SyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (2024)

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  • Irina Higgins DeepMind, London

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  • Peter Wirnsberger DeepMind, London

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  • Andrew Jaegle DeepMind, London

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  • Aleksandar Botev DeepMind, London

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NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing SystemsDecember 2021Article No.: 1960Pages 25591–25605

Published:10 June 2024Publication History

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NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing Systems

SyMetric: measuring the quality of learnt hamiltonian dynamics inferred from vision

Pages 25591–25605

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SyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (3)

ABSTRACT

A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations, like images, using priors informed by Hamiltonian mechanics. While these models have important potential applications in areas like robotics or autonomous driving, there is currently no good way to evaluate their performance: existing methods primarily rely on image reconstruction quality, which does not always reflect the quality of the learnt latent dynamics. In this work, we empirically highlight the problems with the existing measures and develop a set of new measures, including a binary indicator of whether the underlying Hamiltonian dynamics have been faithfully captured, which we call Symplecticity Metric or SyMetric. Our measures take advantage of the known properties of Hamiltonian dynamics and are more discriminative of the model's ability to capture the underlying dynamics than reconstruction error. Using SyMetric, we identify a set of architectural choices that significantly improve the performance of a previously proposed model for inferring latent dynamics from pixels, the Hamiltonian Generative Network (HGN). Unlike the original HGN, the new HGN++ is able to discover an interpretable phase space with physically meaningful latents on some datasets. Furthermore, it is stable for significantly longer rollouts on a diverse range of 13 datasets, producing rollouts of essentially infinite length both forward and backwards in time with no degradation in quality on a subset of the datasets.

