An Iterative Construction of Solutions of the TAP Equations for the Sherrington–Kirkpatrick Model

By E. Bolthausen. 2012

201 citations recorded by the source corpus.

We propose an iterative scheme for the solutions of the TAP-equations in the Sherrington–Kirkpatrick model which is shown to converge up to and including the de Almeida–Thouless line. The main tool is a representation of the iterations which reveals an interesting structure of them. This representation does not depend on the temperature parameter, but for temperatures below the de Almeida–Thouless line, it contains a part which does not converge to zero in the limit.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7c7386bb14d4859ecf7cd3ae56a3b5a13fe15171

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Jean Barbier
2. Lenka Zdeborov'a
3. Nicolas Macris
4. Florent Krzakala
5. Greg Yang
6. Léo Miolane

In Nuclear and High Energy Physics

1. Jean Barbier
2. Lenka Zdeborov'a
3. Nicolas Macris
4. Florent Krzakala
5. Greg Yang
6. Léo Miolane

In Statistical and Nonlinear Physics

1. Florent Krzakala
2. Lenka Zdeborov'a
3. Jean Barbier
4. Nicolas Macris
5. Greg Yang
6. Léo Miolane
7. Tiago P. Peixoto
8. Jorge Kurchan

Citations in the corpus

• Statistical physics of inference: thresholds and algorithms (2015, methodology): “[38] Erwin Bolthausen.”
• Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes (2019, methodology): “(Graph) Convolution Consider a convolution network with L layers, with layer l having n channels, with kernel positions ker (for example, for a 3 × 5 kernel, ker = [3] × [5]), and with feature map pixel positions pos (for example, for a 128× 256 feature map, pos = [128]× [256]).”
• Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation (2019, methodology): “They are proved via a Gaussian conditioning technique first used in Bolthausen (2012) for analyzing the TAP equations in spin glass theory.”
• Optimal errors and phase transitions in high-dimensional generalized linear models (2017, methodology): “GAMP is remarkable in that its asymptotic ( n , m → ∞ , m / n → α ) performance can be analyzed rigorously using the so-called state evolution (42–45).”