In structured output prediction tasks, labeling ground-truth training output is often expensive. However, for many tasks, even when the true output is unknown, we can evaluate predictions using a scalar reward function, which may be easily assembled from human knowledge or non-differentiable pipelines. But searching through the entire output space to find the best output with respect to this reward function is typically intractable. In this paper, we instead use efficient truncated randomized search in this reward function to train structured prediction energy networks (SPENs), which provide efficient test-time inference using gradient-based search on a smooth, learned representation of the score landscape, and have previously yielded state-of-the-art results in structured prediction. In particular, this truncated randomized search in the reward function yields previously unknown local improvements, providing effective supervision to SPENs, avoiding their traditional need for labeled training data.

We study a real-time iteration (RTI) scheme for solving online optimization problem appeared in nonlinear optimal control. The proposed RTI scheme modifies the existing RTI-based model predictive control (MPC) algorithm, by selecting the stepsize of each Newton step at each sampling time using a differentiable exact augmented Lagrangian. The scheme can adaptively select the penalty parameters of augmented Lagrangian on the fly, which are shown to be stabilized after certain time periods. We prove under generic assumptions that, by involving stepsize selection instead of always using a full Newton step (like what most of the existing RTIs do), the scheme converges globally: for any initial point, the KKT residuals of the subproblems converge to zero. A key step is to show that augmented Lagrangian keeps decreasing as horizon moves forward.

Wind energy resource quantification, air pollution monitoring, and weather forecasting all rely on rapid, accurate measurement of local wind conditions. Visual observations of the effects of wind---the swaying of trees and flapping of flags, for example---encode information regarding local wind conditions that can potentially be leveraged for visual anemometry that is inexpensive and ubiquitous. Here, we demonstrate a coupled convolutional neural network and recurrent neural network architecture that extracts the wind speed encoded in visually recorded flow-structure interactions of a flag and tree in naturally occurring wind. Predictions for wind speeds ranging from 0.75-11 m/s showed agreement with measurements from a cup anemometer on site, with a root-mean-squared error approaching the natural wind speed variability due to atmospheric turbulence. Generalizability of the network was demonstrated by successful prediction of wind speed based on recordings of other flags in the field and in a controlled wind tunnel test.

Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solver's solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program.

Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to improve solution quality due to non-smoothness issues that arise when training through a complex optimization layer. To address these shortcomings, we learn a low-dimensional surrogate model of a large optimization problem by representing the feasible space in terms of meta-variables, each of which is a linear combination of the original variables. By training a low-dimensional surrogate model end-to-end, and jointly with the predictive model, we achieve: i) a large reduction in training and inference time; and ii) improved performance by focusing attention on the more important variables in the optimization and learning in a smoother space.

Full waveform inversion (FWI) is widely used in geophysics to reconstruct high-resolution velocity maps from seismic data. The recent success of data-driven FWI methods results in a rapidly increasing demand for open datasets to serve the geophysics community. We present OpenFWI, a collection of large-scale multi-structural benchmark datasets, to facilitate diversified, rigorous, and reproducible research on FWI. In particular, OpenFWI consists of 12 datasets ( 2.1 TB in total) synthesized from multiple sources. It encompasses diverse domains in geophysics (interface, fault, CO _2 reservoir, etc.), covers different geological subsurface structures (flat, curve, etc.), and contain various amounts of data samples (2K - 67K). It also includes a dataset for 3D FWI.

Recently, there have been significant interests in studying the so-called "double-descent" of the generalization error of linear regression models under the overparameterized and overfitting regime, with the hope that such analysis may provide the first step towards understanding why overparameterized deep neural networks (DNN) still generalize well. However, to date most of these studies focused on the min L2-norm solution that overfits the data. In contrast, in this paper we study the overfitting solution that minimizes the L1-norm, which is known as Basis Pursuit (BP) in the compressed sensing literature. Gaussian features, we show that for a large range of p up to a limit that grows exponentially with the number of samples n, with high probability the model error of BP is upper bounded by a value that decreases with p. To the best of our knowledge, this is the first analytical result in the literature establishing the double-descent of overfitting BP for finite n and p. Further, our results reveal significant differences between the double-descent of BP and min L2-norm solutions. Specifically, the double-descent upper-bound of BP is independent of the signal strength, and for high SNR and sparse models the descent-floor of BP can be much lower and wider than that of min L2-norm solutions.

This inversion process is expensive, requiring over a year of human and computational effort. Recently, data-driven approaches equipped with Deep learning (DL) are envisioned to improve SI efficiency. However, these improvements are restricted to data with highly reduced scale and complexity. To extend these approaches to real-scale seismic data, researchers need to process raw nav-merge seismic data into an image and perform convolution. We argue that this convolution-based way of SI is not only computationally expensive but also conceptually problematic. Seismic data is not naturally an image and need not be processed as images.

The success of the Segment Anything Model (SAM) demonstrates the significance of data-centric machine learning. However, due to the difficulties and high costs associated with annotating Remote Sensing (RS) images, a large amount of valuable RS data remains unlabeled, particularly at the pixel level. In this study, we leverage SAM and existing RS object detection datasets to develop an efficient pipeline for generating a large-scale RS segmentation dataset, dubbed SAMRS. SAMRS totally possesses 105,090 images and 1,668,241 instances, surpassing existing high-resolution RS segmentation datasets in size by several orders of magnitude. It provides object category, location, and instance information that can be used for semantic segmentation, instance segmentation, and object detection, either individually or in combination.

Time series forecasting is an important problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. In this paper, we propose to tackle such forecasting problem with Transformer. Although impressed by its performance in our preliminary study, we found its two major weaknesses: (1) locality-agnostics: the point-wise dot- product self-attention in canonical Transformer architecture is insensitive to local context, which can make the model prone to anomalies in time series; (2) memory bottleneck: space complexity of canonical Transformer grows quadratically with sequence length L, making directly modeling long time series infeasible. In order to solve these two issues, we first propose convolutional self-attention by producing queries and keys with causal convolution so that local context can be better incorporated into attention mechanism. Then, we propose LogSparse Transformer with only O(L(log L) 2) memory cost, improving forecasting accuracy for time series with fine granularity and strong long-term dependencies under constrained memory budget.