Related papers: Sequence Modeling with Spectral Mean Flows

Understanding the sequence of cognitive operations that underlie decision-making is a fundamental challenge in cognitive neuroscience. Traditional approaches often rely on group-level statistics, which obscure trial-by-trial variations in…

Data-driven modeling for nonlinear fluid flows using sparse convolution-based mapping into a feature space where the dynamics are Markov linear is explored in this article. The underlying principle of low-order models for fluid systems is…

Deep Neural Networks (DNNs) have begun to thrive in the field of automation systems, owing to the recent advancements in standardising various aspects such as architecture, optimization techniques, and regularization. In this paper, we take…

The class of recurrent mixture density networks is an important class of probabilistic models used extensively in sequence modeling and sequence-to-sequence mapping applications. In this class of models, the density of a target sequence in…

Neural networks are fundamental tools of modern machine learning. The standard paradigm assumes binary interactions (across feedforward linear passes) between inter-tangled units, organized in sequential layers. Generalized architectures…

Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by…

We introduce the Flow Stochastic Segmentation Network (Flow-SSN), a generative segmentation model family featuring discrete-time autoregressive and modern continuous-time flow variants. We prove fundamental limitations of the low-rank…

Modern machine learning frameworks can train neural networks using multiple nodes in parallel, each computing parameter updates with stochastic gradient descent (SGD) and sharing them asynchronously through a central parameter server. Due…

The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…

The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number $Re_0=6\,000$. The…

Missing data scenarios are very common in ML applications in general and time-series/sequence applications are no exceptions. This paper pertains to a novel Recurrent Neural Network (RNN) based solution for sequence prediction under missing…

Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…

As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Integrating model-based machine learning methods into deep neural architectures allows one to leverage both the expressive power of deep neural nets and the ability of model-based methods to incorporate domain-specific knowledge. In…

This paper proposes a novel deep learning approach for learning operators in semigroup, with applications to modeling unknown autonomous dynamical systems using time series data collected at varied time lags. It is a sequel to the previous…

Despite the recent progresses, particularly in developing Language Models, there are fundamental challenges and unanswered questions about how such models can continually learn/memorize, self-improve, and find effective solutions. In this…

Machine learning (ML) is a promising tool for the detection of phases of matter. However, ML models are also known for their black-box construction, which hinders understanding of what they learn from the data and makes their application to…

Numerical investigation of compressible flows faces two main challenges. In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide…