惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

F
Fortinet All Blogs
爱范儿
爱范儿
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
B
Blog
WordPress大学
WordPress大学
Jina AI
Jina AI
GbyAI
GbyAI
aimingoo的专栏
aimingoo的专栏
N
Netflix TechBlog - Medium
腾讯CDC
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
阮一峰的网络日志
阮一峰的网络日志
The GitHub Blog
The GitHub Blog
V
Visual Studio Blog
Google DeepMind News
Google DeepMind News
月光博客
月光博客
博客园 - Franky
Y
Y Combinator Blog
MyScale Blog
MyScale Blog
大猫的无限游戏
大猫的无限游戏
Martin Fowler
Martin Fowler
雷峰网
雷峰网
小众软件
小众软件
H
Hackread – Cybersecurity News, Data Breaches, AI and More

math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Studying Hopfield models via fully lifted random duality ...
Mihailo Stojnic · 2023-11-30 · via math.ST updates on arXiv.org

Relying on a recent progress made in studying bilinearly indexed (bli) random processes in \cite{Stojnicnflgscompyx23,Stojnicsflgscompyx23}, the main foundational principles of fully lifted random duality theory (fl RDT) were established in \cite{Stojnicflrdt23}. We here study famous Hopfield models and show that their statistical behavior can be characterized via the fl RDT. Due to a nestedly lifted nature, the resulting characterizations and, therefore, the whole analytical machinery that produces them, become fully operational only if one can successfully conduct underlying numerical evaluations. After conducting such evaluations for both positive and negative Hopfield models, we observe a remarkably fast convergence of the fl RDT mechanism. Namely, for the so-called square case, the fourth decimal precision is achieved already on the third (second non-trivial) level of lifting (3-sfl RDT) for the positive and on the fourth (third non-trivial) level of lifting (4-sfl RDT) for the corresponding negative model. In particular, we obtain the scaled ground state free energy $\approx 1.7788$ for the positive and $\approx 0.3279$ for the negative model.