Frame Quantization of Neural Networks

We present a post-training quantization algorithm with error estimates relying on ideas originating from frame theory. Specifically, we use first-order Sigma-Delta ($\Sigma\Delta$) quantization for finite unit-norm tight frames to quantize weight matrices and biases in a neural network. In our scenario, we derive an error bound between the original neural network and the quantized neural network in terms of step size and the number of frame elements. We also demonstrate how to leverage the redundancy of frames to achieve a quantized neural network with higher accuracy.

Emergence of the SVD as an interpretable factorization in deep learning for inverse problems

We demonstrate the emergence of weight matrix singular value decomposition (SVD) in interpreting neural networks (NNs) for parameter estimation from noisy signals. The SVD appears naturally as a consequence of initial application of a descrambling transform - a recently-developed technique for addressing interpretability in NNs \cite{amey2021neural}. We find that within the class of noisy parameter estimation problems, the SVD may be the means by which networks memorize the signal model. We substantiate our theoretical findings with empirical evidence from both linear and non-linear settings. Our results also illuminate the connections between a mathematical theory of semantic development \cite{saxe2019mathematical} and neural network interpretability.

Active Learning at the ImageNet Scale

Active learning (AL) algorithms aim to identify an optimal subset of data for annotation, such that deep neural networks (DNN) can achieve better performance when trained on this labeled subset. AL is especially impactful in industrial scale settings where data labeling costs are high and practitioners use every tool at their disposal to improve model performance. The recent success of self-supervised pretraining (SSP) highlights the importance of harnessing abundant unlabeled data to boost model performance. By combining AL with SSP, we can make use of unlabeled data while simultaneously labeling and training on particularly informative samples. In this work, we study a combination of AL and SSP on ImageNet. We find that performance on small toy datasets -- the typical benchmark setting in the literature -- is not representative of performance on ImageNet due to the class imbalanced samples selected by an active learner. Among the existing baselines we test, popular AL algorithms across a variety of small and large scale settings fail to outperform random sampling. To remedy the class-imbalance problem, we propose Balanced Selection (BASE), a simple, scalable AL algorithm that outperforms random sampling consistently by selecting more balanced samples for annotation than existing methods. Our code is available at: https://github.com/zeyademam/active_learning .

Exploring the high dimensional geometry of HSI features

We explore feature space geometries induced by the 3-D Fourier scattering transform and deep neural network with extended attribute profiles on four standard hyperspectral images. We examine the distances and angles of class means, the variability of classes, and their low-dimensional structures. These statistics are compared to that of raw features, and our results provide insight into the vastly different properties of these two methods. We also explore a connection with the newly observed deep learning phenomenon of neural collapse.

Maximal function pooling with applications

Inspired by the Hardy-Littlewood maximal function, we propose a novel pooling strategy which is called maxfun pooling. It is presented both as a viable alternative to some of the most popular pooling functions, such as max pooling and average pooling, and as a way of interpolating between these two algorithms. We demonstrate the features of maxfun pooling with two applications: first in the context of convolutional sparse coding, and then for image classification.

Cortical Features for Defense Against Adversarial Audio Attacks

We propose using a computational model of the auditory cortex as a defense against adversarial attacks on audio. We apply several white-box iterative optimization-based adversarial attacks to an implementation of Amazon Alexa's HW network, and a modified version of this network with an integrated cortical representation, and show that the cortical features help defend against universal adversarial examples. At the same level of distortion, the adversarial noises found for the cortical network are always less effective for universal audio attacks. We make our code publicly available at https://github.com/ilyakava/py3fst.

Witches' Brew: Industrial Scale Data Poisoning via Gradient Matching

Data Poisoning attacks involve an attacker modifying training data to maliciouslycontrol a model trained on this data. Previous poisoning attacks against deep neural networks have been limited in scope and success, working only in simplified settings or being prohibitively expensive for large datasets. In this work, we focus on a particularly malicious poisoning attack that is both "from scratch" and"clean label", meaning we analyze an attack that successfully works against new, randomly initialized models, and is nearly imperceptible to humans, all while perturbing only a small fraction of the training data. The central mechanism of this attack is matching the gradient direction of malicious examples. We analyze why this works, supplement with practical considerations. and show its threat to real-world practitioners, finding that it is the first poisoning method to cause targeted misclassification in modern deep networks trained from scratch on a full-sized, poisoned ImageNet dataset. Finally we demonstrate the limitations of existing defensive strategies against such an attack, concluding that data poisoning is a credible threat, even for large-scale deep learning systems.

cGANs with Multi-Hinge Loss

We propose a new algorithm to incorporate class conditional information into the discriminator of GANs via a multi-class generalization of the commonly used Hinge loss. Our approach is in contrast to most GAN frameworks in that we train a single classifier for K+1 classes with one loss function, instead of a real/fake discriminator, or a discriminator classifier pair. We show that learning a single good classifier and a single state of the art generator simultaneously is possible in supervised and semi-supervised settings. With our multi-hinge loss modification we were able to improve the state of the art CIFAR10 IS & FID to 9.58 & 6.40, CIFAR100 IS & FID to 14.36 & 13.32, and STL10 IS & FID to 12.16 & 17.44. The code written with PyTorch is available at https://github.com/ilyakava/BigGAN-PyTorch.

Transport Model for Feature Extraction

We present a new feature extraction method for complex and large datasets, based on the concept of transport operators on graphs. The proposed approach generalizes and extends the many existing data representation methodologies built upon diffusion processes, to a new domain where dynamical systems play a key role. The main advantage of this approach comes from the ability to exploit different relationships than those arising in the context of e.g., Graph Laplacians. Fundamental properties of the transport operators are proved. We demonstrate the flexibility of the method by introducing several diverse examples of transformations. We close the paper with a series of computational experiments and applications to the problem of classification of hyperspectral satellite imagery, to illustrate the practical implications of our algorithm and its ability to quantify new aspects of relationships within complicated datasets.

Three-Dimensional Fourier Scattering Transform and Classification of Hyperspectral Images

Recent research has resulted in many new techniques that are able to capture the special properties of hyperspectral data for hyperspectral image analysis, with hyperspectral image classification as one of the most active tasks. Time-frequency methods decompose spectra into multi-spectral bands, while hierarchical methods like neural networks incorporate spatial information across scales and model multiple levels of dependencies between spectral features. The Fourier scattering transform is an amalgamation of time-frequency representations with neural network architectures, both of which have recently been proven to provide significant advances in spectral-spatial classification. We test the proposed three dimensional Fourier scattering method on four standard hyperspectral datasets, and present results that indicate that the Fourier scattering transform is highly effective at representing spectral data when compared with other state-of-the-art spectral-spatial classification methods.