Free energy in multi-species mixed p-spin spherical models

Bates, Erik; Youngtak, Sohn,

doi:10.1214/22-ejp780

Cited by 14 publications

(4 citation statements)

References 76 publications

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“…We emphasize that algorithmic symmetry breaking is not a barrier to any algorithm, as the optimal (p, Φ, q 0 ) for the variational principle needs to be computed only once. Moreover ξ is convex in the examples shown in Figure 2, so algorithmic symmetry breaking is not related to the failure of the interpolation method to determine the free energy (obtained for convex ξ in [BS22]).…”

Section: Non-uniqueness Of Maximizers and Algorithmic Symmetry Breakingmentioning

confidence: 99%

“…It was later studied further in [KS85,FKS87a,FKS87b]. Recent rigorous results on the free energy include [BCMT15,Pan15,Sub21b,BS22]. While the analogous lower bound to the Parisi formula applies in general with a similar proof, the upper bound is only known in two non-trivial special cases: models where ξ is convex in the positive orthant, and pure models (assuming the N → ∞ limit exists in the latter case).…”

Section: Other Related Workmentioning

confidence: 99%

“…Due to this limitation of the interpolation method, the proof of our previous result does not generalize to single-species spin glasses with odd interactions, nor to multi-species spin glasses. For the same reason, the Parisi formula for the ground state of a multi-species spin glass is known only in restricted cases [BCMT15,Pan15,Sub21b,BS22].…”

Section: Introductionmentioning

confidence: 99%

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Tight Lipschitz Hardness for optimizing Mean Field Spin Glasses

Huang

Sellke

2022

2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)

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We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lipschitz with respect to the disorder through a variational principle that we study in detail. We rely on the branching overlap gap property introduced in our previous work and develop a new method to establish it that does not require the interpolation method. Consequently our results apply even for models with non-convex covariance, where the Parisi formula for the true ground state remains open. As a special case, we obtain the algorithmic threshold for all single-species spherical spin glasses, which was previously known only for even models. We also obtain closed-form formulas for pure models which coincide with the E∞ value previously determined by the Kac-Rice formula.

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Section: Non-uniqueness Of Maximizers and Algorithmic Symmetry Breakingmentioning

confidence: 99%

Section: Other Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tight Lipschitz Hardness for optimizing Mean Field Spin Glasses

Huang

Sellke

2022

2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)

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“…After Mourrat's interpretation of the Parisi formula as the Hopf-Lax formula for a Hamilton-Jacobi equation [15], the formula was extended for enriched models [18]. For spherical spins, the Parisi formula was proven for the SK model [29], the mixed p-spin model [8], and the multi-species model [4]. Since we have assumed that P N is a product measure, the most relevant works are [19,24,25,18].…”

Section: Introductionmentioning

confidence: 99%

“Cusp-overlap” technique simplifies the implantation of Chinese domestic transcatheter valve in transcatheter aortic valve implantation

Sun

2021

Chinese Medical Journal

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We propose a simpler approach to identifying the limit of free energy in a vector spin glass model by adding a self-overlap correction to the Hamiltonian. This avoids constraining the self-overlap and allows us to identify the limit with the classical Parisi formula, similar to the proof for scalar models with Ising spins. For the upper bound, the correction cancels self-overlap terms in Guerra's interpolation. For the lower bound, we add an extra perturbation term to make the self-overlap concentrate, a technique already used in [16,17] to ensure the Ghirlanda-Guerra identities. We then remove the correction using a Hamilton-Jacobi equation technique, which yields a formula similar to that in [25]. Additionally, we sketch a direct proof of the main result in [18].

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Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature

Collins-Woodfin,

2024

Ann. Henri Poincaré

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Free energy in multi-species mixed p-spin spherical models

Cited by 14 publications

References 76 publications

Tight Lipschitz Hardness for optimizing Mean Field Spin Glasses

Tight Lipschitz Hardness for optimizing Mean Field Spin Glasses

“Cusp-overlap” technique simplifies the implantation of Chinese domestic transcatheter valve in transcatheter aortic valve implantation

Free Energy Fluctuations of the Bipartite Spherical SK Model at Critical Temperature

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