On the tap free energy in the mixed p-spin models

1. [1911.12052v1] A constrained TAP approach for disordered spin models.
2. The Generalized TAP Free Energy II - NSF Public Access.
3. Generalized TAP Free Energy - Chen - Wiley Online Library.
4. PDF FREE ENERGY LANDSCAPES IN SPHERICAL SPIN GLASSES - arX.
5. PDF Wei-KuoChen ArnabSen April25,2022 arXiv:1512.08492v1 [math.PR] 28 Dec 2015.
6. A constrained TAP approach for disordered spin models... - ResearchGate.
7. [PDF] On the TAP free energy in the mixed p-spin models.
8. Free energy in the mixed p-spin models with vector spins.
9. On the TAP Free Energy in the Mixed p-Spin Models - ResearchGate.
10. the_generalized_tap_free_energy_ii__expertsminnesota" title="TAP Free Energy II ExpertsMinnesota">The Generalized TAP Free Energy II ExpertsMinnesota.">TAP Free Energy II ExpertsMinnesota">The Generalized TAP Free Energy II ExpertsMinnesota.
11. PDF Free energy in the mixed p-spin models with vector spins - arX.
12. the_generalized_tap_free_energy_-_researchgate" title="TAP free energy - ResearchGate">The generalized TAP free energy - ResearchGate.">TAP free energy - ResearchGate">The generalized TAP free energy - ResearchGate.
13. P arXiv:1903.01030v1 [math.PR] 4 Mar 2019.
14. the_free_energy_of_spherical_pure_p-spin_models" title="Free energy of spherical pure p-spin models...">The free energy of spherical pure p-spin models.">Free energy of spherical pure p-spin models...">The free energy of spherical pure p-spin models.

[1911.12052v1] A constrained TAP approach for disordered spin models.

Aim of this paper is to investigatethe TAP free energy representation rather than its critical points, in the setting of mixed p-spin models with Ising spins. Our first main result in Theorem 1 below states that the free energy can be written as the supremum of the TAP free energy if the Edwards-Anderson parameter is constrained to the right. In the setting of mixed p-spin models with Ising spins, we prove that the free energy can indeed be written as the supremum of the TAP free energy over the space of local. The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical.

The Generalized TAP Free Energy II - NSF Public Access.

We consider the mixed p-spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer [67].More precisely, we define and compute the generalized TAP correction, and establish the corresponding generalized TAP representation for the free energy. TAP free energy, spin glasses and variational inference. Zhou Fan, Song Mei and Andrea Montanari. 1 Jan 2021 | The Annals of Probability, Vol. 49, No. 1.... On the TAP Free Energy in the Mixed p-Spin Models. Wei-Kuo Chen and Dmitry Panchenko. 4 May 2018 | Communications in Mathematical Physics, Vol. 362, No. 1.

Generalized TAP Free Energy - Chen - Wiley Online Library.

We revisit the metastability properties of the mixed p-spin spherical disordered models. Firstly, using known methods, we show that there is temperature chaos in a broad range of temperatures. Secondly, we modify the definition of the Thouless-Anderson-Palmer free energy density by including constraints that enforce a chosen overlap between the searched metastable states and another reference. Using a replica calculation that the TAP free energy at the magnetization vector coincides with the replica-symmetric prediction for the free energy. Our present study is in large part motivated by a recent renewed interest in these types of mean-field models from the information theory, statistics, and machine learning communities [43, 50, 41,.

PDF FREE ENERGY LANDSCAPES IN SPHERICAL SPIN GLASSES - arX.

We revisit the metastability properties of the mixed p-spin spherical disordered models. Firstly, using known methods, we show that there is temperature chaos in a broad range of temperatures. Secondly, we modify the definition of the Thouless-Anderson-Palmer free energy density by including constraints that enforce a chosen overlap between the searched metastable states and another reference.

PDF Wei-KuoChen ArnabSen April25,2022 arXiv:1512.08492v1 [math.PR] 28 Dec 2015.

with D. Panchenko On the TAP free energy of the mixed p-spin models. Comm. Math. Phys., Vol. 362, No. 1, 219252 2018 with D. Panchenko Disorder chaos in some diluted spin glass models. Ann. App.... Fluctuations of the free energy in the mixed p-spin models with external eld. Probab. Theory Related Fields, Vol 168, No. 1, 4153 2017. Digital Object Identifier DOI Commun. Math. Phys. 362, 219-252 2018 Communications in Mathematical Physics On the TAP. On the TAP Free Energy in the Mixed p-Spin Modelsquot;. en. Aug 2018; COMMUN MATH PHYS; 10-3616; Wei-Kuo Chen; Dmitry Panchenko; Wei-Kuo Chen and Dmitry Panchenko. quot;On the TAP Free Energy in the Mixed.

A constrained TAP approach for disordered spin models... - ResearchGate.

