We propose a new class of implicit networks, the multiscale deep equilibrium model (MDEQ), suited to large-scale and highly hierarchical pattern recognition domains. An MDEQ directly solves for and backpropagates through the equilibrium points of multiple feature resolutions simultaneously, using implicit differentiation to avoid storing intermediate states (and thus requiring only O(1) memory consumption). These simultaneously-learned multi-resolution features allow us to train a single model on a diverse set of tasks and loss functions, such as using a single MDEQ to perform both image classification and semantic segmentation. We illustrate the effectiveness of this approach on two large-scale vision tasks: ImageNet classification and semantic segmentation on high-resolution images from the Cityscapes dataset. In both settings, MDEQs are able to match or exceed the performance of recent competitive computer vision models: the first time such performance and scale have been achieved by an implicit deep learning approach. The code and pre-trained models are at https://github.com/locuslab/mdeq .

Due to the wider availability of modern electronic health records, patient care data is often being stored in the form of time-series. Clustering such time-series data is crucial for patient phenotyping, anticipating patients' prognoses by identifying "similar" patients, and designing treatment guidelines that are tailored to homogeneous patient subgroups. In this paper, we develop a deep learning approach for clustering time-series data, where each cluster comprises patients who share similar future outcomes of interest (e.g., adverse events, the onset of comorbidities). To encourage each cluster to have homogeneous future outcomes, the clustering is carried out by learning discrete representations that best describe the future outcome distribution based on novel loss functions. Experiments on two real-world datasets show that our model achieves superior clustering performance over state-of-the-art benchmarks and identifies meaningful clusters that can be translated into actionable information for clinical decision-making.

Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence to a solution and lack guarantees that a solution exists. On the other hand, Neural ODEs, another class of implicit-depth models, do guarantee existence of a unique solution but perform poorly compared with traditional networks. In this paper, we develop a new class of implicit-depth model based on the theory of monotone operators, the Monotone Operator Equilibrium Network (MON). We show the close connection between finding the equilibrium point of an implicit network and solving a form of monotone operator splitting problem, which admits efficient solvers with guaranteed, stable convergence. We then develop a parameterization of the network which ensures that all operators remain monotone, which guarantees the existence of a unique equilibrium point. Finally, we show how to instantiate several versions of these models, and implement the resulting iterative solvers, for structured linear operators such as multi-scale convolutions. The resulting models vastly outperform the Neural ODE-based models while also being more computationally efficient. Code is available at http://github.com/locuslab/monotone_op_net.

Ensembles of neural networks achieve superior performance compared to stand-alone networks not only in terms of accuracy on in-distribution data but also on data with distributional shift alongside improved uncertainty calibration. Diversity among networks in an ensemble is believed to be key for building strong ensembles, but typical approaches only ensemble different weight vectors of a fixed architecture. Instead, we investigate neural architecture search (NAS) for explicitly constructing ensembles to exploit diversity among networks of varying architectures and to achieve robustness against distributional shift. By directly optimizing ensemble performance, our methods implicitly encourage diversity among networks, without the need to explicitly define diversity. We find that the resulting ensembles are more diverse compared to ensembles composed of a fixed architecture and are therefore also more powerful. We show significant improvements in ensemble performance on image classification tasks both for in-distribution data and during distributional shift with better uncertainty calibration.

Robustness to adversarial attacks has been a major focus in machine learning security [4,12,26], and has been intensively studied in the past few years [8, 15, 32]. However, the theoretical understanding of adversarial robustness is still far from being satisfactory. Research [36] have demonstrated sample complexity may be one of the obstacles in achieving high robustness under standard learning, which is a large challenge since in many real-world applications, labeled examples are few and expensive. To address this challenge, recent works [9, 37] showed that adversarial robustness can be improved by leveraging unlabeled data that come from the same distribution/domain as the original labeled training samples. Nevertheless, that is still limited due to the difficulty to make sure that the unlabeled data are exactly from the same distribution as the labeled data. For example, gathering a large number of unlabeled images that follow the same distribution as CIFAR-10 is challenging, since one would have to carefully match the same lighting conditions, backgrounds, etc. Meanwhile, out-of-domain unlabeled data can be much easier and cheaper to collect. For instance, we used Bing search engine to query a small number of keywords and, within hours, generated a new 500k dataset of noisy CIFAR-10 categories; we call this Cheap-10.

