Built on

V. Jejjala, A. Kar and O. Parrikar, Deep Learning the Hyperbolic Volume of a Knot , Phys. Lett. B 799
Original
1902
Earlier work this paper cites.
J. Halverson, B. Nelson and F. Ruehle, Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning , JHEP 06
Original
1903
Earlier work this paper cites.
G. Kuperberg and E. Samperton, Coloring invariants of knots and links are often intractable , 1907.05981
Original
1907
Earlier work this paper cites.
A. J. Casson and C. M. Gordon, A loop theorem for duality spaces and fibred ribbon knots , Invent. Math. 74
1983
Earlier work this paper cites.
M. H. Freedman and F. Quinn, Topology of 4-manifolds , vol. 39 of Princeton Mathematical Series . Princeton University Press, Princeton, NJ, 1990
1990
Earlier work this paper cites.
Jaeger, F. and Vertigan, D. L. and Welsh, D. J. A., On the computational complexity of the Jones and Tutte polynomials , Mathematical Proceedings of the Cambridge Philosophical Society 108
1990
Earlier work this paper cites.
P. Dehornoy, A fast method for comparing braids , Advances in Mathematics 125
1997
Earlier work this paper cites.
J. Birman, K. H. Ko and S. J. Lee, A new approach to the word and conjugacy problems in the braid groups , Adv. Math. 139
1998
Earlier work this paper cites.
J. Hass, J. C. Lagarias and N. Pippenger, The computational complexity of knot and link problems , J. ACM 46
1999
Earlier work this paper cites.
M. Agrawal, N. Kayal and N. Saxena, Primes is in p , Ann. of Math 2
2002
Earlier work this paper cites.
M. R. Douglas, The Statistics of string / M theory vacua , JHEP 05
2003
Earlier work this paper cites.
R. E. Tuzun and A. S. Sikora, Verification Of The Jones Unknot Conjecture Up To 24 Crossings , 2003.06724
Original
2003
Earlier work this paper cites.
S. Ashok and M. R. Douglas, Counting flux vacua , JHEP 01
2004
Earlier work this paper cites.
S. Gukov, Three-dimensional quantum gravity, Chern-Simons theory, and the A polynomial , Commun. Math. Phys. 255
2005
Earlier work this paper cites.
M. Freedman, R. Gompf, S. Morrison and K. Walker, Man and machine thinking about the smooth 4-dimensional Poincaré conjecture , Quantum Topol. 1
2010
Earlier work this paper cites.

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J. Rasmussen, Khovanov homology and the slice genus , Invent. Math. 182
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A. Graves, G. Wayne and I. Danihelka, Neural turing machines , ArXiv abs/1410.5401
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2014
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2014
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Then

D. Krefl and R.-K. Seong, Machine Learning of Calabi-Yau Volumes , Phys. Rev. D 96
Original
2017
Later among the works it cites.
F. Ruehle, Evolving neural networks with genetic algorithms to study the String Landscape , JHEP 08
Original
2017
Later among the works it cites.
J. Carifio, J. Halverson, D. Krioukov and B. D. Nelson, Machine Learning in the String Landscape , JHEP 09
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Later among the works it cites.
J. Halverson, C. Long and B. Sung, Algorithmic universality in F-theory compactifications , Phys. Rev. D 96
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Later among the works it cites.
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez et al., Attention is all you need , in NIPS , 2017

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2020

Learning to Unknot

Gukov, Sergei, Halverson, James, Ruehle, Fabian et al.

Understand

We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots.

We study the UNKNOT problem of determining whether or not a given knot is the unknot.
After describing an algorithm to randomly generate $N$-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem.
We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform well.

