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Gregory Wornell

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9 papers

1 author row

NeurIPS Conference 2025 Conference Paper

Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems

Minchan Jeong
Jongha (Jon) Ryu
Se-Young Yun
Gregory Wornell

The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify dominant modes of a system in a data-driven manner. Building on this idea, deep learning methods such as VAMPnet and DPNet have been proposed to learn the leading singular subspaces of the Koopman operator. However, these methods require backpropagation through potentially numerically unstable operations on empirical second moment matrices, such as singular value decomposition and matrix inversion, during objective computation, which can introduce biased gradient estimates and hinder scalability to large systems. In this work, we propose a scalable and conceptually simple method for learning the top-$k$ singular functions of the Koopman operator for stochastic dynamical systems based on the idea of low-rank approximation. Our approach eliminates the need for unstable linear-algebraic operations and integrates easily into modern deep learning pipelines. Empirical results demonstrate that the learned singular subspaces are both reliable and effective for downstream tasks such as eigen-analysis and multi-step prediction.

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NeurIPS Conference 2025 Conference Paper

Revisiting Orbital Minimization Method for Neural Operator Decomposition

Jongha (Jon) Ryu
Samuel Zhou
Gregory Wornell

Spectral decomposition of linear operators plays a central role in many areas of machine learning and scientific computing. Recent work has explored training neural networks to approximate eigenfunctions of such operators, enabling scalable approaches to representation learning, dynamical systems, and partial differential equations (PDEs). In this paper, we revisit a classical optimization framework from the computational physics literature known as the orbital minimization method (OMM), originally proposed in the 1990s for solving eigenvalue problems in computational chemistry. We provide a simple linear-algebraic proof of the consistency of the OMM objective, and reveal connections between this method and several ideas that have appeared independently across different domains. Our primary goal is to justify its broader applicability in modern learning pipelines. We adapt this framework to train neural networks to decompose positive semidefinite operators, and demonstrate its practical advantages across a range of benchmark tasks. Our results highlight how revisiting classical numerical methods through the lens of modern theory and computation can provide not only a principled approach for deploying neural networks in numerical simulation, but also effective and scalable tools for machine learning.

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AAAI Conference 2023 Conference Paper

Post-hoc Uncertainty Learning Using a Dirichlet Meta-Model

Maohao Shen
Yuheng Bu
Prasanna Sattigeri
Soumya Ghosh
Subhro Das
Gregory Wornell

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to impose the uncertainty quantification capability so that the learned model can achieve desired performance in accuracy and uncertainty prediction simultaneously. However, training the model from scratch is computationally expensive, and a trade-off might exist between prediction accuracy and uncertainty quantification. To this end, we consider a more practical post-hoc uncertainty learning setting, where a well-trained base model is given, and we focus on the uncertainty quantification task at the second stage of training. We propose a novel Bayesian uncertainty learning approach using the Dirichlet meta-model, which is effective and computationally efficient. Our proposed method requires no additional training data and is flexible enough to quantify different uncertainties and easily adapt to different application settings, including out-of-domain data detection, misclassification detection, and trustworthy transfer learning. Finally, we demonstrate our proposed meta-model approach's flexibility and superior empirical performance on these applications over multiple representative image classification benchmarks.

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NeurIPS Conference 2023 Conference Paper

Score-based Source Separation with Applications to Digital Communication Signals

Tejas Jayashankar
Gary C. F. Lee
Alejandro Lancho
Amir Weiss
Yury Polyanskiy
Gregory Wornell

We propose a new method for separating superimposed sources using diffusion-based generative models. Our method relies only on separately trained statistical priors of independent sources to establish a new objective function guided by $\textit{maximum a posteriori}$ estimation with an $\textit{$\alpha$-posterior}$, across multiple levels of Gaussian smoothing. Motivated by applications in radio-frequency (RF) systems, we are interested in sources with underlying discrete nature and the recovery of encoded bits from a signal of interest, as measured by the bit error rate (BER). Experimental results with RF mixtures demonstrate that our method results in a BER reduction of 95\% over classical and existing learning-based methods. Our analysis demonstrates that our proposed method yields solutions that asymptotically approach the modes of an underlying discrete distribution. Furthermore, our method can be viewed as a multi-source extension to the recently proposed score distillation sampling scheme, shedding additional light on its use beyond conditional sampling. The project webpage is available at https: //alpha-rgs. github. io.

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NeurIPS Conference 2021 Conference Paper

A Computationally Efficient Method for Learning Exponential Family Distributions

Abhin Shah
Devavrat Shah
Gregory Wornell

We consider the question of learning the natural parameters of a $k$ parameter \textit{minimal} exponential family from i. i. d. samples in a computationally and statistically efficient manner. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We provide finite sample guarantees to achieve an ($\ell_2$) error of $\alpha$ in the parameter estimation with sample complexity $O(\mathrm{poly}(k/\alpha))$ and computational complexity ${O}(\mathrm{poly}(k/\alpha))$. To establish these results, we show that, at the population level, our method can be viewed as the maximum likelihood estimation of a re-parameterized distribution belonging to the same class of exponential family.

