Papers
Topics
Authors
Recent
Search
2000 character limit reached

Benchmarking the optimization optical machines with the planted solutions

Published 12 Nov 2023 in stat.CO, cond-mat.stat-mech, physics.comp-ph, and physics.optics | (2311.06859v2)

Abstract: We introduce universal, easy-to-reproduce generative models for the QUBO instances to differentiate the performance of the hardware/solvers effectively. Our benchmark process extends the well-known Hebb's rule of associative memory with the asymmetric pattern weights. We provide a comprehensive overview of calculations conducted across various scales and using different classes of dynamical equations. Our aim is to analyze their results, including factors such as the probability of encountering the ground state, planted state, spurious state, or states falling outside the predetermined energy range. Moreover, the generated problems show additional properties, such as the easy-hard-easy complexity transition and complicated cluster structures of planted solutions. Our method establishes a prospective platform to potentially address other questions related to the fundamental principles behind device physics and algorithms for novel computing machines.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (70)
  1. I. Dunning, S. Gupta, and J. Silberholz, “What works best when? a systematic evaluation of heuristics for max-cut and qubo,” INFORMS Journal on Computing, vol. 30, no. 3, pp. 608–624, 2018.
  2. G. Kochenberger, J.-K. Hao, F. Glover, M. Lewis, Z. Lü, H. Wang, and Y. Wang, “The unconstrained binary quadratic programming problem: a survey,” Journal of combinatorial optimization, vol. 28, no. 1, pp. 58–81, 2014.
  3. A. Lucas, “Ising formulations of many np problems,” Frontiers in physics, p. 5, 2014.
  4. S. Mücke, N. Piatkowski, and K. Morik, “Learning bit by bit: Extracting the essence of machine learning.,” in LWDA, pp. 144–155, 2019.
  5. CRC Press, 2018.
  6. P. Minzioni, C. Lacava, T. Tanabe, J. Dong, X. Hu, G. Csaba, W. Porod, G. Singh, A. E. Willner, A. Almaiman, et al., “Roadmap on all-optical processing,” Journal of Optics, vol. 21, no. 6, p. 063001, 2019.
  7. D. Woods and T. J. Naughton, “Optical computing,” Applied Mathematics and Computation, vol. 215, no. 4, pp. 1417–1430, 2009.
  8. H. Wu and Q. Dai, “Artificial intelligence accelerated by light,” 2021.
  9. N. Stroev and N. G. Berloff, “Analog photonics computing for information processing, inference, and optimization,” Advanced Quantum Technologies, p. 2300055, 2023.
  10. N. G. Berloff, M. Silva, K. Kalinin, A. Askitopoulos, J. D. Töpfer, P. Cilibrizzi, W. Langbein, and P. G. Lagoudakis, “Realizing the classical xy hamiltonian in polariton simulators,” Nature materials, vol. 16, no. 11, p. 1120, 2017.
  11. K. P. Kalinin and N. G. Berloff, “Networks of non-equilibrium condensates for global optimization,” New Journal of Physics, vol. 20, no. 11, p. 113023, 2018.
  12. M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Physical review letters, vol. 106, no. 22, p. 223901, 2011.
  13. V. Pal, C. Tradonsky, R. Chriki, A. A. Friesem, and N. Davidson, “Observing dissipative topological defects with coupled lasers,” Physical review letters, vol. 119, no. 1, p. 013902, 2017.
  14. C. Tradonsky, O. Raz, V. Pal, R. Chriki, A. A. Friesem, and N. Davidson, “Rapid phase retrieval by lasing,” arXiv preprint arXiv:1805.10967, 2018.
  15. P. L. McMahon, A. Marandi, Y. Haribara, R. Hamerly, C. Langrock, S. Tamate, T. Inagaki, H. Takesue, S. Utsunomiya, K. Aihara, et al., “A fully programmable 100-spin coherent ising machine with all-to-all connections,” Science, vol. 354, no. 6312, pp. 614–617, 2016.
  16. R. Hamerly, T. Inagaki, P. L. McMahon, D. Venturelli, A. Marandi, T. Onodera, E. Ng, C. Langrock, K. Inaba, T. Honjo, et al., “Experimental investigation of performance differences between coherent ising machines and a quantum annealer,” Science advances, vol. 5, no. 5, p. eaau0823, 2019.
  17. F. Böhm, T. Inagaki, K. Inaba, T. Honjo, K. Enbutsu, T. Umeki, R. Kasahara, and H. Takesue, “Understanding dynamics of coherent ising machines through simulation of large-scale 2d ising models,” Nature communications, vol. 9, no. 1, p. 5020, 2018.
  18. D. Pierangeli, G. Marcucci, and C. Conti, “Large-scale photonic ising machine by spatial light modulation,” Physical Review Letters, vol. 122, no. 21, p. 213902, 2019.
  19. G. Mourgias-Alexandris, H. Ballani, N. G. Berloff, J. H. Clegg, D. Cletheroe, C. Gkantsidis, I. Haller, V. Lyutsarev, F. Parmigiani, L. Pickup, et al., “Analog iterative machine (aim): using light to solve quadratic optimization problems with mixed variables,” arXiv preprint arXiv:2304.12594, 2023.
