Theoretical results show that neural networks can be approximated by Gaussian processes in the infinite-width limit. However, for fully connected networks, it has been previously shown that for any fixed network width, $n$, the Gaussian approximation gets worse as the network depth, $d$, increases. Given that modern networks are deep, this raises the question of how well modern architectures, like ResNets, are captured by the infinite-width limit. To provide a better approximation, we study ReLU ResNets in the infinite-depth-and-width limit, where both depth and width tend to infinity as their ratio, $d/n$, remains constant. In contrast to the Gaussian infinite-width limit, we show theoretically that the network exhibits log-Gaussian behaviour at initialization in the infinite-depth-and-width limit, with parameters depending on the ratio $d/n$. Using Monte Carlo simulations, we demonstrate that even basic properties of standard ResNet architectures are poorly captured by the Gaussian limit, but remarkably well captured by our log-Gaussian limit. Moreover, our analysis reveals that ReLU ResNets at initialization are hypoactivated: fewer than half of the ReLUs are activated. Additionally, we calculate the interlayer correlations, which have the effect of exponentially increasing the variance of the network output. Based on our analysis, we introduce Balanced ResNets, a simple architecture modification, which eliminates hypoactivation and interlayer correlations and is more amenable to theoretical analysis.

Leveraging time-parallel methods for differential equations, Multiple Shooting Layers (MSLs) seek solutions of initial value problems via parallelizable root-finding algorithms. MSLs broadly serve as drop-in replacements for neural ordinary differential equations (Neural ODEs) with improved efficiency in number of function evaluations (NFEs) and wall-clock inference time. We develop the algorithmic framework of MSLs, analyzing the different choices of solution methods from a theoretical and computational perspective. MSLs are showcased in long horizon optimal control of ODEs and PDEs and as latent models for sequence generation. Finally, we investigate the speedups obtained through application of MSL inference in neural controlled differential equations (Neural CDEs) for time series classification of medical data.

Although deep learning models have driven state-of-the-art performance on a wide array of tasks, they are prone to learning spurious correlations that should not be learned as predictive clues. To mitigate this problem, we propose a causality-based training framework to reduce the spurious correlations caused by observable confounders. We give theoretical analysis on the underlying general Structural Causal Model (SCM) and propose to perform Maximum Likelihood Estimation (MLE) on the interventional distribution instead of the observational distribution, namely Counterfactual Maximum Likelihood Estimation (CMLE). As the interventional distribution, in general, is hidden from the observational data, we then derive two different upper bounds of the expected negative log-likelihood and propose two general algorithms, Implicit CMLE and Explicit CMLE, for causal predictions of deep learning models using observational data. We conduct experiments on two real-world tasks: Natural Language Inference (NLI) and Image Captioning. The results show that CMLE methods outperform the regular MLE method in terms of out-of-domain generalization performance and reducing spurious correlations, while maintaining comparable performance on the regular evaluations.

We propose a simple post hoc calibration method to estimate the confidence/uncertainty that a model prediction is correct on data with covariate shift, as represented by the large-scale corrupted data benchmark [Ovadia et al., 2019]. We achieve this by synthesizing surrogate calibration sets by corrupting the calibration set with varying intensities of a known corruption. Our method demonstrates significant improvements on the benchmark on a wide range of covariate shifts.

Superpixels serve as a powerful preprocessing tool in many computer vision tasks. By using superpixel representation, the number of image primitives can be largely reduced by orders of magnitudes. The majority of superpixel methods use handcrafted features, which usually do not translate well into strong adherence to object boundaries. A few recent superpixel methods have introduced deep learning into the superpixel segmentation process. However, none of these methods is able to produce superpixels in near real-time, which is crucial to the applicability of a superpixel method in practice. In this work, we propose a two-stage graph-based framework for superpixel segmentation. In the first stage, we introduce an efficient Deep Affinity Learning (DAL) network that learns pairwise pixel affinities by aggregating multi-scale information. In the second stage, we propose a highly efficient superpixel method called Hierarchical Entropy Rate Segmentation (HERS). Using the learned affinities from the first stage, HERS builds a hierarchical tree structure that can produce any number of highly adaptive superpixels instantaneously. We demonstrate, through visual and numerical experiments, the effectiveness and efficiency of our method compared to various state-of-the-art superpixel methods.

