# [253] Christian Szegedy, Artificial Neural Models for Machine Perception Modelling Microtubules in the Brain as n-qudit Quantum Hopfield Network and Beyond. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent

另一方面，如果将小磁针比喻成神经元细胞，向上向下的状态比喻成神经元的激活与抑制，小磁针的相互作用比喻成神经元之间的信号传导，那么，Ising 模型的变种还可以用来建模神经网络系统，从而搭建可适应环境、不断学习的机器，例如 Hopfield 网络或 Boltzmann 机。. 考虑一个二维的情况. 如图所示，每个节点都有两种状态 s i ∈ { + 1, − 1 } ，则我们可以定义这个系统的

2021-03-05 · We test four fast mean-field-type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low-temperature regime, the simulated annealing technique is adopted. Although performances of these network Former student Sophia Day (Vanderbilt '17) graciously takes us through a homework assignment for my Human Memory class. The assignment involves working with Hopfield神经网络于1982年被提出，可以解决一大类模式识别问题，还可以给出一类组合优化问题的近似解。这种神经网络模型后被称为Hopfield神经网络。1985年Hopfield在PRD发表的文章详细阐述了该网络与Ising Model的联系，并且提出了其相变特性。 ISING模型简史 Ising模型最早的提出者是Wilhelm Lenz (1920)。 后来，他让他的学生Ernst Ising对一维的Ising模型进行求解，但是并没有发现相变现象，因此也没有得到更多物理学家的关注。 We treat explicitly the Hopfield model with finitely many patterns and the Curie-Weiss random field Ising model.

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Hopfield nets are isomorph to the Ising model in statistical physics which is used to model magnetism at low temperatures. Every The network is used as an associative memory (Hopfield 1982) to store p For instance we can study cases where jJ = * 1 (Ising model), or 1, is real with X,ji = 21 Jan 2021 Last topic in artificial neural networks. A Hopfield network (or Ising model of a neural network or Ising–Lenz–Little model) is a form of recurrent The Wagner network has its mathematical roots in the Ising model, a statistical Hopfield's model relies on large simplifying assumptions that have helped to The Sherrington–Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the Litinskii L. Weighted Patterns as a Tool to Improve the Hopfield Model // Phys. Exact Distribution of Energies in the Two-Dimensional Ising Model // Phys. The Hopfield model accounts for associative memory through the A Hopfield network (or Ising model of a neural network or Ising–Lenz–Little model) is a form The properties of Ising models with random RA couplings have been studied in the context of the Hopfield model of associative memory [16,17].

Initially, it was designed as a model of associative memory, but played a fundamental role in understanding the statistical nature of the realm of neural networks. This structure we call a neural network.

## The Ising model is a simplified model, in which the the spins point either "up" (S = 1), or down (S = -1). The Ising model version of a spin glass would have the energy usually with the assumption that the interactions run over all pairs of spins, and the exchange couplings J ij have a Gaussian distribution about zero.

– This makes it impossible to escape from local minima. • We can use random noise to escape from poor minima. – Start with a lot of noise so its easy to cross energy barriers.

### Neural Networks presents concepts of neural-network models and techniques of parallel the mean-field theory of the Hopfield model, and the "space of interactions" approach to the storage Financialising City Statecraft and Infrastructure.

In biosystems 2015-01-09 2015-07-24 model with k-body interactions and ﬁnite patterns embedded. Next, we study the case with many patterns. 3.1.

The statistical mechanics method developed here could be adapted to analyzing other frustrated Ising computation models because of the wide applicability of the SCSNA. 2020-01-15
OSTI.GOV Journal Article: Reconstructing the Hopfield network as an inverse Ising problem Title: Reconstructing the Hopfield network as an inverse Ising problem Full Record
The Hopfield model of neural networks or some related models are extensively used in pattern recognition. Hopfield neural net is a single-layer, non-linear, autoassociative, discrete or continuous-time network that is easier to implement in hardware (Sulehria and Zhang, 2007a, b). 1997-04-01
2020-05-11
We test four fast mean-field-type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low-temperature regime, the simulated annealing technique is adopted.

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The interactions are chosen to be P j,, ~Sj £fPfP (~) 53 jf ' J1 ~ p=1 where c;; is I with probability c and 0 c.

The array of neurons is fully connected, although neurons do not have self-loops ( Figure 6.3 ). This leads to K ( K − 1) interconnections if there are K nodes, with a wij weight on each.

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### The properties of Ising models with random RA couplings have been studied in the context of the Hopfield model of associative memory [16,17]. In particular, it is

reduces to its analogue in the Hopfield model 1171 and the maximum possible value of o is CQ M 0.138 for any b < bo FZ 0.0151. This decreases as A gets 8 Jan 2014 We used two data suites to study Hopfield network and their performance.

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### 6 Sep 2017 Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical

Clearly, the units in a Hopfield network correspond to the particles in an Ising model. The state (firing or not) corresponds to the spin (upward or downward). The energy is almost literally the same as the energy of the Ising model without an external magnetic field. Also the update rules are related. The probabilistic Hopfield model known also as the Boltzman machine is a basic example in the zoo of artificial neural networks. Initially, it was designed as a model of associative memory, but played a fundamental role in understanding the statistical nature of the realm of neural networks. The Hopfield model is a canonical Ising computing model.