  20. N. Stroev and N. G. Berloff, “Discrete polynomial optimization with coherent networks of condensates and complex coupling switching,” Physical Review Letters, vol. 126, no. 5, p. 050504, 2021.
  21. D. A. Chermoshentsev, A. O. Malyshev, E. S. Tiunov, D. Mendoza, A. Aspuru-Guzik, A. K. Fedorov, and A. I. Lvovsky, “Polynomial unconstrained binary optimisation inspired by optical simulation,” arXiv preprint arXiv:2106.13167, 2021.
  22. E. S. Tiunov, A. E. Ulanov, and A. Lvovsky, “Annealing by simulating the coherent ising machine,” Optics express, vol. 27, no. 7, pp. 10288–10295, 2019.
  23. K. P. Kalinin and N. G. Berloff, “Computational complexity continuum within ising formulation of np problems,” Communications Physics, vol. 5, no. 1, pp. 1–10, 2022.
  24. L. Zdeborová, “Statistical physics of hard optimization problems,” arXiv preprint arXiv:0806.4112, 2008.
  25. L. Zdeborová and F. Krzakala, “Statistical physics of inference: Thresholds and algorithms,” Advances in Physics, vol. 65, no. 5, pp. 453–552, 2016.
  26. I. P. Gent and T. Walsh, “The sat phase transition,” in ECAI, vol. 94, pp. 105–109, PITMAN, 1994.
  27. B. Aubin, A. Maillard, F. Krzakala, N. Macris, L. Zdeborová, et al., “The committee machine: Computational to statistical gaps in learning a two-layers neural network,” Advances in Neural Information Processing Systems, vol. 31, 2018.
  28. F. Gerace, B. Loureiro, F. Krzakala, M. Mézard, and L. Zdeborová, “Generalisation error in learning with random features and the hidden manifold model,” in International Conference on Machine Learning, pp. 3452–3462, PMLR, 2020.
  29. F. Hamze, J. Raymond, C. A. Pattison, K. Biswas, and H. G. Katzgraber, “Wishart planted ensemble: A tunably rugged pairwise ising model with a first-order phase transition,” Physical Review E, vol. 101, no. 5, p. 052102, 2020.
  30. F. Hamze, D. C. Jacob, A. J. Ochoa, D. Perera, W. Wang, and H. G. Katzgraber, “From near to eternity: spin-glass planting, tiling puzzles, and constraint-satisfaction problems,” Physical Review E, vol. 97, no. 4, p. 043303, 2018.
  31. F. Krzakala and L. Zdeborová, “Statistical physics methods in optimization and machine learning,” 2021.
  32. A. Abbaras, B. Aubin, F. Krzakala, and L. Zdeborová, “Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning,” in Mathematical and Scientific Machine Learning, pp. 27–54, PMLR, 2020.
  33. J. Barbier, F. Krzakala, N. Macris, L. Miolane, and L. Zdeborová, “Optimal errors and phase transitions in high-dimensional generalized linear models,” Proceedings of the National Academy of Sciences, vol. 116, no. 12, pp. 5451–5460, 2019.
  34. F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborová, “Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2012, no. 08, p. P08009, 2012.
  35. D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proceedings of the National Academy of Sciences, vol. 106, no. 45, pp. 18914–18919, 2009.
  36. T. Aonishi, K. Mimura, M. Okada, and Y. Yamamoto, “L0 regularization-based compressed sensing with quantum-classical hybrid approach,” Quantum Science and Technology, 2022.
  37. D. Gamarnik, “The overlap gap property: A topological barrier to optimizing over random structures,” Proceedings of the National Academy of Sciences, vol. 118, no. 41, p. e2108492118, 2021.
  38. D. Gamarnik, C. Moore, and L. Zdeborová, “Disordered systems insights on computational hardness,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2022, no. 11, p. 114015, 2022.
  39. J.-G. Liu, X. Gao, M. Cain, M. D. Lukin, and S.-T. Wang, “Computing solution space properties of combinatorial optimization problems via generic tensor networks,” arXiv preprint arXiv:2205.03718, 2022.
  40. D. O. Hebb, “Organization of behavior. new york: Wiley,” J. Clin. Psychol, vol. 6, no. 3, pp. 335–307, 1949.
  41. J. J. Hopfield, “Neural networks and physical systems with emergent collective computational abilities.,” Proceedings of the national academy of sciences, vol. 79, no. 8, pp. 2554–2558, 1982.
  42. M. J. Schuetz, J. K. Brubaker, and H. G. Katzgraber, “Combinatorial optimization with physics-inspired graph neural networks,” Nature Machine Intelligence, vol. 4, no. 4, pp. 367–377, 2022.
  43. M. Mohseni, D. Eppens, J. Strumpfer, R. Marino, V. Denchev, A. K. Ho, S. V. Isakov, S. Boixo, F. Ricci-Tersenghi, and H. Neven, “Nonequilibrium monte carlo for unfreezing variables in hard combinatorial optimization,” arXiv preprint arXiv:2111.13628, 2021.
