Related papers: Sequence Modeling with Spectral Mean Flows
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This…
Graphs emerge in almost every real-world application domain, ranging from online social networks all the way to health data and movie viewership patterns. Typically, such real-world graphs are big and dynamic, in the sense that they evolve…
We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…
In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social…
We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…
Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…
We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in…
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of…
Stable diffusion models have ushered in a new era of advancements in image generation, currently reigning as the state-of-the-art approach, exhibiting unparalleled performance. The process of diffusion, accompanied by denoising through…
Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…
Sum-product networks (SPNs) have recently emerged as a novel deep learning architecture enabling highly efficient probabilistic inference. Since their introduction, SPNs have been applied to a wide range of data modalities and extended to…
Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the…
Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…
Deep neural networks (DNN) have shown promises in the lesion segmentation of multiple sclerosis (MS) from multicontrast MRI including T1, T2, proton density (PD) and FLAIR sequences. However, one challenge in deploying such networks into…
We propose a methodology for generating time-dependent turbulent inflow data with the aid of machine learning (ML), which has a possibility to replace conventional driver simulations or synthetic turbulent inflow generators. As for the ML…
Understanding the intricate operations of Recurrent Neural Networks (RNNs) mechanistically is pivotal for advancing their capabilities and applications. In this pursuit, we propose the Episodic Memory Theory (EMT), illustrating that RNNs…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
We propose a randomized neural network approach called RaNNDy for learning transfer operators and their spectral decompositions from data. The weights of the hidden layers of the neural network are randomly selected and only the output…