@misc{murfet_dmurfet/2simplicialtransformer_2019,
title = {dmurfet/2simplicialtransformer},
url = {https://github.com/dmurfet/2simplicialtransformer},
abstract = {Code for the 2-simplicial Transformer paper. Contribute to dmurfet/2simplicialtransformer development by creating an account on GitHub.},
urldate = {2019-11-22},
author = {Murfet, Daniel},
month = oct,
year = {2019},
note = {ZSCC: NoCitationData[s0]
original-date: 2019-08-29T13:26:13Z},
keywords = {Abstract machines, Algebra, Implementation, Machine learning, Semantics}
}
@article{murfet_logic_2019,
title = {Logic and the \$2\$-{Simplicial} {Transformer}},
url = {http://arxiv.org/abs/1909.00668},
abstract = {We introduce the \$2\$-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive bias for logical reasoning in the context of deep reinforcement learning.},
urldate = {2019-11-21},
journal = {arXiv:1909.00668 [cs, stat]},
author = {Murfet, Daniel and Clift, James and Doryn, Dmitry and Wallbridge, James},
month = sep,
year = {2019},
note = {ZSCC: 0000000
arXiv: 1909.00668
version: 1},
keywords = {Abstract machines, Algebra, Machine learning, Semantics}
}
@inproceedings{izbicki_algebraic_2013,
title = {Algebraic classifiers: a generic approach to fast cross-validation, online training, and parallel training},
shorttitle = {Algebraic classifiers},
abstract = {We use abstract algebra to derive new algorithms for fast cross-validation, online learning, and parallel learning. To use these algorithms on a classification model, we must show that the model has appropriate algebraic structure. It is easy to give algebraic structure to some models, and we do this explicitly for Bayesian classifiers and a novel variation of decision stumps called HomStumps. But not all classifiers have an obvious structure, so we introduce the Free HomTrainer. This can be used to give a "generic" algebraic structure to any classifier. We use the Free HomTrainer to give algebraic structure to bagging and boosting. In so doing, we derive novel online and parallel algorithms, and present the first fast cross-validation schemes for these classifiers.},
booktitle = {{ICML}},
author = {Izbicki, Michael},
year = {2013},
note = {ZSCC: 0000013},
keywords = {Algebra, Categorical ML, Machine learning}
}
@misc{watanabe_algebraic_2009,
title = {Algebraic {Geometry} and {Statistical} {Learning} {Theory}},
url = {/core/books/algebraic-geometry-and-statistical-learning-theory/9C8FD1BDC817E2FC79117C7F41544A3A},
abstract = {Cambridge Core - Pattern Recognition and Machine Learning - Algebraic Geometry and Statistical Learning Theory - by Sumio Watanabe},
language = {en},
urldate = {2019-11-22},
journal = {Cambridge Core},
author = {Watanabe, Sumio},
month = aug,
year = {2009},
doi = {10.1017/CBO9780511800474},
note = {ZSCC: 0000276 },
keywords = {Algebra, Bayesianism, Purely theoretical, Statistical learning theory}
}
@article{philipona_is_2003,
title = {Is {There} {Something} {Out} {There}? {Inferring} {Space} from {Sensorimotor} {Dependencies}},
volume = {15},
shorttitle = {Is {There} {Something} {Out} {There}?},
doi = {10/frg7gs},
abstract = {This letter suggests that in biological organisms, the perceived structure of reality, in particular the notions of body, environment, space, object, and attribute, could be a consequence of an effort on the part of brains to account for the dependency between their inputs and their outputs in terms of a small number of parameters. To validate this idea, a procedure is demonstrated whereby the brain of a (simulated) organism with arbitrary input and output connectivity can deduce the dimensionality of the rigid group of the space underlying its input-output relationship, that is, the dimension of what the organism will call physical space.},
journal = {Neural computation},
author = {Philipona, David and O’Regan, J. and Nadal, Jean-Pierre},
month = oct,
year = {2003},
note = {ZSCC: 0000225},
keywords = {Algebra, Neuroscience},
pages = {2029--49}
}
@book{engeler_combinatory_1995,
series = {Progress in {Theoretical} {Computer} {Science}},
title = {The {Combinatory} {Programme}},
isbn = {978-0-8176-3801-6},
url = {https://www.springer.com/gb/book/9780817638016},
abstract = {Combinatory logic started as a programme in the foundation of mathematics and in an historical context at a time when such endeavours attracted the most gifted among the mathematicians. This small volume arose under quite differ ent circumstances, namely within the context of reworking the mathematical foundations of computer science. I have been very lucky in finding gifted students who agreed to work with me and chose, for their Ph. D. theses, subjects that arose from my own attempts 1 to create a coherent mathematical view of these foundations. The result of this collaborative work is presented here in the hope that it does justice to the individual contributor and that the reader has a chance of judging the work as a whole. E. Engeler ETH Zurich, April 1994 lCollected in Chapter III, An Algebraization of Algorithmics, in Algorithmic Properties of Structures, Selected Papers of Erwin Engeler, World Scientific PubJ. Co. , Singapore, 1993, pp. 183-257. I Historical and Philosophical Background Erwin Engeler In the fall of 1928 a young American turned up at the Mathematical Institute of Gottingen, a mecca of mathematicians at the time; he was a young man with a dream and his name was H. B. Curry. He felt that he had the tools in hand with which to solve the problem of foundations of mathematics mice and for all. His was an approach that came to be called "formalist" and embodied that later became known as Combinatory Logic.},
language = {en},
urldate = {2019-11-26},
publisher = {Birkhäuser Basel},
author = {Engeler, Erwin},
year = {1995},
doi = {10.1007/978-1-4612-4268-0},
note = {ZSCC: NoCitationData[s1] },
keywords = {Algebra, Programming language theory, Purely theoretical}
}
@misc{murfet_algebra_nodate,
title = {Algebra and {Artiﬁcial} {Intelligence}},
language = {en},
author = {Murfet, Daniel},
note = {ZSCC: NoCitationData[s0]},
keywords = {Algebra, Classical ML, Machine learning, Sketchy}
}