arXiv subjects

Wojciech Czaja

Publications and source records attributed to Wojciech Czaja.

At least 19 recordsLinked to original sources

arXiv2025

Translation-Invariant Behavior of General Scattering Transforms

The main result of our paper offers an alternative, simpler, proof of Mallat's result on the translation invariance of the limiting behavior of sequences of Wavelet Scattering Transforms, which (unlike Mallat's proof) does not rely on the admissibility condition or on the density of a logarithmic Sobolev space in $L^2$. Furthermore, this result is generalized to a broader class of scattering transforms, including, for instance, a modification of the Fourier Scattering Transform. As a result, we also prove a new upper bound for the translation contraction for the Fourier Scattering Transform.

math.FA↗

arXiv2025

Neumann eigenmaps for landmark embedding

We present Neumann eigenmaps (NeuMaps), a novel approach for enhancing the standard diffusion map embedding using landmarks, i.e distinguished samples within the dataset. By interpreting these landmarks as a subgraph of the larger data graph, NeuMaps are obtained via the eigendecomposition of a renormalized Neumann Laplacian. We show that NeuMaps offer two key advantages: (1) they provide a computationally efficient embedding that accurately recovers the diffusion distance associated with the reflecting random walk on the subgraph, and (2) they naturally incorporate the Nyström extension within the diffusion map framework through the discrete Neumann boundary condition. Through examples in digit classification and molecular dynamics, we demonstrate that NeuMaps not only improve upon existing landmark-based embedding methods but also enhance the stability of diffusion map embeddings to the removal of highly significant points.

math.ST↗

arXiv2025

Input layer regularization and automated regularization hyperparameter tuning for myelin water estimation using deep learning

We propose a novel deep learning method which combines classical regularization with data augmentation for estimating myelin water fraction (MWF) in the brain via biexponential analysis. Our aim is to design an accurate deep learning technique for analysis of signals arising in magnetic resonance relaxometry. In particular, we study the biexponential model, one of the signal models used for MWF estimation. We greatly extend our previous work on \emph{input layer regularization (ILR)} in several ways. We now incorporate optimal regularization parameter selection via a dedicated neural network or generalized cross validation (GCV) on a signal-by-signal, or pixel-by-pixel, basis to form the augmented input signal, and now incorporate estimation of MWF, rather than just exponential time constants, into the analysis. On synthetically generated data, our proposed deep learning architecture outperformed both classical methods and a conventional multi-layer perceptron. On in vivo brain data, our architecture again outperformed other comparison methods, with GCV proving to be somewhat superior to a NN for regularization parameter selection. Thus, ILR improves estimation of MWF within the biexponential model. In addition, classical methods such as GCV may be combined with deep learning to optimize MWF imaging in the human brain.

q-bio.QM↗

arXiv2024

On the limits of neural network explainability via descrambling

We characterize the exact solutions to neural network descrambling--a mathematical model for explaining the fully connected layers of trained neural networks (NNs). By reformulating the problem to the minimization of the Brockett function arising in graph matching and complexity theory we show that the principal components of the hidden layer preactivations can be characterized as the optimal explainers or descramblers for the layer weights, leading to descrambled weight matrices. We show that in typical deep learning contexts these descramblers take diverse and interesting forms including (1) matching largest principal components with the lowest frequency modes of the Fourier basis for isotropic hidden data, (2) discovering the semantic development in two-layer linear NNs for signal recovery problems, and (3) explaining CNNs by optimally permuting the neurons. Our numerical experiments indicate that the eigendecompositions of the hidden layer data--now understood as the descramblers--can also reveal the layer's underlying transformation. These results illustrate that the SVD is more directly related to the explainability of NNs than previously thought and offers a promising avenue for discovering interpretable motifs for the hidden action of NNs, especially in contexts of operator learning or physics-informed NNs, where the input/output data has limited human readability.

cs.LG↗

arXiv2024

Hyperspectral Reconstruction of Skin Through Fusion of Scattering Transform Features

Hyperspectral imagery (HSI) is an established technique with an array of applications, but its use is limited due to both practical and technical issues associated with spectral devices. The goal of the ICASSP 2024 'Hyper-Skin' Challenge is to extract skin HSI from matching RGB images and an infrared band. To address this problem we propose a model using features of the scattering transform - a type of convolutional neural network with predefined filters. Our model matches and inverts those features, rather than the pixel values, reducing the complexity of matching while grouping similar features together, resulting in an improved learning process.

eess.IV↗

arXiv2024

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 ($ΣΔ$) 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.

cs.LG↗

arXiv2021

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 .

cs.CV↗

arXiv2021

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.

cs.SD↗

arXiv2021

Witches' Brew: Industrial Scale Data Poisoning via Gradient Matching

Data Poisoning attacks modify training data to maliciously control a model trained on such data. In this work, we focus on targeted poisoning attacks which cause a reclassification of an unmodified test image and as such breach model integrity. We consider 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. Previous poisoning attacks against deep neural networks in this setting have been limited in scope and success, working only in simplified settings or being prohibitively expensive for large datasets. The central mechanism of the new 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.

