Related papers: On associative neural networks for sparse patterns…
High-capacity associative memories based on Kernel Logistic Regression (KLR) achieve strong retrieval performance but typically require substantial computational resources. This paper investigates the compressibility of KLR Hopfield…
We consider two models of Hopfield-like associative memory with $q$-valued neurons: Potts-glass neural network (PGNN) and parametrical neural network (PNN). In these models neurons can be in more than two different states. The models have…
Krotov and Hopfield (2021) proposed a biologically plausible two-layer associative memory network with memory storage capacity exponential in the number of visible neurons. However, the capacity was only linear in the number of hidden…
An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed (non-i.i.d.) way. Further,…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…
Motivated by biological considerations, we study sparse neural maps from an input layer to a target layer with sparse activity, and specifically the problem of storing $K$ input-target associations $(x,y)$, or memories, when the target…
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…
In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…
We study the storage of multiple phase-coded patterns as stable dynamical attractors in recurrent neural networks with sparse connectivity. To determine the synaptic strength of existent connections and store the phase-coded patterns, we…
We investigate dense higher-order associative memories in the high storage regime when the stored patterns are biased, namely when the entries of the patterns are not symmetrically distributed around zero. In this setting, the standard…
Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological…
Variable order sequence modeling is an important problem in artificial and natural intelligence. While overcomplete Hidden Markov Models (HMMs), in theory, have the capacity to represent long-term temporal structure, they often fail to…
This paper updates the cognitive model, firstly by creating two systems and then unifying them over the same structure. It represents information at the semantic level only, where labelled patterns are aggregated into a 'type-set-match'…
Associative memories are structures that store data patterns and retrieve them given partial inputs. Sparse Clustered Networks (SCNs) are recently-introduced binary-weighted associative memories that significantly improve the storage and…
The brain can reproduce memories from partial data; this ability is critical for memory recall. The process of memory recall has been studied using auto-associative networks such as the Hopfield model. This kind of model reliably converges…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
One of the most well established brain principles, hebbian learning, has led to the theoretical concept of neural assemblies. Based on it, many interesting brain theories have spawned. Palm's work implements this concept through binary…
We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…
In the present paper, we analyze symmetric mixed states corresponding to the so-called concept formation on a sparsely encoded associative memory model with 0-1 neurons. Three types of mixed states, OR, AND and a majority decision mixed…
A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…