P. Thomas Fletcher

Yinzhu Jin, Matthew B. Dwyer, P. Thomas Fletcher

This paper introduces a new technique to measure the feature dependency of neural network models. The motivation is to better understand a model by querying whether it is using information from human-understandable features, e.g., anatomical shape, volume, or image texture. Our method is based on the principle that if a model is dependent on a feature, then removal of that feature should significantly harm its performance. A targeted feature is "removed" by collapsing the dimension in the data distribution that corresponds to that feature. We perform this by moving data points along the feature dimension to a baseline feature value while staying on the data manifold, as estimated by a deep generative model. Then we observe how the model's performance changes on the modified test data set, with the target feature dimension removed. We test our method on deep neural network models trained on synthetic image data with known ground truth, an Alzheimer's disease prediction task using MRI and hippocampus segmentations from the OASIS-3 dataset, and a cell nuclei classification task using the Lizard dataset.

Tyler Spears, Shen Zhu, Yinzhu Jin et al.

In this work, we introduce MedIL, a first-of-its-kind autoencoder built for encoding medical images with heterogeneous sizes and resolutions for image generation. Medical images are often large and heterogeneous, where fine details are of vital clinical importance. Image properties change drastically when considering acquisition equipment, patient demographics, and pathology, making realistic medical image generation challenging. Recent work in latent diffusion models (LDMs) has shown success in generating images resampled to a fixed-size. However, this is a narrow subset of the resolutions native to image acquisition, and resampling discards fine anatomical details. MedIL utilizes implicit neural representations to treat images as continuous signals, where encoding and decoding can be performed at arbitrary resolutions without prior resampling. We quantitatively and qualitatively show how MedIL compresses and preserves clinically-relevant features over large multi-site, multi-resolution datasets of both T1w brain MRIs and lung CTs. We further demonstrate how MedIL can influence the quality of images generated with a diffusion model, and discuss how MedIL can enhance generative models to resemble raw clinical acquisitions.

Shen Zhu, Yinzhu Jin, Tyler Spears et al.

We propose image-to-image diffusion models that are designed to enhance the realism and details of generated brain images by introducing sharp edges, fine textures, subtle anatomical features, and imaging noise. Generative models have been widely adopted in the biomedical domain, especially in image generation applications. Latent diffusion models achieve state-of-the-art results in generating brain MRIs. However, due to latent compression, generated images from these models are overly smooth, lacking fine anatomical structures and scan acquisition noise that are typically seen in real images. This work formulates the realism enhancing and detail adding process as image-to-image diffusion models, which refines the quality of LDM-generated images. We employ commonly used metrics like FID and LPIPS for image realism assessment. Furthermore, we introduce new metrics to demonstrate the realism of images generated by RealDeal in terms of image noise distribution, sharpness, and texture.

Tyler Spears, P. Thomas Fletcher

Our understanding of the human connectome is fundamentally limited by the resolution of diffusion MR images. Reconstructing a connectome's constituent neural pathways with tractography requires following a continuous field of fiber directions. Typically, this field is found with simple trilinear interpolation in low-resolution, noisy diffusion MRIs. However, trilinear interpolation struggles following fine-scale changes in low-quality data. Recent deep learning methods in super-resolving diffusion MRIs have focused on upsampling to a fixed spatial grid, but this does not satisfy tractography's need for a continuous field. In this work, we propose FENRI, a novel method that learns spatially-continuous fiber orientation density functions from low-resolution diffusion-weighted images. To quantify FENRI's capabilities in tractography, we also introduce an expanded simulated dataset built for evaluating deep-learning tractography models. We demonstrate that FENRI accurately predicts high-resolution fiber orientations from realistic low-quality data, and that FENRI-based tractography offers improved streamline reconstruction over the current use of trilinear interpolation.

Chenxiao Zhao, P. Thomas Fletcher, Mixue Yu et al.

Many deep learning models are vulnerable to the adversarial attack, i.e., imperceptible but intentionally-designed perturbations to the input can cause incorrect output of the networks. In this paper, using information geometry, we provide a reasonable explanation for the vulnerability of deep learning models. By considering the data space as a non-linear space with the Fisher information metric induced from a neural network, we first propose an adversarial attack algorithm termed one-step spectral attack (OSSA). The method is described by a constrained quadratic form of the Fisher information matrix, where the optimal adversarial perturbation is given by the first eigenvector, and the model vulnerability is reflected by the eigenvalues. The larger an eigenvalue is, the more vulnerable the model is to be attacked by the corresponding eigenvector. Taking advantage of the property, we also propose an adversarial detection method with the eigenvalues serving as characteristics. Both our attack and detection algorithms are numerically optimized to work efficiently on large datasets. Our evaluations show superior performance compared with other methods, implying that the Fisher information is a promising approach to investigate the adversarial attacks and defenses.

Hang Shao, Abhishek Kumar, P. Thomas Fletcher

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.

Abhishek Kumar, Prasanna Sattigeri, P. Thomas Fletcher

Semi-supervised learning methods using Generative Adversarial Networks (GANs) have shown promising empirical success recently. Most of these methods use a shared discriminator/classifier which discriminates real examples from fake while also predicting the class label. Motivated by the ability of the GANs generator to capture the data manifold well, we propose to estimate the tangent space to the data manifold using GANs and employ it to inject invariances into the classifier. In the process, we propose enhancements over existing methods for learning the inverse mapping (i.e., the encoder) which greatly improves in terms of semantic similarity of the reconstructed sample with the input sample. We observe considerable empirical gains in semi-supervised learning over baselines, particularly in the cases when the number of labeled examples is low. We also provide insights into how fake examples influence the semi-supervised learning procedure.

Anant Raj, Abhishek Kumar, Youssef Mroueh et al.

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide excess risk bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated-MNIST and performs comparably to the recently proposed group-equivariant CNN.

Jacob Hinkle, Prasanna Muralidharan, P. Thomas Fletcher et al.

In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull growth data of Bookstein as well as the analysis of the shape changes associated with aging of the corpus callosum from the OASIS Alzheimer's study.