Reinforcement learning competitions have formed the basis for standard research benchmarks, galvanized advances in the state-of-the-art, and shaped the direction of the field. Despite this, a majority of challenges suffer from the same fundamental problems: participant solutions to the posed challenge are usually domain-specific, biased to maximally exploit compute resources, and not guaranteed to be reproducible. In this paper, we present a new framework of competition design that promotes the development of algorithms that overcome these barriers. We propose four central mechanisms for achieving this end: submission retraining, domain randomization, desemantization through domain obfuscation, and the limitation of competition compute and environment-sample budget. To demonstrate the efficacy of this design, we proposed, organized, and ran the MineRL 2020 Competition on Sample-Efficient Reinforcement Learning. In this work, we describe the organizational outcomes of the competition and show that the resulting participant submissions are reproducible, non-specific to the competition environment, and sample/resource efficient, despite the difficult competition task.

A novel non-parametric quantile estimation method for continuous random variables is introduced, based on a minimal neural network architecture consisting of a single unit. Its advantage over estimations from ranking the order statistics is shown, specifically for small sample size. In a regression context, the method can be used to quantify predictive uncertainty under the split conformal prediction setting, where prediction intervals are estimated from the residuals of a pre-trained model on a held-out validation set to quantify the uncertainty in future predictions. Benchmarking experiments demonstrate that the method is competitive in quality and coverage with state-of-the-art solutions, with the added benefit of being more computationally efficient.

We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose joint rank and sparsity minimization for defect detection. In particular, we propose a non-convex approach based on the iteratively reweighted nuclear and $\ell_1-$norm (a double-reweighted approach) to obtain a higher accuracy compared to the conventional nuclear norm and $\ell_1-$norm minimization. To this end, an iterative algorithm is designed to estimate the low-rank and sparse contributions. Further, we propose deep learning to learn the parameters of the algorithm (i.e., algorithm unfolding) to improve the accuracy and the speed of convergence of the algorithm. Our numerical results show that the proposed approach outperforms the conventional approaches in terms of mean square errors of the recovered low-rank and sparse components and the speed of convergence.

Sparse neural networks are becoming increasingly important as the field seeks to improve the performance of existing models by scaling them up, while simultaneously trying to reduce power consumption and computational footprint. Unfortunately, most existing methods for inducing performant sparse models still entail the instantiation of dense parameters, or dense gradients in the backward-pass, during training. For very large models this requirement can be prohibitive. In this work we propose Top-KAST, a method that preserves constant sparsity throughout training (in both the forward and backward-passes). We demonstrate the efficacy of our approach by showing that it performs comparably to or better than previous works when training models on the established ImageNet benchmark, whilst fully maintaining sparsity. In addition to our ImageNet results, we also demonstrate our approach in the domain of language modeling where the current best performing architectures tend to have tens of billions of parameters and scaling up does not yet seem to have saturated performance. Sparse versions of these architectures can be run with significantly fewer resources, making them more widely accessible and applicable. Furthermore, in addition to being effective, our approach is straightforward and can easily be implemented in a wide range of existing machine learning frameworks with only a few additional lines of code. We therefore hope that our contribution will help enable the broader community to explore the potential held by massive models, without incurring massive computational cost.

This paper develops probabilistic PV forecasters by taking advantage of recent breakthroughs in deep learning. It tailored forecasting tool, named encoder-decoder, is implemented to compute intraday multi-output PV quantiles forecasts to efficiently capture the time correlation. The models are trained using quantile regression, a non-parametric approach that assumes no prior knowledge of the probabilistic forecasting distribution. The case study is composed of PV production monitored on-site at the University of Li\`ege (ULi\`ege), Belgium. The weather forecasts from the regional climate model provided by the Laboratory of Climatology are used as inputs of the deep learning models. The forecast quality is quantitatively assessed by the continuous ranked probability and interval scores. The results indicate this architecture improves the forecast quality and is computationally efficient to be incorporated in an intraday decision-making tool for robust optimization.