Built on

V. Jejjala, A. Kar and O. Parrikar, Deep Learning the Hyperbolic Volume of a Knot , Phys. Lett. B 799
Original
1902
Earlier work this paper cites.
J. Halverson, B. Nelson and F. Ruehle, Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning , JHEP 06
Original
1903
Earlier work this paper cites.
G. Kuperberg and E. Samperton, Coloring invariants of knots and links are often intractable , 1907.05981
Original
1907
Earlier work this paper cites.
A. J. Casson and C. M. Gordon, A loop theorem for duality spaces and fibred ribbon knots , Invent. Math. 74
1983
Earlier work this paper cites.
M. H. Freedman and F. Quinn, Topology of 4-manifolds , vol. 39 of Princeton Mathematical Series . Princeton University Press, Princeton, NJ, 1990
1990
Earlier work this paper cites.
Jaeger, F. and Vertigan, D. L. and Welsh, D. J. A., On the computational complexity of the Jones and Tutte polynomials , Mathematical Proceedings of the Cambridge Philosophical Society 108
1990
Earlier work this paper cites.
P. Dehornoy, A fast method for comparing braids , Advances in Mathematics 125
1997
Earlier work this paper cites.
J. Birman, K. H. Ko and S. J. Lee, A new approach to the word and conjugacy problems in the braid groups , Adv. Math. 139
1998
Earlier work this paper cites.
J. Hass, J. C. Lagarias and N. Pippenger, The computational complexity of knot and link problems , J. ACM 46
1999
Earlier work this paper cites.
M. Agrawal, N. Kayal and N. Saxena, Primes is in p , Ann. of Math 2
2002
Earlier work this paper cites.
M. R. Douglas, The Statistics of string / M theory vacua , JHEP 05
2003
Earlier work this paper cites.
R. E. Tuzun and A. S. Sikora, Verification Of The Jones Unknot Conjecture Up To 24 Crossings , 2003.06724
Original
2003
Earlier work this paper cites.
S. Ashok and M. R. Douglas, Counting flux vacua , JHEP 01
2004
Earlier work this paper cites.
S. Gukov, Three-dimensional quantum gravity, Chern-Simons theory, and the A polynomial , Commun. Math. Phys. 255
2005
Earlier work this paper cites.
M. Freedman, R. Gompf, S. Morrison and K. Walker, Man and machine thinking about the smooth 4-dimensional Poincaré conjecture , Quantum Topol. 1
2010
Earlier work this paper cites.

Similar

J. Rasmussen, Khovanov homology and the slice genus , Invent. Math. 182
2010
Cited alongside, same era.
S. Akbulut, Cappell-Shaneson homotopy spheres are standard , Ann. of Math. (2) 171
2010
Cited alongside, same era.
M. Jamroz, W. Niemyska, E. J. Rawdon, A. Stasiak, K. C. Millett, P. Sulkowski et al., KnotProt: a database of proteins with knots and slipknots , Nucleic Acids Research 43
2014
Cited alongside, same era.
A. Graves, G. Wayne and I. Danihelka, Neural turing machines , ArXiv abs/1410.5401
Original
2014
Cited alongside, same era.
D. Bahdanau, K. Cho and Y. Bengio, Neural machine translation by jointly learning to align and translate , CoRR abs/1409.0473
Original
2014
Cited alongside, same era.

Then

D. Krefl and R.-K. Seong, Machine Learning of Calabi-Yau Volumes , Phys. Rev. D 96
Original
2017
Later among the works it cites.
F. Ruehle, Evolving neural networks with genetic algorithms to study the String Landscape , JHEP 08
Original
2017
Later among the works it cites.
J. Carifio, J. Halverson, D. Krioukov and B. D. Nelson, Machine Learning in the String Landscape , JHEP 09
Original
2017
Later among the works it cites.
J. Halverson, C. Long and B. Sung, Algorithmic universality in F-theory compactifications , Phys. Rev. D 96
Original
2017
Later among the works it cites.
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez et al., Attention is all you need , in NIPS , 2017

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

G. Kuperberg, Knottedness is in np, modulo GRH , Adv. Math. 256

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W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua , JHEP 12

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T. Luong, H. Pham and C. D. Manning, Effective approaches to attention-based neural machine translation , in EMNLP , 2015

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A. Andoni, P. Indyk, T. Laarhoven, I. P. Razenshteyn and L. Schmidt, Practical and optimal lsh for angular distance , in NIPS , 2015

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J. Schulman, S. Levine, P. Abbeel, M. Jordan and P. Moritz, Trust region policy optimization , vol. 37 of Proceedings of Machine Learning Research , (Lille, France), pp. 1889–1897, PMLR, 07–09 Jul, 2015, http://arxiv.org/abs/1502.05477 [ 1502.05477 ]

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D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche et al., Mastering the game of Go with deep neural networks and tree search , Nature 529

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V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley et al., Asynchronous methods for deep reinforcement learning , in International conference on machine learning , pp. 1928–1937, 2016, http://arxiv.org/abs/1602.01783 [ 1602.01783 ]

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