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References

  1. J. L. F. Abascal and C. Vega. A general purpose model for the condensed phases of water: Tip4p/2005. J. Chem. Phys., 123:234505, 2005.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (4)Cross Ref
  2. R. Abraham and J.E. Marsden. Foundations of Mechanics. AMS Chelsea publishing. AMS Chelsea Pub./American Mathematical Society, 2008.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (6)
  3. Christine Allen-Blanchette, Sushant Veer, Anirudha Majumdar, and Naomi Ehrich Leonard. LagNetViP: A Lagrangian neural network for video prediction. In Proceedings of AAAI Conference on Artificial Intelligence, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (7)
  4. Omri Azencot, N Benjamin Erichson, Vanessa Lin, and Michael W Mahoney. Forecasting sequential data using consistent Koopman autoencoders. In Proceedings of International Conference on Machine Learning (ICML), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (8)
  5. James P Bailey and Georgios Piliouras. Multi-agent learning in network zero-sum games is a Hamiltonian system. In Proceedings of the International Conference on Autonomous Agents and Multiagent Systems (AAMAS), 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (9)
  6. David Balduzzi, Sebastien Racaniere, James Martens, Jakob Foerster, Karl Tuyls, and Thore Graepel. The mechanics of n-player differentiable games. In International Conference on Machine Learning, pages 354–363, 2018.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (10)
  7. Alexandar Botev, Andrew Jaegle, Peter Wirnsberger, Daniel Hennes, and Irina Higgins. Which priors matter? Benchmarking models for learning latent dynamics. In Proceedings of Neural Information Processing Systems (NeurIPS), 2021.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (11)
  8. Zhengdao Chen, Jianyu Zhang, Martin Arjovsky, and Léon Bottou. Symplectic recurrent neural networks. In Proceedings of International Conference on Learning Representations (ICLR), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (12)
  9. Anshul Choudhary, John F Lindner, Elliott G Holliday, Scott T Miller, Sudeshna Sinha, and William L Ditto. Forecasting Hamiltonian dynamics without canonical coordinates. Nonlinear Dynamics, pages 1–10, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (13)
  10. Wendy D. Cornell, Piotr Cieplak, Christopher I. Bayly, Ian R. Gould, Kenneth M. Merz, David M. Ferguson, David C. Spellmeyer, Thomas Fox, James W. Caldwell, and Peter A. Kollman. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J. Am. Chem. Soc., 117(19):5179–5197, 1995.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (14)Cross Ref
  11. Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel, and Shirley Ho. Lagrangian neural networks. In ICLR Deep Differential Equations Workshop, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (16)
  12. Shaan A. Desai, Marios Mattheakis, and StephenJ. Roberts. Variational integrator graph networks for learning energy-conserving dynamical systems. Physical Review E., 104(3), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (17)Cross Ref
  13. Jay L. Devore. Probability and Statistics for Engineering and the Sciences. Spinger, 2008.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (19)
  14. Daniel M. DiPietro, Shiying Xiong, and BoZhu. Sparse symplectically integrated neural networks. In Proceedings of Neural Information Processing Systems (NeurIPS), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (20)
  15. Alexey Dosovitskiy and Thomas Brox. Generating images with perceptual similarity metrics based on deep networks. In Proceedings of Neural Information Processing Systems (NeurIPS), 2016.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (21)
  16. Sunny Duan, Loic Matthey, Andre Saraiva, Nicholas Watters, Christopher P Burgess, Alexander Lerchner, and Irina Higgins. Unsupervised model selection for variational disentangled representation learning. In Proceedings of International Conference on Learning Representations (ICLR), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (22)
  17. Marc Finzi, Ke Alexander Wang, and Andrew Gordon Wilson. Simplifying Hamiltonian and Lagrangian neural networks via explicit constraints. In Proceedings of Neural Information Processing Systems (NeurIPS), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (23)
  18. Jason Frank. Symplectic flows and maps and volume preservation. https://webspace.science.uu.nl/ frank011/Classes/numwisk/ch16.pdf, 2008.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (24)
  19. Daan Frenkel and Berend Smit. Understanding Molecular Simulation. Academic Press, San Diego, second edition, 2002.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (25)
  20. Samuel Greydanus, Misko Dzamba, and Jason Yosinski. Hamiltonian neural networks. In Proceedings of Neural Information Processing Systems (NeurIPS), 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (26)
  21. Niklas Heim, Václav Šmídl, and Tomáš Pevnỳ. Rodent: Relevance determination in differential equations. arXiv preprint arXiv:1912.00656, 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (27)
  22. Irina Higgins, Loic Matthey, Arka Pal, Christopher Burgess, Xavier Glorot, Matthew Botvinick, Shakir Mohamed, and Alexander Lerchner. β-VAE: Learning basic visual concepts with a constrained variational framework. In Proceedings of International Conference on Learning Representations (ICLR), 2017.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (28)
  23. William G. Hoover. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, 31:1695–1697, 1985.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (29)Cross Ref
  24. In Huh, Eunho Yang, Sung Ju Hwang, and Jinwoo Shin. Time-reversal symmetric ODE network. In Proceedings of Neural Information Processing Systems (NeurIPS), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (31)
  25. Maxim Jeffs. Harvard, Lecture Notes: Classical mechanics and symplectic geometry, 2020. URL: http://people.math.harvard.edu/~jeffs/SymplecticNotes.pdf.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (32)
  26. Pengzhan Jin, Zhen Zhang, Aiqing Zhu, Yifa Tang, and George Em Karniadakis. SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Neural Networks, 132:166–179, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (33)Cross Ref
  27. J. E. Jones and Sydney Chapman. On the determination of molecularfields. –II. From the equation of state of a gas. Proc. R. Soc. Lond. A, 106(738):463–477, 1924.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (35)Cross Ref
  28. Rishabh Kabra, Chris Burgess, Loic Matthey, Raphael Lopez Kaufman, Klaus Greff, Malcolm Reynolds, and Alexander Lerchner. Multi-object datasets. https://github.com/deepmind/multi-object-datasets/, 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (37)
  29. Lev Davidovich Landau and Evgenii Mikhailovich Lifsh*tz. Course of theoretical physics. Elsevier, 2013.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (38)
  30. Anders Boesen Lindbo Larsen, Søren Kaae Sønderby, Hugo Larochelle, and Ole Winther. Autoencoding beyond pixels using a learned similarity metric. In Proceedings of International Conference on Machine Learning (ICML), 2016.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (39)