Parametric causal modelling techniques rarely provide functionality for counterfactual estimation, often at the expense of modelling complexity. Since causal estimations depend on the family of functions used to model the data, simplistic models could entail imprecise characterizations of the generative mechanism, and, consequently, unreliable results. This limits their applicability to real-life datasets, with non-linear relationships and high interaction between variables. We propose Deep Causal Graphs, an abstract specification of the required functionality for a neural network to model causal distributions, and provide a model that satisfies this contract: Normalizing Causal Flows. We demonstrate its expressive power in modelling complex interactions and showcase applications of the method to machine learning explainability and fairness, using true causal counterfactuals.

In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions. However, this is certainly not the case in real world signals which naturally originate from a spatio-temporal configuration. As a result, the conventional vectorization process disrupts all of the spatio-temporal information about the order/place of data whether it be $1$D, $2$D, $3$D, or $4$D. In this paper, the problem of orthogonality is first investigated through conventional $k$-means of images, where images are to be processed as vectors. As a solution, shift-invariant $k$-means is proposed in a novel framework with the help of sparse representations. A generalization of shift-invariant $k$-means, convolutional dictionary learning, is then utilized as an unsupervised feature extraction method for classification. Experiments suggest that Gabor feature extraction as a simulation of shallow convolutional neural networks provides a little better performance compared to convolutional dictionary learning. Many alternatives of convolutional-logic are also discussed for spatio-temporal information preservation, including a spatio-temporal hypercomplex encoding scheme.

The wide-spread availability of rich data has fueled the growth of machine learning applications in numerous domains. However, growth in domains with highly-sensitive data (e.g., medical) is largely hindered as the private nature of data prohibits it from being shared. To this end, we propose Gradient-sanitized Wasserstein Generative Adversarial Networks (GS-WGAN), which allows releasing a sanitized form of the sensitive data with rigorous privacy guarantees. In contrast to prior work, our approach is able to distort gradient information more precisely, and thereby enabling training deeper models which generate more informative samples. Moreover, our formulation naturally allows for training GANs in both centralized and federated (i.e., decentralized) data scenarios. Through extensive experiments, we find our approach consistently outperforms state-of-the-art approaches across multiple metrics (e.g., sample quality) and datasets.

Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this study, we reconsider a way to generalize the fundamental components of neural networks in a single hyperbolic geometry model, and propose novel methodologies to construct a multinomial logistic regression, fully-connected layers, convolutional layers, and attention mechanisms under a unified mathematical interpretation, without increasing the parameters. A series of experiments show the parameter efficiency of our methods compared to a conventional hyperbolic component, and stability and outperformance over their Euclidean counterparts.

We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and redundancy principles. By two different interpretations (exploiting properties of power series of matrices and relying on Markov chains fundamentals) we can evaluate the values of paths (i.e., feature subsets) of arbitrary lengths, eventually go to infinite, from which we dub our framework Infinite Feature Selection (Inf-FS). Going to infinite allows to constrain the computational complexity of the selection process, and to rank the features in an elegant way, that is, considering the value of any path (subset) containing a particular feature. We also propose a simple unsupervised strategy to cut the ranking, so providing the subset of features to keep. In the experiments, we analyze diverse settings with heterogeneous features, for a total of 11 benchmarks, comparing against 18 widely-known comparative approaches. The results show that Inf-FS behaves better in almost any situation, that is, when the number of features to keep are fixed a priori, or when the decision of the subset cardinality is part of the process.