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A note on the capacity of the binary perceptron (2401.15092v1)

Published 22 Jan 2024 in math.PR, cs.DM, cs.LG, and stat.ML

Abstract: Determining the capacity $\alpha_c$ of the Binary Perceptron is a long-standing problem. Krauth and Mezard (1989) conjectured an explicit value of $\alpha_c$, approximately equal to .833, and a rigorous lower bound matching this prediction was recently established by Ding and Sun (2019). Regarding the upper bound, Kim and Roche (1998) and Talagrand (1999) independently showed that $\alpha_c$ < .996, while Krauth and Mezard outlined an argument which can be used to show that $\alpha_c$ < .847. The purpose of this expository note is to record a complete proof of the bound $\alpha_c$ < .847. The proof is a conditional first moment method combined with known results on the spherical perceptron

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References (13)
  1. Altschuler, D. J. Zero-one laws for random feasibility problems. arXiv preprint arXiv:2309.13133 (2023).
  2. Capacity lower bound for the Ising perceptron. In STOC’19—Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (2019), ACM, New York, pp. 816–827.
  3. Gardner, E. Maximum storage capacity in neural networks. Europhysics letters 4, 4 (1987), 481.
  4. Gardner, E. The space of interactions in neural network models. J. Phys. A 21, 1 (1988), 257–270.
  5. Optimal storage properties of neural network models. J. Phys. A 21, 1 (1988), 271–284.
  6. On the optimal capacity of binary neural networks: Rigorous combinatorial approaches. In Proceedings of the eighth annual Conference on Learning Theory (1995), pp. 240–249.
  7. Storage capacity of memory networks with binary couplings. Journal de Physique 50, 20 (1989), 3057–3066.
  8. Sharp threshold sequence and universality for Ising perceptron models. In Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (2023), SIAM, Philadelphia, PA, pp. 638–674.
  9. On the volume of the intersection of a sphere with random half spaces. C. R. Math. Acad. Sci. Paris 334, 9 (2002), 803–806.
  10. Talagrand, M. Intersecting random half cubes. vol. 15. 1999, pp. 436–449. Statistical physics methods in discrete probability, combinatorics, and theoretical computer science (Princeton, NJ, 1997).
  11. Talagrand, M. Mean field models for spin glasses. Volume I. Springer-Verlag, Berlin, 2011.
  12. Talagrand, M. Mean field models for spin glasses. Volume II. Springer, Heidelberg, 2011.
  13. Xu, C. Sharp threshold for the Ising perceptron model. Ann. Probab. 49, 5 (2021), 2399–2415.
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