相关论文: Networks of neural networks: more is different

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet…

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking…

Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming…

The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…

In this paper we study, via equilibrium statistical mechanics, the properties of the internal energy of an Hopfield neural network whose patterns are stored continuously (Gaussian distributed). The model is shown to be equivalent to a…

The Hopfield network has been applied to solve optimization problems over decades. However, it still has many limitations in accomplishing this task. Most of them are inherited from the optimization algorithms it implements. The computation…

Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…

In this paper, the commensurate fractional-order variant of an Hopfield neuronal network is analyzed. The system is integrated with the ABM method for fractional-order equations. Beside the standard stability analysis of equilibria, the…

We consider a three-layer Sejnowski machine and show that features learnt via contrastive divergence have a dual representation as patterns in a dense associative memory of order P=4. The latter is known to be able to Hebbian-store an…

The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…

"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but…

We present a detailed comparison of two types of sequence to sequence models trained to conduct a compositional task. The models are architecturally identical at inference time, but differ in the way that they are trained: our baseline…

We consider Hopfield networks, where neurons interact pair-wise by Hebbian couplings built over $i$. a set of definite patterns (ground truths), $ii$. a sample of labeled examples (supervised setting), $iii$. a sample of unlabeled examples…

This paper introduces a novel unsupervised learning paradigm inspired by Gerald Edelman's theory of neuronal group selection ("Neural Darwinism"). The presented automaton learns to recognize arbitrary symbols (e.g., letters of an alphabet)…

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…

The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfy constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining…

The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…

We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…