Polarity Sampling: Quality and Diversity Control of Pre-Trained Generative Networks via Singular Values

We present Polarity Sampling, a theoretically justified plug-and-play method for controlling the generation quality and diversity of pre-trained deep generative networks DGNs). Leveraging the fact that DGNs are, or can be approximated by, continuous piecewise affine splines, we derive the analytical DGN output space distribution as a function of the product of the DGN's Jacobian singular values raised to a power $\rho$. We dub $\rho$ the $\textbf{polarity}$ parameter and prove that $\rho$ focuses the DGN sampling on the modes ($\rho < 0$) or anti-modes ($\rho > 0$) of the DGN output-space distribution. We demonstrate that nonzero polarity values achieve a better precision-recall (quality-diversity) Pareto frontier than standard methods, such as truncation, for a number of state-of-the-art DGNs. We also present quantitative and qualitative results on the improvement of overall generation quality (e.g., in terms of the Frechet Inception Distance) for a number of state-of-the-art DGNs, including StyleGAN3, BigGAN-deep, NVAE, for different conditional and unconditional image generation tasks. In particular, Polarity Sampling redefines the state-of-the-art for StyleGAN2 on the FFHQ Dataset to FID 2.57, StyleGAN2 on the LSUN Car Dataset to FID 2.27 and StyleGAN3 on the AFHQv2 Dataset to FID 3.95. Demo: bit.ly/polarity-demo-colab

Spatial Transformer K-Means

K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $K$-means performances at the cost of reduced theoretical guarantees and interpretability of the results. Instead, we propose preserving the intrinsic data space and augment K-means with a similarity measure invariant to non-rigid transformations. This enables (i) the reduction of intrinsic nuisances associated with the data, reducing the complexity of the clustering task and increasing performances and producing state-of-the-art results, (ii) clustering in the input space of the data, leading to a fully interpretable clustering algorithm, and (iii) the benefit of convergence guarantees.

MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining

Deep Generative Networks (DGNs) are extensively employed in Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), and their variants to approximate the data manifold, and data distribution on that manifold. However, training samples are often obtained based on preferences, costs, or convenience producing artifacts in the empirical data distribution e.g., the large fraction of smiling faces in the CelebA dataset or the large fraction of dark-haired individuals in FFHQ. These inconsistencies will be reproduced when sampling from the trained DGN, which has far-reaching potential implications for fairness, data augmentation, anomaly detection, domain adaptation, and beyond. In response, we develop a differential geometry based sampler -- coined MaGNET -- that, given any trained DGN, produces samples that are uniformly distributed on the learned manifold. We prove theoretically and empirically that our technique produces a uniform distribution on the manifold regardless of the training set distribution. We perform a range of experiments on various datasets and DGNs. One of them considers the state-of-the-art StyleGAN2 trained on FFHQ dataset, where uniform sampling via MaGNET increases distribution precision and recall by 4.1% & 3.0% and decreases gender bias by 41.2%, without requiring labels or retraining.

Thermal Image Processing via Physics-Inspired Deep Networks

We introduce DeepIR, a new thermal image processing framework that combines physically accurate sensor modeling with deep network-based image representation. Our key enabling observations are that the images captured by thermal sensors can be factored into slowly changing, scene-independent sensor non-uniformities (that can be accurately modeled using physics) and a scene-specific radiance flux (that is well-represented using a deep network-based regularizer). DeepIR requires neither training data nor periodic ground-truth calibration with a known black body target--making it well suited for practical computer vision tasks. We demonstrate the power of going DeepIR by developing new denoising and super-resolution algorithms that exploit multiple images of the scene captured with camera jitter. Simulated and real data experiments demonstrate that DeepIR can perform high-quality non-uniformity correction with as few as three images, achieving a 10dB PSNR improvement over competing approaches.

Double Descent and Other Interpolation Phenomena in GANs

We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the generalization error as a function of latent space dimension and identify two main behaviors, depending on the learning setting. First, we show that overparameterized generative models that learn distributions by minimizing a metric or $f$-divergence do not exhibit double descent in generalization errors; specifically, all the interpolating solutions achieve the same generalization error. Second, we develop a new pseudo-supervised learning approach for GANs where the training utilizes pairs of fabricated (noise) inputs in conjunction with real output samples. Our pseudo-supervised setting exhibits double descent (and in some cases, triple descent) of generalization errors. We combine pseudo-supervision with overparameterization (i.e., overly large latent space dimension) to accelerate training while performing better, or close to, the generalization performance without pseudo-supervision. While our analysis focuses mostly on linear GANs, we also apply important insights for improving generalization of nonlinear, multilayer GANs.