  44. World Scientific, 2000.
  45. B. A. Wilson, Z. A. Kudyshev, A. V. Kildishev, S. Kais, V. M. Shalaev, and A. Boltasseva, “Machine learning framework for quantum sampling of highly constrained, continuous optimization problems,” Applied Physics Reviews, vol. 8, no. 4, p. 041418, 2021.
  46. V. Ros and Y. V. Fyodorov, “The high-d landscapes paradigm: spin-glasses, and beyond,” arXiv preprint arXiv:2209.07975, 2022.
  47. P. G. Wolynes, “Landscapes, funnels, glasses, and folding: From metaphor to software,” Proceedings of the American Philosophical Society, vol. 145, no. 4, pp. 555–563, 2001.
  48. R. H. Austin, “Free energies, landscapes, and fitness in evolution dynamics,” in Quantitative Biology: From Molecular to Cellular Systems, pp. 1–21, CRC Press, 2012.
  49. P. Krugman, “Complex landscapes in economic geography,” The American Economic Review, vol. 84, no. 2, pp. 412–416, 1994.
  50. M. Goldstein, “Viscous liquids and the glass transition: a potential energy barrier picture,” The Journal of Chemical Physics, vol. 51, no. 9, pp. 3728–3739, 1969.
  51. D. O. Hebb, The organization of behavior: A neuropsychological theory. Psychology Press, 2005.
  52. W. A. Little, “The existence of persistent states in the brain,” Mathematical biosciences, vol. 19, no. 1-2, pp. 101–120, 1974.
  53. D. Krotov and J. J. Hopfield, “Dense associative memory for pattern recognition,” Advances in neural information processing systems, vol. 29, 2016.
  54. H. Ramsauer, B. Schäfl, J. Lehner, P. Seidl, M. Widrich, T. Adler, L. Gruber, M. Holzleitner, M. Pavlović, G. K. Sandve, et al., “Hopfield networks is all you need,” arXiv preprint arXiv:2008.02217, 2020.
  55. S. Chen, G. Huang, G. Piccioli, and L. Zdeborová, “Planted x y model: Thermodynamics and inference,” Physical Review E, vol. 106, no. 5, p. 054115, 2022.
  56. D. Perera, I. Akpabio, F. Hamze, S. Mandra, N. Rose, M. Aramon, and H. G. Katzgraber, “Chook–a comprehensive suite for generating binary optimization problems with planted solutions,” arXiv preprint arXiv:2005.14344, 2020.
  57. I. Hen, J. Job, T. Albash, T. F. Rønnow, M. Troyer, and D. A. Lidar, “Probing for quantum speedup in spin-glass problems with planted solutions,” Physical Review A, vol. 92, no. 4, p. 042325, 2015.
  58. J. Dong, L. Valzania, A. Maillard, T.-a. Pham, S. Gigan, and M. Unser, “Phase retrieval: From computational imaging to machine learning: A tutorial,” IEEE Signal Processing Magazine, vol. 40, no. 1, pp. 45–57, 2023.
  59. A. Maillard, B. Loureiro, F. Krzakala, and L. Zdeborová, “Phase retrieval in high dimensions: Statistical and computational phase transitions,” Advances in Neural Information Processing Systems, vol. 33, pp. 11071–11082, 2020.
  60. J. J. Hopfield and D. W. Tank, ““neural” computation of decisions in optimization problems,” Biological cybernetics, vol. 52, no. 3, pp. 141–152, 1985.
  61. J. M. Kosterlitz, D. J. Thouless, and R. C. Jones, “Spherical model of a spin-glass,” Physical Review Letters, vol. 36, no. 20, p. 1217, 1976.
  62. World Scientific Publishing Company, 1987.
  63. CRC Press, 1990.
  64. S. N. Majumdar and G. Schehr, “Top eigenvalue of a random matrix: large deviations and third order phase transition,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2014, no. 1, p. P01012, 2014.
  65. M. Syed and N. G. Berloff, “Physics-enhanced bifurcation optimisers: All you need is a canonical complex network,” arXiv preprint arXiv:2207.11256, 2022.
  66. John Wiley & Sons, 2009.
  67. F. C. Hoppensteadt and E. M. Izhikevich, “Synchronization of mems resonators and mechanical neurocomputing,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 48, no. 2, pp. 133–138, 2001.
  68. H. Goto, K. Tatsumura, and A. R. Dixon, “Combinatorial optimization by simulating adiabatic bifurcations in nonlinear hamiltonian systems,” Science advances, vol. 5, no. 4, p. eaav2372, 2019.
  69. H. Goto, K. Endo, M. Suzuki, Y. Sakai, T. Kanao, Y. Hamakawa, R. Hidaka, M. Yamasaki, and K. Tatsumura, “High-performance combinatorial optimization based on classical mechanics,” Science Advances, vol. 7, no. 6, p. eabe7953, 2021.
  70. T. Kanao and H. Goto, “Simulated bifurcation assisted by thermal fluctuation,” arXiv preprint arXiv:2203.08361, 2022.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 1 like about this paper.

Sign Up for Free