The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models

Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce successful models and do not have a clear theoretical foundation. In this study, we examine the use of convex optimization theory and sparse recovery models to refine the training process of neural networks and provide a better interpretation of their optimal weights. We focus on training two-layer neural networks with piecewise linear activations and demonstrate that they can be formulated as a finite-dimensional convex program. These programs include a regularization term that promotes sparsity, which constitutes a variant of group Lasso. We first utilize semi-infinite programming theory to prove strong duality for finite width neural networks and then we express these architectures equivalently as high dimensional convex sparse recovery models. Remarkably, the worst-case complexity to solve the convex program is polynomial in the number of samples and number of neurons when the rank of the data matrix is bounded, which is the case in convolutional networks. To extend our method to training data of arbitrary rank, we develop a novel polynomial-time approximation scheme based on zonotope subsampling that comes with a guaranteed approximation ratio. We also show that all the stationary of the nonconvex training objective can be characterized as the global optimum of a subsampled convex program. Our convex models can be trained using standard convex solvers without resorting to heuristics or extensive hyper-parameter tuning unlike non-convex methods. Through extensive numerical experiments, we show that convex models can outperform traditional non-convex methods and are not sensitive to optimizer hyperparameters.

Detecting Technical Debt Using Natural Language Processing Approaches -- A Systematic Literature Review

Context: Technical debt (TD) is a well-known metaphor for the long-term effects of architectural decisions in software development and the trade-off between producing high-quality, effective, and efficient code and meeting a release schedule. Thus, the code degrades and needs refactoring. A lack of resources, time, knowledge, or experience on the development team might cause TD in any software development project. Objective: In the context of TD detection, NLP has been utilized to identify the presence of TD automatically and even recognize specific types of TD. However, the enormous variety of feature extraction approaches and ML/DL algorithms employed in the literature often hinders researchers from trying to improve their performance. Method: In light of this, this SLR proposes a taxonomy of feature extraction techniques and algorithms used in technical debt detection: its objective is to compare and benchmark their performance in the examined studies. Results: We selected 55 articles that passed the quality evaluation of this SLR. We then investigated which feature extractions and algorithms were employed to identify TD in each SDLC phase. All approaches proposed in the analyzed studies were grouped into NLP, NLP+ML, and NLP+DL. This allows us to discuss the performance in three different ways. Conclusion: Overall, the NLP+DL group consistently outperforms in precision and F1-score for all projects, and in all but one project for the recall metric. Regarding the feature extraction techniques, the PTWE consistently achieves higher precision, recall, and F1-score for each project analyzed. Furthermore, TD types have been mapped, when possible, to SDLC phases: this served to determine the best-performing feature extractions and algorithms for each SDLC phase. Finally, based on the SLR results, we also identify implications that could be of concern to researchers and practitioners.

Dynamic Neural Fields for Learning Atlases of 4D Fetal MRI Time-series

We present a method for fast biomedical image atlas construction using neural fields. Atlases are key to biomedical image analysis tasks, yet conventional and deep network estimation methods remain time-intensive. In this preliminary work, we frame subject-specific atlas building as learning a neural field of deformable spatiotemporal observations. We apply our method to learning subject-specific atlases and motion stabilization of dynamic BOLD MRI time-series of fetuses in utero. Our method yields high-quality atlases of fetal BOLD time-series with $\sim$5-7$\times$ faster convergence compared to existing work. While our method slightly underperforms well-tuned baselines in terms of anatomical overlap, it estimates templates significantly faster, thus enabling rapid processing and stabilization of large databases of 4D dynamic MRI acquisitions. Code is available at https://github.com/Kidrauh/neural-atlasing

Robustifying Language Models with Test-Time Adaptation

Large-scale language models achieved state-of-the-art performance over a number of language tasks. However, they fail on adversarial language examples, which are sentences optimized to fool the language models but with similar semantic meanings for humans. While prior work focuses on making the language model robust at training time, retraining for robustness is often unrealistic for large-scale foundation models. Instead, we propose to make the language models robust at test time. By dynamically adapting the input sentence with predictions from masked words, we show that we can reverse many language adversarial attacks. Since our approach does not require any training, it works for novel tasks at test time and can adapt to novel adversarial corruptions. Visualizations and empirical results on two popular sentence classification datasets demonstrate that our method can repair adversarial language attacks over 65% o

MWSIS: Multimodal Weakly Supervised Instance Segmentation with 2D Box Annotations for Autonomous Driving

Instance segmentation is a fundamental research in computer vision, especially in autonomous driving. However, manual mask annotation for instance segmentation is quite time-consuming and costly. To address this problem, some prior works attempt to apply weakly supervised manner by exploring 2D or 3D boxes. However, no one has ever successfully segmented 2D and 3D instances simultaneously by only using 2D box annotations, which could further reduce the annotation cost by an order of magnitude. Thus, we propose a novel framework called Multimodal Weakly Supervised Instance Segmentation (MWSIS), which incorporates various fine-grained label generation and correction modules for both 2D and 3D modalities to improve the quality of pseudo labels, along with a new multimodal cross-supervision approach, named Consistency Sparse Cross-modal Supervision (CSCS), to reduce the inconsistency of multimodal predictions by response distillation. Particularly, transferring the 3D backbone to downstream tasks not only improves the performance of the 3D detectors, but also outperforms fully supervised instance segmentation with only 5% fully supervised annotations. On the Waymo dataset, the proposed framework demonstrates significant improvements over the baseline, especially achieving 2.59% mAP and 12.75% mAP increases for 2D and 3D instance segmentation tasks, respectively. The code is available at https://github.com/jiangxb98/mwsis-plugin.

