Related papers: Aggregation of isotropic autoregressive fields
We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of $0$s and $1$s with about $\log N$ $1$s, only. We compare different synaptic weights, architectures and retrieval…
The potential for associative recall of diluted neuronal networks is investigated with respect to several biologically relevant configurations, more specifically the position of the cells along the input space and the spatial distribution…
The entropic associative memory (EAM) is a computational model of natural memory incorporating some of its putative properties of being associative, distributed, declarative, abstractive and constructive. Previous experiments satisfactorily…
Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the…
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…
We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…
We develop the complete theory for the collective plasmon modes of an interacting electron system in the presence of explicit mass (or velocity) anisotropy in the corresponding non-interacting situation, with the effective Fermi velocity…
We exactly rewrite the Z(2) lattice gauge theory with standard plaquette action as a random surface model equivalent to the untruncated set of its strong coupling graphs. By extending the worm approach applied to spin models we simulate…
For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…
We present a detailed numerical study of the orthogonality catastrophe exponent for a one-dimensional lattice model of spinless fermions with nearest neighbor interaction using the density matrix remormalization group algorithm. Keeping up…
We introduce a Hopfield-type associative memory in which effective connectivity is multiplicatively modulated by astrocytic gains evolving under an entropy-regularized replicator equation. The coupled neuron-astrocyte dynamics admit a…
An autoregressive model with a power-law type memory kernel is studied as a stochastic process that exhibits a self-affine-fractal-like behavior for a small time scale. We find numerically that the root-mean-square displacement for the time…
The slowing of Moore's law and the increasing energy demands of machine learning present critical challenges for both the hardware and machine learning communities, and drive the development of novel computing paradigms. Of particular…
Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…
Sampling of physical fields with mobile sensors is an upcoming field of interest. This offers greater advantages in terms of cost as often just a single sensor can be used for the purpose and this can be employed almost everywhere without…
We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. We adopt the geometric view of admixture models - alternatively known as topic models - as a…
Time-series data with regular and/or seasonal long-memory are often aggregated before analysis. Often, the aggregation scale is large enough to remove any short-memory components of the underlying process but too short to eliminate seasonal…
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…