Related papers: Contracting Neural Networks: Sharp LMI Conditions …
This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number of useful general algebraic results on matrix polytopes and products of…
This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…
This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global…
In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…
Critical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established…
Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…
Concurrent estimation and control of robotic systems remains an ongoing challenge, where controllers rely on data extracted from states/parameters riddled with uncertainties and noises. Framework suitability hinges on task complexity and…
The neural mechanisms supporting flexible relational inferences, especially in novel situations, are a major focus of current research. In the complementary learning systems framework, pattern separation in the hippocampus allows rapid…
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works…
Priming is the ability of the brain to more quickly activate a target concept in response to a related stimulus (prime). Experiments point to the existence of an overlap between the populations of the neurons coding for different stimuli.…
We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…
A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives…
Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks…
We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable…
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that updating all weights is…
In this work we focus on examination and comparison of whole-brain functional connectivity patterns measured with fMRI across experimental conditions. Direct examination and comparison of condition-specific matrices is challenging due to…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…