Related papers: Fast, accurate, and interpretable decoding of elec…

This paper introduces a new theoretical and computational framework for a data driven Koopman mode analysis of nonlinear dynamics. To alleviate the potential problem of ill-conditioned eigenvectors in the existing implementations of the…

Accurate hand gesture prediction is crucial for effective upper-limb prosthetic limbs control. As the high flexibility and multiple degrees of freedom exhibited by human hands, there has been a growing interest in integrating deep networks…

Differential Dynamic Microscopy (DDM) analyzes traditional real-space microscope images to extract information on sample dynamics in a way akin to light scattering, by decomposing each image in a sequence into Fourier modes, and evaluating…

This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

In the past five years, the use of generative and foundational AI systems has greatly improved the decoding of brain activity. Visual perception, in particular, can now be decoded from functional Magnetic Resonance Imaging (fMRI) with…

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit…

With the thriving of deep learning, 3D Convolutional Neural Networks have become a popular choice in volumetric image analysis due to their impressive 3D contexts mining ability. However, the 3D convolutional kernels will introduce a…

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…

Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…

Neural decoding involves correlating signals acquired from the brain to variables in the physical world like limb movement or robot control in Brain Machine Interfaces. In this context, this work starts from a specific pre-existing dataset…

The encoder-decoder networks are commonly used in medical image segmentation due to their remarkable performance in hierarchical feature fusion. However, the expanding path for feature decoding and spatial recovery does not consider the…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Current brain-computer interfaces primarily decode single motor variables, limiting their ability to support natural, high-bandwidth neural control that requires simultaneous extraction of multiple correlated motor dimensions. We introduce…

This paper introduces a fast algorithm for randomized computation of a low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this matrix to represent the development of a spatial grid through time e.g. data from a static…

Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases can not be uniquely…

Compared to real-valued signals, complex-valued signals provide a unique and intuitive representation of the phase of real physical systems and processes, which holds fundamental significance and is widely applied across many fields of…

The interpretability of neural networks has recently received extensive attention. Previous prototype-based explainable networks involved prototype activation in both reasoning and interpretation processes, requiring specific explainable…

Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…