We consider the mixed pspin meanfield spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer [67]. A duality principle in spin glasses with A. Auffinger Electron. J. Probab., Vol 22, No. 61 2017 Fluctuations of the free energy in the mixed p-spin models with external field with P. Dey and D. Panchenko Probab. Theory Related Fields. Nov 13, 2021 In a recent paper Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math., we developed the generalized TAP approach for mixed p-spin models with Ising spins at.

[PDF] On the TAP free energy in the mixed p-spin models.

In a recent paper Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math., we developed the generalized TAP approach for mixed p-spin models with Ising spins at. The mixed p-spin model with vector spins by HN= k Hk N k. 6 We will consider only mixed even p-spin models, so we will assume thatpk=0 for all odd p 3.Our main goal will be to compute the limit of the free energy FN = 1 N Elog Z N expHNdN. 7.

Free energy in the mixed p-spin models with vector spins.

TAP approach for multi-species spherical spin glasses I: general theory. Preprint. On the second moment method and RS phase of multi-species spherical spin glasses. Preprint. Concentration of the complexity of spherical pure p-spin models at arbitrary energies with Ofer Zeitouni. The free energy of spherical pure p-spin models -- computation. Feb 6, 2019 Abstract. We reinterpret the ThoulessAndersonPalmer approach to mean field spin glass models as a variational principle in the spirit of the Gibbs variational principle and the BraggWilliams approximation. We prove this TAPPlefka variational principle rigorously in the case of the spherical SherringtonKirkpatrick model. Nov 10, 2020 In a recent paper Chen et al. in The generalized TAP free energy, to appear in Comm. Pure Appl. Math., we developed the generalized TAP approach for mixed p-spin models with Ising spins at positive temperature. Here we extend these results in two directions. We find a simplified representation for the energy of the generalized TAP states in terms of the Parisi measure of the model and, in.

On the TAP Free Energy in the Mixed p-Spin Models - ResearchGate.

Standard knowledge on the metastability of the spherical p-spin models suggests that the behaviour of the mixed case should be different from the one of the monomial model in many respects. Is known as the TAP free energy, and its first-order stationarity conditions are known as the TAP equations. The relationship between the TAP equations and the Gibbs measure has been... mixed p-spin spherical models and for models on the torus. These models are simpler because of the underlying symmetry [5-7, 13]. Jul 11, 2022 In 1977, Thouless, Anderson, and Palmer TAP derived a system of consistent equations in terms of the effective magnetization in order to study the free energy in the Sherrington-Kirkpatrick SK spin glass model. The solutions to their equations were predicted to contain vital information about the landscapes in the SK Hamiltonian and the TAP free energy and moreover have direct connections.

TAP Free Energy II ExpertsMinnesota">The Generalized TAP Free Energy II ExpertsMinnesota.

For the spherical single-species mixed p-spin models, the Parisi formula for the limit of the free energy was proved by Talagrand [31] for models with even interactions, and later generalized to. Nov 13, 2021 Importantly, the pure multi-species models do not satisfy the convexity assumption on the mixture which was crucial in the recent proofs of the Parisi formula for the multi-species Sherrington-Kirkpatrick model by Barra et al. 2015 and Panchenko 2015 and for the multi-species spherical mixed p-spin models by Bates and Sohn 2021. Task dataset model metric name metric value global rank remove.

PDF Free energy in the mixed p-spin models with vector spins - arX.

ArXiv:1709.03468v2 [math.PR] 12 Jan 2019 On the TAP free energy in the mixed p-spin models Wei-Kuo Chen Dmitry Panchenko January 15, 2019 Abstract In [41], Thouless, Anderso. We consider the mixed pspin meanfield spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer [67].

TAP free energy - ResearchGate">The generalized TAP free energy - ResearchGate.

Jan 12, 2021 January 2021; Authors. May 3, 2023 We compute the free energy at all temperatures for the spherical pure p-spin models from the generalized ThoulessAndersonPalmer representation.This is the first example of a mixed p-spin model for which the free energy is computed in the whole replica symmetry breaking phase, without appealing to the famous Parisi formula.

P arXiv:1903.01030v1 [math.PR] 4 Mar 2019.

The Parisi formula for the free energy in the SherringtonKirkpatrick and mixed p-spin models was proved by M. Talagrand in [24] following the discovery of the replica symmetry breaking interpolation scheme by F. Guerra in [8]. However, for technical reasons only the case of p-spin interactions for even p 2 was considered. We consider the mixed -spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer. More precisely, we define and compute the generalized TAP correction, and establish the corresponding generalized TAP representation for the free energy.

Free energy of spherical pure p-spin models...">The free energy of spherical pure p-spin models.

Computing the free energy of mean-field spin glass models... [AJ19], and generalizations of the TAP free energy [Sub18, CPS23]. The phase diagram has also received a tremendous amount of attention [Ton02, AC15, JT17]. In particular,... was subsequently extended to Ising mixed p-spin models [EAMS21, Sel21b]; these algorithms also find. Sep 11, 2017 In the setting of mixed p-spin models with Ising spins, we prove that the free energy can indeed be written as the supremum of the TAP free energy over the space of local magnetizations whose EdwardsAnderson order parameter self-overlap is to the right of the support of the Parisi measure.