相关论文: On the Critical Capacity of the Hopfield Model
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…
Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…
In this paper the three dimensional random field Ising model is studied at both zero temperature and positive temperature. Critical exponents are extracted at zero temperature by finite size scaling analysis of large discontinuities in the…
Gardner's analysis of the optimal storage capacity of neural networks is extended to study finite-temperature effects. The typical volume of the space of interactions is calculated for strongly-diluted networks as a function of the storage…
We present a complementary estimation of the critical exponent $\alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $\alpha = 0.12(2)$ is consistent with the estimation…
We investigate the computational limits of the memory retrieval dynamics of modern Hopfield models from the fine-grained complexity analysis. Our key contribution is the characterization of a phase transition behavior in the efficiency of…
We study analytically and numerically a Hopfield fully-connected network with $d$-dimensional vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins, where $P$ examples are…
The storage capacity of the extremely diluted Hopfield Model is studied by using Monte Carlo techniques. In this work, instead of diluting the synapses according to a given distribution, the dilution of the synapses is obtained…
The effective potential of $\lambda\phi^4_{1+3}$ model with both sign of parameter $m^2$ is evaluated at T=0 by means of a simple but effective method for regularization and renormalization. Then at $T\ne 0$, the effective potential is…
The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on…
Based on recent work by Gripon and Berrou, we introduce a new model of an associative memory. We show that this model has an efficiency bounded away from 0 and is therefore significantly more effective than the well known Hopfield model. We…
We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various…
When a semi-infinite body is heated from below by a sudden increase in temperature (or cooled from above) an error function temperature profile grows as the heat diffuses into the fluid. The stability of such a profile is investigated using…
Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the…
We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states…
The random-field XY model is studied in spatial dimensions d=3 and 4, and in-between, as the limit q --> \infty of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the…
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…
We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate…
In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small…
In the last five decades, mean-field neural-networks have played a crucial role in modelling associative memories and, in particular, the Hopfield model has been extensively studied using tools borrowed from the statistical mechanics of…