CACTO-SL: Using Sobolev Learning to improve Continuous Actor-Critic with Trajectory Optimization

Trajectory Optimization (TO) and Reinforcement Learning (RL) are powerful and complementary tools to solve optimal control problems. On the one hand, TO can efficiently compute locally-optimal solutions, but it tends to get stuck in local minima if the problem is not convex. On the other hand, RL is typically less sensitive to non-convexity, but it requires a much higher computational effort. Recently, we have proposed CACTO (Continuous Actor-Critic with Trajectory Optimization), an algorithm that uses TO to guide the exploration of an actor-critic RL algorithm. In turns, the policy encoded by the actor is used to warm-start TO, closing the loop between TO and RL. In this work, we present an extension of CACTO exploiting the idea of Sobolev learning. To make the training of the critic network faster and more data efficient, we enrich it with the gradient of the Value function, computed via a backward pass of the differential dynamic programming algorithm. Our results show that the new algorithm is more efficient than the original CACTO, reducing the number of TO episodes by a factor ranging from 3 to 10, and consequently the computation time. Moreover, we show that CACTO-SL helps TO to find better minima and to produce more consistent results.

Sample-Efficient Learning to Solve a Real-World Labyrinth Game Using Data-Augmented Model-Based Reinforcement Learning

Motivated by the challenge of achieving rapid learning in physical environments, this paper presents the development and training of a robotic system designed to navigate and solve a labyrinth game using model-based reinforcement learning techniques. The method involves extracting low-dimensional observations from camera images, along with a cropped and rectified image patch centered on the current position within the labyrinth, providing valuable information about the labyrinth layout. The learning of a control policy is performed purely on the physical system using model-based reinforcement learning, where the progress along the labyrinth's path serves as a reward signal. Additionally, we exploit the system's inherent symmetries to augment the training data. Consequently, our approach learns to successfully solve a popular real-world labyrinth game in record time, with only 5 hours of real-world training data.

Automatic nonlinear MPC approximation with closed-loop guarantees

In this paper, we address the problem of automatically approximating nonlinear model predictive control (MPC) schemes with closed-loop guarantees. First, we discuss how this problem can be reduced to a function approximation problem, which we then tackle by proposing ALKIA-X, the Adaptive and Localized Kernel Interpolation Algorithm with eXtrapolated reproducing kernel Hilbert space norm. ALKIA-X is a non-iterative algorithm that ensures numerically well-conditioned computations, a fast-to-evaluate approximating function, and the guaranteed satisfaction of any desired bound on the approximation error. Hence, ALKIA-X automatically computes an explicit function that approximates the MPC, yielding a controller suitable for safety-critical systems and high sampling rates. In a numerical experiment, we apply ALKIA-X to a nonlinear MPC scheme, demonstrating reduced offline computation and online evaluation time compared to a state-of-the-art method.

Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equations

Long-term time series forecasting (LTSF) is a challenging task that has been investigated in various domains such as finance investment, health care, traffic, and weather forecasting. In recent years, Linear-based LTSF models showed better performance, pointing out the problem of Transformer-based approaches causing temporal information loss. However, Linear-based approach has also limitations that the model is too simple to comprehensively exploit the characteristics of the dataset. To solve these limitations, we propose LTSF-DNODE, which applies a model based on linear ordinary differential equations (ODEs) and a time series decomposition method according to data statistical characteristics. We show that LTSF-DNODE outperforms the baselines on various real-world datasets. In addition, for each dataset, we explore the impacts of regularization in the neural ordinary differential equation (NODE) framework.

ScribblePrompt: Fast and Flexible Interactive Segmentation for Any Medical Image

Semantic medical image segmentation is a crucial part of both scientific research and clinical care. With enough labelled data, deep learning models can be trained to accurately automate specific medical image segmentation tasks. However, manually segmenting images to create training data is highly labor intensive. In this paper, we present ScribblePrompt, an interactive segmentation framework for medical imaging that enables human annotators to segment unseen structures using scribbles, clicks, and bounding boxes. Scribbles are an intuitive and effective form of user interaction for complex tasks, however most existing methods focus on click-based interactions. We introduce algorithms for simulating realistic scribbles that enable training models that are amenable to multiple types of interaction. To achieve generalization to new tasks, we train on a diverse collection of 65 open-access biomedical datasets -- using both real and synthetic labels. We test ScribblePrompt on multiple network architectures and unseen datasets, and demonstrate that it can be used in real-time on a single CPU. We evaluate ScribblePrompt using manually-collected scribbles, simulated interactions, and a user study. ScribblePrompt outperforms existing methods in all our evaluations. In the user study, ScribblePrompt reduced annotation time by 28% while improving Dice by 15% compared to existing methods. We showcase ScribblePrompt in an online demo and provide code at https://scribbleprompt.csail.mit.edu