Related papers: On the supra-linear storage in dense networks of g…
Grid cells in the medial entorhinal cortex and place cells in the hippocampus together support spatial navigation. The two regions are reciprocally connected, and there is a chicken-and-egg problem for how both arise and reinforce each…
We derive the Gardner storage capacity for associative networks of threshold linear units, and show that with Hebbian learning they can operate closer to such Gardner bound than binary networks, and even surpass it. This is largely achieved…
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…
We introduce a three-dimensional vectorial extension of the Hopfield associative-memory model in which each neuron is a unit vector on $S^2$ and synaptic couplings are $3\times 3$ blocks generated through a vectorial Hebbian rule. The…
We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of…
Connectomes are spatially embedded networks whose architecture has been shaped by physical constraints and communication needs throughout evolution. Using a decentralized navigation protocol, we investigate the relationship between the…
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…
Grid cells enable the brain to model the physical space of the world and navigate effectively via path integration, updating self-position using information from self-movement. Recent proposals suggest that the brain might use similar…
Many recent models study the downstream projection from grid cells to place cells, while recent data has pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input 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…
Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…
A vast majority of the current research in the field of Machine Learning is done using algorithms with strong arguments pointing to their biological implausibility such as Backpropagation, deviating the field's focus from understanding its…
Deep learning networks generally use non-biological learning methods. By contrast, networks based on more biologically plausible learning, such as Hebbian learning, show comparatively poor performance and difficulties of implementation.…
When an object moves smoothly across a field of view, the identify of the object is unchanged, but the activation pattern of the photoreceptors on the retina changes drastically. One of the major computational roles of our visual system is…
Synaptic plasticity is widely accepted to be the mechanism behind learning in the brain's neural networks. A central question is how synapses, with access to only local information about the network, can still organize collectively and…
The human brain possesses the extraordinary capability to contextualize the information it receives from our environment. The entorhinal-hippocampal plays a critical role in this function, as it is deeply engaged in memory processing and…
We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach…
The Hebbian unlearning algorithm, i.e. an unsupervised local procedure used to improve the retrieval properties in Hopfield-like neural networks, is numerically compared to a supervised algorithm to train a linear symmetric perceptron. We…