Math Operation Embeddings for Open-ended Solution Analysis and Feedback

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually constructing cognitive models and anticipating student errors for each question. This process requires significant human effort and does not scale to most questions used in homework and practices that do not come with this information. In this paper, we analyze students' step-by-step solution processes to equation solving questions in an attempt to scale up error diagnostics and feedback mechanisms developed for a small number of questions to a much larger number of questions. Leveraging a recent math expression encoding method, we represent each math operation applied in solution steps as a transition in the math embedding vector space. We use a dataset that contains student solution steps in the Cognitive Tutor system to learn implicit and explicit representations of math operations. We explore whether these representations can i) identify math operations a student intends to perform in each solution step, regardless of whether they did it correctly or not, and ii) select the appropriate feedback type for incorrect steps. Experimental results show that our learned math operation representations generalize well across different data distributions.

Fast Jacobian-Vector Product for Deep Networks

Jacobian-vector products (JVPs) form the backbone of many recent developments in Deep Networks (DNs), with applications including faster constrained optimization, regularization with generalization guarantees, and adversarial example sensitivity assessments. Unfortunately, JVPs are computationally expensive for real world DN architectures and require the use of automatic differentiation to avoid manually adapting the JVP program when changing the DN architecture. We propose a novel method to quickly compute JVPs for any DN that employ Continuous Piecewise Affine (e.g., leaky-ReLU, max-pooling, maxout, etc.) nonlinearities. We show that our technique is on average $2\times$ faster than the fastest alternative over $13$ DN architectures and across various hardware. In addition, our solution does not require automatic differentiation and is thus easy to deploy in software, requiring only the modification of a few lines of codes that do not depend on the DN architecture.

Max-Affine Spline Insights Into Deep Network Pruning

In this paper, we study the importance of pruning in Deep Networks (DNs) and motivate it based on the current absence of data aware weight initialization. Current DN initializations, focusing primarily at maintaining first order statistics of the feature maps through depth, force practitioners to overparametrize a model in order to reach high performances. This overparametrization can then be pruned a posteriori, leading to a phenomenon known as "winning tickets". However, the pruning literature still relies on empirical investigations, lacking a theoretical understanding of (1) how pruning affects the decision boundary, (2) how to interpret pruning, (3) how to design principled pruning techniques, and (4) how to theoretically study pruning. To tackle those questions, we propose to employ recent advances in the theoretical analysis of Continuous Piecewise Affine (CPA) DNs. From this viewpoint, we can study the DNs' input space partitioning and detect the early-bird (EB) phenomenon, guide practitioners by identifying when to stop the first training step, provide interpretability into current pruning techniques, and develop a principled pruning criteria towards efficient DN training. Finally, we conduct extensive experiments to show the effectiveness of the proposed spline pruning criteria in terms of both layerwise and global pruning over state-of-the-art pruning methods.

SASSI -- Super-Pixelated Adaptive Spatio-Spectral Imaging

We introduce a novel video-rate hyperspectral imager with high spatial, and temporal resolutions. Our key hypothesis is that spectral profiles of pixels in a super-pixel of an oversegmented image tend to be very similar. Hence, a scene-adaptive spatial sampling of an hyperspectral scene, guided by its super-pixel segmented image, is capable of obtaining high-quality reconstructions. To achieve this, we acquire an RGB image of the scene, compute its super-pixels, from which we generate a spatial mask of locations where we measure high-resolution spectrum. The hyperspectral image is subsequently estimated by fusing the RGB image and the spectral measurements using a learnable guided filtering approach. Due to low computational complexity of the superpixel estimation step, our setup can capture hyperspectral images of the scenes with little overhead over traditional snapshot hyperspectral cameras, but with significantly higher spatial and spectral resolutions. We validate the proposed technique with extensive simulations as well as a lab prototype that measures hyperspectral video at a spatial resolution of $600 \times 900$ pixels, at a spectral resolution of 10 nm over visible wavebands, and achieving a frame rate at $18$fps.