Related papers: Oscillator-Based Associative Memory with Exponenti…
Attractor networks are an influential theory for memory storage in brain systems. This theory has recently been challenged by the observation of strong temporal variability in neuronal recordings during memory tasks. In this work, we study…
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…
The Transformer architecture, underpinned by the self-attention mechanism, has become the de facto standard for sequence modeling tasks. However, its core computational primitive scales quadratically with sequence length (O(N^2)), creating…
High-capacity associative memory models, such as Kernel Logistic Regression (KLR) Hopfield networks, have demonstrated strong storage capabilities but typically rely on computationally expensive synchronous updates. This reliance poses a…
Hopfield networks are a variant of associative memory that recall information stored in the couplings of an Ising model. Stored memories are fixed points for the network dynamics that correspond to energetic minima of the spin state. We…
We analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We…
We investigate the retrieval phase diagrams of an asynchronous fully-connected attractor network with non-monotonic transfer function by means of a mean-field approximation. We find for the noiseless zero-temperature case that this…
We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories. We present a tight analysis by establishing a connection between the…
Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
Models of interacting complex systems provide the fundamental statistical physics reference frame for the study and the understanding of associative memories, machine learning, and the dynamics of neural networks. On the other hand,…
Can a simple oscillator system, as in cellular automata, sustain complex nature upon discretization in time and space? The answer is by no means trivial as even the most simple, two-state, nearest neighbours cellular automata can lead to…
We propose a self-organizing memory architecture for perceptual experience, capable of supporting autonomous learning and goal-directed problem solving in the absence of any prior information about the agent's environment. The architecture…
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…
In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be…
Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an {\em a priori} fixed connectivity pattern…
In this paper, we present a neural network system related to about memory and recall that consists of one neuron group (the "cue ball") and a one-layer neural net (the "recall net"). This system realizes the bidirectional memorization…
A ternary/binary data coding algorithm and conditions under which Hopfield networks implement optimal convolutional or Hamming decoding algorithms has been described. Using the coding/decoding approach (an optimal Binary Signal Detection…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of…
We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…