  31. Yunzhu Li, Toru Lin, Kexin Yi, Daniel Bear, Daniel LK Yamins, Jiajun Wu, Joshua B Tenenbaum, and Antonio Torralba. Visual grounding of learned physical models. In Proceedings of International Conference on Machine Learning (ICML), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (40)
  32. Michael Lutter, Christian Ritter, and Jan Peters. Deep Lagrangian networks: Using physics as model prior for deep learning. In Proceedings of International Conference on Learning Representations (ICLR), 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (41)
  33. Andrew L Maas, Awni Y Hannun, and Andrew Y Ng. Rectifier nonlinearities improve neural network acoustic models. In Proceedings of International Conference on Machine Learning (ICML), 2013.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (42)
  34. Lars Mescheder, Andreas Geiger, and Sebastian Nowozin. Which training methods for GANs do actually converge? In Proceedings of International Conference on Machine Learning (ICML), 2018.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (43)
  35. Lars Mescheder, Sebastian Nowozin, and Andreas Geiger. The numericsofGANs. In Proceedings of Neural Information Processing Systems (NeurIPS), 2017.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (44)
  36. Luke Metz, Ben Poole, David Pfau, and Jascha Sohl-Dickstein. Unrolled generative adversarial networks. In Proceedings of International Conference on Learning Representations (ICLR), 2017.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (45)
  37. Shuichi Nosé. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys., 81(1):511–519, 1984.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (46)Cross Ref
  38. Chongli Qin, Yan Wu, Jost Tobias Springenberg, Andrew Brock, Jeff Donahue, Timothy P Lillicrap, and Pushmeet Kohli. Training generative adversarial networks by solving ordinary differential equations. In Proceedings of Neural Information Processing Systems (NeurIPS), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (48)
  39. Prajit Ramachandran, Barret Zoph, and Quoc V Le. Swish: a self-gated activation function. arXiv preprint arXiv:1710.05941.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (49)
  40. Katharina Rath, Christopher G. Albert, Bernd Bischl, and Udo von Toussaint. Symplectic Gaussian process regression of maps in Hamiltonian systems. Chaos, 31, 2021.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (50)
  41. Danilo Jimenez Rezende, Sébastien Racanière, Irina Higgins, and Peter Toth. Equivariant Hamiltonian flows. In NeurIPS workshop: Machine Learning and the Physical Sciences, 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (51)
  42. Danilo Jimenez Rezende and Fabio Viola. Taming VAEs. arXiv preprint arXiv:1810.00597, 2018.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (52)
  43. Manuel A Roehrl, Thomas A Runkler, Veronika Brandtstetter, Michel Tokic, and Stefan Ober-mayer. Modeling system dynamics with physics-informed neural networks based on Lagrangian mechanics. In International Federation of Automatic Control (IFAC) World Congress, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (53)Cross Ref
  44. Oleh Rybkin. The reasonable ineffectiveness of pixel metrics for future prediction (and what to do about it), 2018. URL: https://bit.ly/2YHPRg2.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (55)
  45. Steindor Saemundsson, Alexander Terenin, Katja Hofmann, and Marc Deisenroth. Variational integrator networks for physically structured embeddings. In International Conference on Artificial Intelligence and Statistics (AISTATS), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (56)
  46. Iain W. Stewart. MIT, Lecture Notes: Advanced Classical Mechanics, 2016. URL: https://bit.ly/3oP7fuc.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (57)
  47. Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2012.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (58)Cross Ref
  48. Yunjin Tong, Shiying Xiong, Xingzhe He, Guanghan Pan, and Bo Zhu. Symplectic neural networks in Taylor series form for Hamiltonian systems. Journal of Computational Physics, 437, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (60)
  49. Peter Toth, Danilo Jimenez Rezende, Andrew Jaegle, Sébastien Racanière, Aleksandar Botev, and Irina Higgins. Hamiltonian generative networks. In Proceedings of International Conference on Learning Representations (ICLR), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (61)
  50. Silviu-Marian Udrescu and Max Tegmark. Symbolic pregression: Discovering physical laws from raw distorted video. Physical Review E, 103, 2021.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (62)
  51. David Warde-Farley and Yoshua Bengio. Improving generative adversarial networks with denoising feature matching. In Proceedings of International Conference on Learning Representations (ICLR), 2017.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (63)
  52. Nicholas Watters, Loic Matthey, Christopher P Burgess, and Alexander Lerchner. Spatial broadcast decoder: A simple architecture for learning disentangled representations in VAEs. arXiv preprint arXiv:1901.07017, 2019.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (64)
  53. Jinshan Wu. Hamiltonian formalism of game theory. arXiv preprint quant-ph/0501088, 2005.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (65)
  54. Shiying Xiong, Yunjin Tong, Xingzhe He, Cheng Yang, Shuqi Yang, and Bo Zhu. Nonseparable symplectic neural networks. In Proceedings of International Conference on Learning Representations (ICLR), 2021.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (66)
  55. Yaofeng Desmond Zhong, Biswadip Dey, and Amit Chakraborty. Dissipative SymODENet: Encoding Hamiltonian dynamics with dissipation and control into deep learning. arXiv preprint arXiv:2002.08860, 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (67)
  56. Yaofeng Desmond Zhong, Biswadip Dey, and Amit Chakraborty. Symplectic ODE-net: Learning Hamiltonian dynamics with control. In Proceedings of International Conference on Learning Representations (ICLR), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (68)
  57. Yaofeng Desmond Zhong, Biswadip Dey, and Amit Chakraborty. Benchmarking energy-conserving neural networks for learning dynamics from data. In Conference on Learning for Dynamics and Control (L4DC), 2021.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (69)
  58. Yaofeng Desmond Zhong and Naomi Leonard. Unsupervised learning of Lagrangian dynamics from images for prediction and control. Proceedings of Neural Information Processing Systems (NeurIPS), 2020.Google ScholarSyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (70)

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      SyMetric | Proceedings of the 35th International Conference on Neural Information Processing Systems (72)

      NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing Systems

      December 2021

      30517 pages

      ISBN:9781713845393

      • Editors:
      • M. Ranzato,
      • A. Beygelzimer,
      • Y. Dauphin,
      • P.S. Liang,
      • J. Wortman Vaughan

      Copyright © 2021 Neural Information Processing Systems Foundation, Inc.

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          • Published: 10 June 2024

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