Related papers: Prototype Analysis in Hopfield Networks with Hebbi…
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…
The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near…
In many complex systems, elementary units live in a chaotic environment and need to adapt their strategies to perform a task, by extracting information from the environment and controlling the feedback loop on it. One of the main example of…
We generalize the standard Hopfield model to the case when a weight is assigned to each input pattern. The weight can be interpreted as the frequency of the pattern occurrence at the input of the network. In the framework of the statistical…
Motivated by the geometric advantages of quaternions in representing rotations and postures, we propose a quaternion-valued supervised learning Hopfield-structured neural network (QSHNN) with a fully connected structure inspired by the…
Recent research has established a connection between modern Hopfield networks (HNs) and transformer attention heads, with guarantees of exponential storage capacity. However, these models still face challenges scaling storage efficiently.…
Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
We present a protocol to store a polynomial number of arbitrary bit strings, encoded as spin configurations, in the approximately degenerate low-energy manifold of an all-to-all connected Ising spin glass. The iterative protocol is inspired…
The Hopfield network model and its generalizations were introduced as a model of associative, or content-addressable, memory. They were widely investigated both as an unsupervised learning method in artificial intelligence and as a model of…
Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences…
Energy-based probabilistic models learned by maximizing the likelihood of the data are limited by the intractability of the partition function. A widely used workaround is to maximize the pseudo-likelihood, which replaces the global…
The modular and hierarchical organization of the brain is believed to support the coexistence of segregated (specialization) and integrated (binding) information processes. A relevant question is yet to understand how such architecture…
In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an…
Correlation-based Hebbian plasticity is thought to shape neuronal connectivity during development and learning, whereas homeostatic plasticity would stabilize network activity. Here we investigate another, new aspect of this dichotomy: Can…
Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…
Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…
The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-states of the network dynamics.…