cs.CV↗

arXiv2021

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.

cs.CV↗

arXiv2021

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.

cs.CV↗

arXiv2020

Three-Dimensional Fourier Scattering Transform and Classification of Hyperspectral Images

Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to classification can now be solved by taking advantage of very efficient algorithms which have their roots in representation theory and in computational approximation. Time-frequency methods are one example of such techniques. They provide means to analyze and extract the spectral content from data. On the other hand, hierarchical methods such as neural networks incorporate spatial information across scales and model multiple levels of dependencies between spectral features. Both of these approaches have recently been proven to provide significant advances in the spectral-spatial classification of hyperspectral imagery. The 3D Fourier scattering transform, which is introduced in this paper, is an amalgamation of time-frequency representations with neural network architectures. It leverages the benefits provided by the Short-Time Fourier Transform with the numerical efficiency of deep learning network structures. We test the proposed method on several standard hyperspectral datasets, and we present results that indicate that the 3D Fourier scattering transform is highly effective at representing spectral content when compared with other state-of-the-art spectral-spatial classification methods.

cs.CV↗

arXiv2020

cGANs with Multi-Hinge Loss

We propose a new algorithm to incorporate class conditional information into the critic of GANs via a multi-class generalization of the commonly used Hinge loss that is compatible with both supervised and semi-supervised settings. We study the compromise between training a state of the art generator and an accurate classifier simultaneously, and propose a way to use our algorithm to measure the degree to which a generator and critic are class conditional. We show the trade-off between a generator-critic pair respecting class conditioning inputs and generating the highest quality images. With our multi-hinge loss modification we are able to improve Inception Scores and Frechet Inception Distance on the Imagenet dataset. We make our tensorflow code available at https://github.com/ilyakava/gan.

cs.LG↗

arXiv2019

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.

cs.LG↗

arXiv2018

Superresolution of Noisy Remotely Sensed Images Through Directional Representations

We develop an algorithm for single-image superresolution of remotely sensed data, based on the discrete shearlet transform. The shearlet transform extracts directional features of signals, and is known to provide near-optimally sparse representations for a broad class of images. This often leads to superior performance in edge detection and image representation when compared to isotropic frames. We justify the use of shearlets mathematically, before presenting a denoising single-image superresolution algorithm that combines the shearlet transform with sparse mixing estimators (SME). Our algorithm is compared with a variety of single-image superresolution methods, including wavelet SME superresolution. Our numerical results demonstrate competitive performance in terms of PSNR and SSIM.

cs.CV↗

arXiv2018

Adversarial Examples in Remote Sensing

This paper considers attacks against machine learning algorithms used in remote sensing applications, a domain that presents a suite of challenges that are not fully addressed by current research focused on natural image data such as ImageNet. In particular, we present a new study of adversarial examples in the context of satellite image classification problems. Using a recently curated data set and associated classifier, we provide a preliminary analysis of adversarial examples in settings where the targeted classifier is permitted multiple observations of the same location over time. While our experiments to date are purely digital, our problem setup explicitly incorporates a number of practical considerations that a real-world attacker would need to take into account when mounting a physical attack. We hope this work provides a useful starting point for future studies of potential vulnerabilities in this setting.

cs.CV↗

arXiv2018

Analysis of time-frequency scattering transforms

In this paper we address the problem of constructing a feature extractor which combines Mallat's scattering transform framework with time-frequency (Gabor) representations. To do this, we introduce a class of frames, called uniform covering frames, which includes a variety of semi-discrete Gabor systems. Incorporating a uniform covering frame with a neural network structure yields the Fourier scattering transform $\mathcal{S}_\mathcal{F}$ and the truncated Fourier scattering transform. We prove that $\mathcal{S}_\mathcal{F}$ propagates energy along frequency decreasing paths and its energy decays exponentially as a function of the depth. These quantitative estimates are fundamental in showing that $\mathcal{S}_\mathcal{F}$ satisfies the typical scattering transform properties, and in controlling the information loss due to width and depth truncation. We introduce the fast Fourier scattering transform algorithm, and illustrate the algorithm's performance. The time-frequency covering techniques developed in this paper are flexible and give insight into the analysis of scattering transforms.

math.FA↗

arXiv2017

Rotationally invariant time-frequency scattering transforms

In this paper we construct directionally sensitive functions that can be viewed as directional time-frequency representations. We call such a sequence a rotational uniform covering frame and by studying rotations of the frame, we derive the rotational Fourier scattering transform and the truncated rotational Fourier scattering transform. We prove that both operators are rotationally invariant, are bounded above and below, are non-expansive, and contract small translations and additive diffeomorphisms. We also construct finite uniform covering frames.

math.FA↗