Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for the closed-loop system with provable guarantees. The algorithmic structure consists of two neural networks and a satisfiability modulo theories (SMT) solver. The first neural network is responsible for learning the unknown dynamics. The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller.

First-order methods for quadratic optimization such as OSQP are widely used for large-scale machine learning and embedded optimal control, where many related problems must be rapidly solved. These methods face two persistent challenges: manual hyperparameter tuning and convergence time to high-accuracy solutions. To address these, we explore how Reinforcement Learning (RL) can learn a policy to tune parameters to accelerate convergence. In experiments with well-known QP benchmarks we find that our RL policy, RLQP, significantly outperforms state-of-the-art QP solvers by up to 3x.

Sentence summarization aims at compressing a long sentence into a short one that keeps the main gist, and has extensive real-world applications such as headline generation. In previous work, researchers have developed various approaches to improve the ROUGE score, which is the main evaluation metric for summarization, whereas controlling the summary length has not drawn much attention. In our work, we address a new problem of explicit character-level length control for summarization, and propose a dynamic programming algorithm based on the Connectionist Temporal Classification (CTC) model. Results show that our approach not only achieves higher ROUGE scores but also yields more complete sentences.

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1'' and the deliberative, logical "System-2''. For existing System-1-like methods in visual activity understanding, it is crucial to integrate System-2 processing to improve explainability, generalization, and data efficiency. One possible path of activity reasoning is building a symbolic system composed of symbols and rules, where one rule connects multiple symbols, implying human knowledge and reasoning abilities.Previous methods have made progress, but are defective with limited symbols from handcraft and limited rules from visual-based annotations, failing to cover the complex patterns of activities and lacking compositional generalization. To overcome the defects, we propose a new symbolic system with two ideal important properties: broad-coverage symbols and rational rules. Collecting massive human knowledge via manual annotations is expensive to instantiate this symbolic system.

Learning a robust classifier from a few samples remains a key challenge in machine learning. A major thrust of research has been focused on developing k-nearest neighbor (k-NN) based algorithms combined with metric learning that captures similarities between samples. When the samples are limited, robustness is especially crucial to ensure the generalization capability of the classifier. In this paper, we study a minimax distributionally robust formulation of weighted k-nearest neighbors, which aims to find the optimal weighted k-NN classifiers that hedge against feature uncertainties. We develop an algorithm, Dr.k-NN, that efficiently solves this functional optimization problem and features in assigning minimax optimal weights to training samples when performing classification.

Multi-task learning aims to explore task relatedness to improve individual tasks, which is of particular significance in the challenging scenario that only limited data is available for each task. To tackle this challenge, we propose variational multi-task learning (VMTL), a general probabilistic inference framework for learning multiple related tasks. We cast multi-task learning as a variational Bayesian inference problem, in which task relatedness is explored in a unified manner by specifying priors. To incorporate shared knowledge into each task, we design the prior of a task to be a learnable mixture of the variational posteriors of other related tasks, which is learned by the Gumbel-Softmax technique. In contrast to previous methods, our VMTL can exploit task relatedness for both representations and classifiers in a principled way by jointly inferring their posteriors.

Large language models (LLMs) based on the generative pre-training transformer (GPT) have demonstrated remarkable effectiveness across a diverse range of downstream tasks. Inspired by the advancements of the GPT, we present PointGPT, a novel approach that extends the concept of GPT to point clouds, addressing the challenges associated with disorder properties, low information density, and task gaps. Specifically, a point cloud auto-regressive generation task is proposed to pre-train transformer models. Our method partitions the input point cloud into multiple point patches and arranges them in an ordered sequence based on their spatial proximity. Then, an extractor-generator based transformer decode, with a dual masking strategy, learns latent representations conditioned on the preceding point patches, aiming to predict the next one in an auto-regressive manner.

Deep learning models have been found with a tendency of relying on shortcuts, i.e., decision rules that perform well on standard benchmarks but fail when transferred to more challenging testing conditions. Such reliance may hinder deep learning models from learning other task-related features and seriously affect their performance and robustness. Although recent studies have shown some characteristics of shortcuts, there are few investigations on how to help the deep learning models to solve shortcut problems. This paper proposes a framework to address this issue by setting up roadblocks on shortcuts. Specifically, roadblocks are placed when the model is urged to learn to complete a gently modified task to ensure that the learned knowledge, including shortcuts, is insufficient the complete the task. Therefore, the model trained on the modified task will no longer over-rely on shortcuts.

In this paper, we consider an inverse problem in graph learning domain -- "given the graph representations smoothed by Graph Convolutional Network (GCN), how can we reconstruct the input graph signal?" We propose Graph Deconvolutional Network (GDN) and motivate the design of GDN via a combination of inverse filters in spectral domain and de-noising layers in wavelet domain, as the inverse operation results in a high frequency amplifier and may amplify the noise. We demonstrate the effectiveness of the proposed method on several tasks including graph feature imputation and graph structure generation.

We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. Even though the learner's objective is not convex-concave (and so the minimax theorem does not apply), we give a simple algorithm that can compete with the setting in which the adversary must announce their action first, with optimally diminishing regret. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains, ranging from multicalibration to a large set of no-regret algorithms, to a variant of Blackwell's approachability theorem for polytopes with fast convergence rates. As a new application, we show how to (multi)calibeat'' an arbitrary collection of forecasters --- achieving an exponentially improved dependence on the number of models we are competing against, compared to prior work.