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NeurIPS Conference 2021 Conference Paper

An Exact Characterization of the Generalization Error for the Gibbs Algorithm

Gholamali Aminian
Yuheng Bu
Laura Toni
Miguel Rodrigues
Gregory Wornell

Various approaches have been developed to upper bound the generalization error of a supervised learning algorithm. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm. Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm (a. k. a. Gibbs posterior) using symmetrized KL information between the input training samples and the output hypothesis. Our result can be applied to tighten existing expected generalization error and PAC-Bayesian bounds. Our approach is versatile, as it also characterizes the generalization error of the Gibbs algorithm with data-dependent regularizer and that of the Gibbs algorithm in the asymptotic regime, where it converges to the empirical risk minimization algorithm. Of particular relevance, our results highlight the role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm.

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NeurIPS Conference 2019 Conference Paper

Computational Mirrors: Blind Inverse Light Transport by Deep Matrix Factorization

Miika Aittala
Prafull Sharma
Lukas Murmann
Adam Yedidia
Gregory Wornell
Bill Freeman
Fredo Durand

We recover a video of the motion taking place in a hidden scene by observing changes in indirect illumination in a nearby uncalibrated visible region. We solve this problem by factoring the observed video into a matrix product between the unknown hidden scene video and an unknown light transport matrix. This task is extremely ill-posed, as any non-negative factorization will satisfy the data. Inspired by recent work on the Deep Image Prior, we parameterize the factor matrices using randomly initialized convolutional neural networks trained in a one-off manner, and show that this results in decompositions that reflect the true motion in the hidden scene.

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NeurIPS Conference 2019 Conference Paper

Learning New Tricks From Old Dogs: Multi-Source Transfer Learning From Pre-Trained Networks

Joshua Lee
Prasanna Sattigeri
Gregory Wornell

The advent of deep learning algorithms for mobile devices and sensors has led to a dramatic expansion in the availability and number of systems trained on a wide range of machine learning tasks, creating a host of opportunities and challenges in the realm of transfer learning. Currently, most transfer learning methods require some kind of control over the systems learned, either by enforcing constraints during the source training, or through the use of a joint optimization objective between tasks that requires all data be co-located for training. However, for practical, privacy, or other reasons, in a variety of applications we may have no control over the individual source task training, nor access to source training samples. Instead we only have access to features pre-trained on such data as the output of "black-boxes. '' For such scenarios, we consider the multi-source learning problem of training a classifier using an ensemble of pre-trained neural networks for a set of classes that have not been observed by any of the source networks, and for which we have very few training samples. We show that by using these distributed networks as feature extractors, we can train an effective classifier in a computationally-efficient manner using tools from (nonlinear) maximal correlation analysis. In particular, we develop a method we refer to as maximal correlation weighting (MCW) to build the required target classifier from an appropriate weighting of the feature functions from the source networks. We illustrate the effectiveness of the resulting classifier on datasets derived from the CIFAR-100, Stanford Dogs, and Tiny ImageNet datasets, and, in addition, use the methodology to characterize the relative value of different source tasks in learning a target task.

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NeurIPS Conference 2018 Conference Paper

Co-regularized Alignment for Unsupervised Domain Adaptation

Abhishek Kumar
Prasanna Sattigeri
Kahini Wadhawan
Leonid Karlinsky
Rogerio Feris
Bill Freeman
Gregory Wornell

Deep neural networks, trained with large amount of labeled data, can fail to generalize well when tested with examples from a target domain whose distribution differs from the training data distribution, referred as the source domain. It can be expensive or even infeasible to obtain required amount of labeled data in all possible domains. Unsupervised domain adaptation sets out to address this problem, aiming to learn a good predictive model for the target domain using labeled examples from the source domain but only unlabeled examples from the target domain. Domain alignment approaches this problem by matching the source and target feature distributions, and has been used as a key component in many state-of-the-art domain adaptation methods. However, matching the marginal feature distributions does not guarantee that the corresponding class conditional distributions will be aligned across the two domains. We propose co-regularized domain alignment for unsupervised domain adaptation, which constructs multiple diverse feature spaces and aligns source and target distributions in each of them individually, while encouraging that alignments agree with each other with regard to the class predictions on the unlabeled target examples. The proposed method is generic and can be used to improve any domain adaptation method which uses domain alignment. We instantiate it in the context of a recent state-of-the-art method and observe that it provides significant performance improvements on several domain adaptation benchmarks.

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