara Araújo, João G. M. Veličković, Petar Machine Learning Artificial Intelligence Category Theory Rings and Algebras We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory. |
| title | Position: Categorical Deep Learning is an Algebraic Theory of All Architectures |
| topic | Machine Learning Artificial Intelligence Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2402.15332 |