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Timo Bremer

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NeurIPS Conference 2022 Conference Paper

Models Out of Line: A Fourier Lens on Distribution Shift Robustness

Sara Fridovich-Keil
Brian Bartoldson
James Diffenderfer
Bhavya Kailkhura
Timo Bremer

Improving the accuracy of deep neural networks on out-of-distribution (OOD) data is critical to an acceptance of deep learning in real world applications. It has been observed that accuracies on in-distribution (ID) versus OOD data follow a linear trend and models that outperform this baseline are exceptionally rare (and referred to as ``effectively robust”). Recently, some promising approaches have been developed to improve OOD robustness: model pruning, data augmentation, and ensembling or zero-shot evaluating large pretrained models. However, there still is no clear understanding of the conditions on OOD data and model properties that are required to observe effective robustness. We approach this issue by conducting a comprehensive empirical study of diverse approaches that are known to impact OOD robustness on a broad range of natural and synthetic distribution shifts of CIFAR-10 and ImageNet. In particular, we view the "effective robustness puzzle" through a Fourier lens and ask how spectral properties of both models and OOD data correlate with OOD robustness. We find this Fourier lens offers some insight into why certain robust models, particularly those from the CLIP family, achieve OOD robustness. However, our analysis also makes clear that no known metric is consistently the best explanation of OOD robustness. Thus, to aid future research into the OOD puzzle, we address the gap in publicly-available models with effective robustness by introducing a set of pretrained CIFAR-10 models---$RobustNets$---with varying levels of OOD robustness.

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NeurIPS Conference 2022 Conference Paper

Single Model Uncertainty Estimation via Stochastic Data Centering

Jayaraman Thiagarajan
Rushil Anirudh
Vivek Sivaraman Narayanaswamy
Timo Bremer

We are interested in estimating the uncertainties of deep neural networks, which play an important role in many scientific and engineering problems. In this paper, we present a striking new finding that an ensemble of neural networks with the same weight initialization, trained on datasets that are shifted by a constant bias gives rise to slightly inconsistent trained models, where the differences in predictions are a strong indicator of epistemic uncertainties. Using the neural tangent kernel (NTK), we demonstrate that this phenomena occurs in part because the NTK is not shift-invariant. Since this is achieved via a trivial input transformation, we show that this behavior can therefore be approximated by training a single neural network -- using a technique that we call $\Delta-$UQ -- that estimates uncertainty around prediction by marginalizing out the effect of the biases during inference. We show that $\Delta-$UQ's uncertainty estimates are superior to many of the current methods on a variety of benchmarks-- outlier rejection, calibration under distribution shift, and sequential design optimization of black box functions. Code for $\Delta-$UQ can be accessed at github. com/LLNL/DeltaUQ

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NeurIPS Conference 2020 Conference Paper

A Statistical Mechanics Framework for Task-Agnostic Sample Design in Machine Learning

Bhavya Kailkhura
Jayaraman Thiagarajan
Qunwei Li
Jize Zhang
Yi Zhou
Timo Bremer

In this paper, we present a statistical mechanics framework to understand the effect of sampling properties of training data on the generalization gap of machine learning (ML) algorithms. We connect the generalization gap to the spatial properties of a sample design characterized by the pair correlation function (PCF). In particular, we express generalization gap in terms of the power spectra of the sample design and that of the function to be learned. Using this framework, we show that space-filling sample designs, such as blue noise and Poisson disk sampling, which optimize spectral properties, outperform random designs in terms of the generalization gap and characterize this gain in a closed-form. Our analysis also sheds light on design principles for constructing optimal task-agnostic sample designs that minimize the generalization gap. We corroborate our findings using regression experiments with neural networks on: a) synthetic functions, and b) a complex scientific simulator for inertial confinement fusion (ICF).

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