Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. In fact, our result even holds for Borel-Turing computability., i.e., there does not exist an algorithm which performs the training of a neural network on digital hardware for any given accuracy. This establishes a conceptual barrier on the capabilities of neural networks for finite-dimensional inverse problems given that the computations are performed on digital hardware.
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Given some observed data and a probabilistic generative model, Bayesian inference aims at obtaining the distribution of a model's latent parameters that could have yielded the data. This task is challenging for large population studies where thousands of measurements are performed over a cohort of hundreds of subjects, resulting in a massive latent parameter space. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that can efficiently tackle large population studies. To this end, our main idea is to share the parameterization and learning across the different i.i.d. variables in a generative model -symbolized by the model's plates. We name this concept plate amortization, and illustrate the powerful synergies it entitles, resulting in expressive, parsimoniously parameterized and orders of magnitude faster to train large scale hierarchical variational distributions. We illustrate the practical utility of PAVI through a challenging Neuroimaging example featuring a million latent parameters, demonstrating a significant step towards scalable and expressive Variational Inference.
We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors. This insight allows us to construct new algorithms for community detection and parameter estimation for the PABM, as well as improve an existing algorithm that relies on Sparse Subspace Clustering. Using established asymptotic properties of Adjacency Spectral Embedding for the GRDPG, we derive asymptotic properties of these algorithms. In particular, we demonstrate that the absolute number of community detection errors tends to zero as the number of graph vertices tends to infinity. Simulation experiments illustrate these properties.
This paper will describe and analyze a new phenomenon that was not known before, which we call "Early Transferability". Its essence is that the adversarial perturbations transfer among different networks even at extremely early stages in their training. In fact, one can initialize two networks with two different independent choices of random weights and measure the angle between their adversarial perturbations after each step of the training. What we discovered was that these two adversarial directions started to align with each other already after the first few training steps (which typically use only a small fraction of the available training data), even though the accuracy of the two networks hadn't started to improve from their initial bad values due to the early stage of the training. The purpose of this paper is to present this phenomenon experimentally and propose plausible explanations for some of its properties.
Digital whole slides images contain an enormous amount of information providing a strong motivation for the development of automated image analysis tools. Particularly deep neural networks show high potential with respect to various tasks in the field of digital pathology. However, a limitation is given by the fact that typical deep learning algorithms require (manual) annotations in addition to the large amounts of image data, to enable effective training. Multiple instance learning exhibits a powerful tool for learning deep neural networks in a scenario without fully annotated data. These methods are particularly effective in this domain, due to the fact that labels for a complete whole slide image are often captured routinely, whereas labels for patches, regions or pixels are not. This potential already resulted in a considerable number of publications, with the majority published in the last three years. Besides the availability of data and a high motivation from the medical perspective, the availability of powerful graphics processing units exhibits an accelerator in this field. In this paper, we provide an overview of widely and effectively used concepts of used deep multiple instance learning approaches, recent advances and also critically discuss remaining challenges and future potential.
Due to the widespread use of complex machine learning models in real-world applications, it is becoming critical to explain model predictions. However, these models are typically black-box deep neural networks, explained post-hoc via methods with known faithfulness limitations. Generalized Additive Models (GAMs) are an inherently interpretable class of models that address this limitation by learning a non-linear shape function for each feature separately, followed by a linear model on top. However, these models are typically difficult to train, require numerous parameters, and are difficult to scale. We propose an entirely new subfamily of GAMs that utilizes basis decomposition of shape functions. A small number of basis functions are shared among all features, and are learned jointly for a given task, thus making our model scale much better to large-scale data with high-dimensional features, especially when features are sparse. We propose an architecture denoted as the Neural Basis Model (NBM) which uses a single neural network to learn these bases. On a variety of tabular and image datasets, we demonstrate that for interpretable machine learning, NBMs are the state-of-the-art in accuracy, model size, and, throughput and can easily model all higher-order feature interactions. Source code is available at //github.com/facebookresearch/nbm-spam.
We present CAISAR, an open-source platform under active development for the characterization of AI systems' robustness and safety. CAISAR provides a unified entry point for defining verification problems by using WhyML, the mature and expressive language of the Why3 verification platform. Moreover, CAISAR orchestrates and composes state-of-the-art machine learning verification tools which, individually, are not able to efficiently handle all problems but, collectively, can cover a growing number of properties. Our aim is to assist, on the one hand, the V\&V process by reducing the burden of choosing the methodology tailored to a given verification problem, and on the other hand the tools developers by factorizing useful features-visualization, report generation, property description-in one platform. CAISAR will soon be available at //git.frama-c.com/pub/caisar.
Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep Neural Networks (DNNs) to perform this task. This is surprising as deep learning has seen very successful applications in the last years. DNNs have indeed revolutionized the field of computer vision especially with the advent of novel deeper architectures such as Residual and Convolutional Neural Networks. Apart from images, sequential data such as text and audio can also be processed with DNNs to reach state-of-the-art performance for document classification and speech recognition. In this article, we study the current state-of-the-art performance of deep learning algorithms for TSC by presenting an empirical study of the most recent DNN architectures for TSC. We give an overview of the most successful deep learning applications in various time series domains under a unified taxonomy of DNNs for TSC. We also provide an open source deep learning framework to the TSC community where we implemented each of the compared approaches and evaluated them on a univariate TSC benchmark (the UCR/UEA archive) and 12 multivariate time series datasets. By training 8,730 deep learning models on 97 time series datasets, we propose the most exhaustive study of DNNs for TSC to date.
In this paper, we propose a deep reinforcement learning framework called GCOMB to learn algorithms that can solve combinatorial problems over large graphs. GCOMB mimics the greedy algorithm in the original problem and incrementally constructs a solution. The proposed framework utilizes Graph Convolutional Network (GCN) to generate node embeddings that predicts the potential nodes in the solution set from the entire node set. These embeddings enable an efficient training process to learn the greedy policy via Q-learning. Through extensive evaluation on several real and synthetic datasets containing up to a million nodes, we establish that GCOMB is up to 41% better than the state of the art, up to seven times faster than the greedy algorithm, robust and scalable to large dynamic networks.
Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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