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In this work we present denoiSplit, a method to tackle a new analysis task, i.e. the challenge of joint semantic image splitting and unsupervised denoising. This dual approach has important applications in fluorescence microscopy, where semantic image splitting has important applications but noise does generally hinder the downstream analysis of image content. Image splitting involves dissecting an image into its distinguishable semantic structures. We show that the current state-of-the-art method for this task struggles in the presence of image noise, inadvertently also distributing the noise across the predicted outputs. The method we present here can deal with image noise by integrating an unsupervised denoising sub-task. This integration results in improved semantic image unmixing, even in the presence of notable and realistic levels of imaging noise. A key innovation in denoiSplit is the use of specifically formulated noise models and the suitable adjustment of KL-divergence loss for the high-dimensional hierarchical latent space we are training. We showcase the performance of denoiSplit across 4 tasks on real-world microscopy images. Additionally, we perform qualitative and quantitative evaluations and compare results to existing benchmarks, demonstrating the effectiveness of using denoiSplit: a single Variational Splitting Encoder-Decoder (VSE) Network using two suitable noise models to jointly perform semantic splitting and denoising.

Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this paper, we discuss a systematic approach to constructing neural architectures for modeling a subclass of dynamical systems, namely, Linear Time-Invariant (LTI) systems. We use a variant of continuous-time neural networks in which the output of each neuron evolves continuously as a solution of a first-order or second-order Ordinary Differential Equation (ODE). Instead of deriving the network architecture and parameters from data, we propose a gradient-free algorithm to compute sparse architecture and network parameters directly from the given LTI system, leveraging its properties. We bring forth a novel neural architecture paradigm featuring horizontal hidden layers and provide insights into why employing conventional neural architectures with vertical hidden layers may not be favorable. We also provide an upper bound on the numerical errors of our neural networks. Finally, we demonstrate the high accuracy of our constructed networks on three numerical examples.

Decision making and learning in the presence of uncertainty has attracted significant attention in view of the increasing need to achieve robust and reliable operations. In the case where uncertainty stems from the presence of adversarial attacks this need is becoming more prominent. In this paper we focus on linear and nonlinear classification problems and propose a novel adversarial training method for robust classifiers, inspired by Support Vector Machine (SVM) margins. We view robustness under a data driven lens, and derive finite sample complexity bounds for both linear and non-linear classifiers in binary and multi-class scenarios. Notably, our bounds match natural classifiers' complexity. Our algorithm minimizes a worst-case surrogate loss using Linear Programming (LP) and Second Order Cone Programming (SOCP) for linear and non-linear models. Numerical experiments on the benchmark MNIST and CIFAR10 datasets show our approach's comparable performance to state-of-the-art methods, without needing adversarial examples during training. Our work offers a comprehensive framework for enhancing binary linear and non-linear classifier robustness, embedding robustness in learning under the presence of adversaries.

Numerous Deep Learning (DL) models have been developed for a large spectrum of medical image analysis applications, which promises to reshape various facets of medical practice. Despite early advances in DL model validation and implementation, which encourage healthcare institutions to adopt them, some fundamental questions remain: are the DL models capable of generalizing? What causes a drop in DL model performances? How to overcome the DL model performance drop? Medical data are dynamic and prone to domain shift, due to multiple factors such as updates to medical equipment, new imaging workflow, and shifts in patient demographics or populations can induce this drift over time. In this paper, we review recent developments in generalization methods for DL-based classification models. We also discuss future challenges, including the need for improved evaluation protocols and benchmarks, and envisioned future developments to achieve robust, generalized models for medical image classification.

Explainable AI is crucial in medical imaging. In the challenging field of neuroscience, visual topics present a high level of complexity, particularly within three-dimensional space. The application of neuroscience, which involves identifying brain sulcal features from MRI, faces significant hurdles due to varying annotation protocols among experts and the intricate three-dimension functionality of the brain. Consequently, traditional explainability approaches fall short in effectively validating and evaluating these networks. To address this, we first present a mathematical formulation delineating various categories of explanation needs across diverse computer vision tasks, categorized into self-explanatory, semi-explanatory, non-explanatory, and new-pattern learning applications based on the reliability of the validation protocol. With respect to this mathematical formulation, we propose a 3D explainability framework aimed at validating the outputs of deep learning networks in detecting the paracingulate sulcus an essential brain anatomical feature. The framework integrates local 3D explanations, global explanations through dimensionality reduction, concatenated global explanations, and statistical shape features, unveiling new insights into pattern learning. We trained and tested two advanced 3D deep learning networks on the challenging TOP-OSLO dataset, significantly improving sulcus detection accuracy, particularly on the left hemisphere. During evaluation with diverse annotation protocols for this dataset, we highlighted the crucial role of an unbiased annotation process in achieving precise predictions and effective pattern learning within our proposed 3D framework. The proposed framework not only annotates the variable sulcus but also uncovers hidden AI knowledge, promising to advance our understanding of brain anatomy and function.

Recently, the increasing availability of repeated measurements in biomedical studies has motivated the development of several statistical methods for the dynamic prediction of survival in settings where a large (potentially high-dimensional) number of longitudinal covariates is available. These methods differ in both how they model the longitudinal covariates trajectories, and how they specify the relationship between the longitudinal covariates and the survival outcome. Because these methods are still quite new, little is known about their applicability, limitations and performance when applied to real-world data. To investigate these questions, we present a comparison of the predictive performance of the aforementioned methods and two simpler prediction approaches to three datasets that differ in terms of outcome type, sample size, number of longitudinal covariates and length of follow-up. We discuss how different modelling choices can have an impact on the possibility to accommodate unbalanced study designs and on computing time, and compare the predictive performance of the different approaches using a range of performance measures and landmark times.

In many communication contexts, the capabilities of the involved actors cannot be known beforehand, whether it is a cell, a plant, an insect, or even a life form unknown to Earth. Regardless of the recipient, the message space and time scale could be too fast, too slow, too large, or too small and may never be decoded. Therefore, it pays to devise a way to encode messages agnostic of space and time scales. We propose the use of fractal functions as self-executable infinite-frequency carriers for sending messages, given their properties of structural self-similarity and scale invariance. We call it `fractal messaging'. Starting from a spatial embedding, we introduce a framework for a space-time scale-free messaging approach to this challenge. When considering a space and time-agnostic framework for message transmission, it would be interesting to encode a message such that it could be decoded at several spatio-temporal scales. Hence, the core idea of the framework proposed herein is to encode a binary message as waves along infinitely many frequencies (in power-like distributions) and amplitudes, transmit such a message, and then decode and reproduce it. To do so, the components of the Weierstrass function, a known fractal, are used as carriers of the message. Each component will have its amplitude modulated to embed the binary stream, allowing for a space-time-agnostic approach to messaging.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.