Related papers: Parallel dynamics of continuous Hopfield model rev…
It has been shown that approximate message passing algorithm is effective in reconstruction problems for compressed sensing. To evaluate dynamics of such an algorithm, the state evolution (SE) has been proposed. If an algorithm can cancel…
We study the synchronous dynamics of the Hopfield model when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. We use a generating functional technique to derive analytical expressions for the order parameters…
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…
We propose graph-based predictable feature analysis (GPFA), a new method for unsupervised learning of predictable features from high-dimensional time series, where high predictability is understood very generically as low variance in the…
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium…
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to…
Recently, representation learning over graph networks has gained popularity, with various models showing promising results. Despite this, several challenges persist: 1) most methods are designed for static or discrete-time dynamic graphs;…
Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an algorithm that performs dimensionality reduction on high dimensional input signal. It extracts those subsignals that are most predictable according to a certain…
Gaussian process factor analysis (GPFA) is a latent variable modeling technique commonly used to identify smooth, low-dimensional latent trajectories underlying high-dimensional neural recordings. Specifically, researchers model spiking…
Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform the computation of a finite automaton in parallel by…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
Multi-subject fMRI studies are challenging due to the high variability of both brain anatomy and functional brain topographies across participants. An effective way of aggregating multi-subject fMRI data is to extract a shared…
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the…
Canonical Correlation Analysis (CCA) and its regularised versions have been widely used in the neuroimaging community to uncover multivariate associations between two data modalities (e.g., brain imaging and behaviour). However, these…
In neuroscience, researchers typically conduct experiments under multiple conditions to acquire neural responses in the form of high-dimensional spike train datasets. Analysing high-dimensional spike data is a challenging statistical…
We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths…
A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent…
In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems \`a la Mattis, by thinking at the Dyson model as a single-pattern hierarchical neural network and we…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Extended Predictable Feature Analysis (PFAx) [Richthofer and Wiskott, 2017] is an extension of PFA [Richthofer and Wiskott, 2015] that allows generating a goal-directed control signal of an agent whose dynamics has previously been learned…