我们开发了包含几何信息和拓扑信息的数据驱动方法，以从观察值中学习非线性动力学的简约表示。我们开发了使用与变异自动编码器（VAE）相关的训练策略来学习一般歧管潜在空间动力学的非线性状态空间模型的方法。我们的方法称为几何动力学（GD）变化自动编码器（GD-VAE）。我们根据包括一般多层感知器（MLP），卷积神经网络（CNNS）和转置CNN（T-CNN）在内的深层神经网络体系结构学习系统状态和进化的编码器和分解器。由参数化的PDE和物理学引起的问题的促进，我们研究了我们在学习非线性汉堡方程，约束机械系统和反应扩散系统的空间场的低维表示任务方面的性能。 GD-VAE提供了用于获取表示涉及动态任务的表示形式的方法。

敏捷飞行或穿越不规则地形的激进运动会导致激光扫描中的运动失真，从而降低状态估计和映射。存在一些减轻这种效果的方法，但是对于资源受限的移动机器人来说，它们仍然太简单或计算成本高。为此，本文介绍了直接的激光惯性进程（DLIO），这是一种轻巧的激光惯性射击算法，采用新的粗到精细方法来构建连续的时间轨迹进行精确运动校正。我们方法的关键在于构建一组分析方程，这些方程仅通过时间来参数化，从而实现快速和可行的点。此方法之所以可行，仅仅是因为我们新颖的非线性几何观察者具有强大的收敛性能，该观察者提供了可证明正确的状态估计值来初始化敏感的IMU整合步骤。此外，通过同时执行运动校正和前期，并直接将每次扫描注册到地图并绕过扫描到扫描，DLIO的凝结体系结构在计算上的计算效率比当前最新的ART高20％精度提高12％。我们通过多种公共基准和自收集的数据集进行了广泛的测试，证明了DLIO的出色本地化精度，地图质量和较低的计算开销，与四种最先进的算法相比。

We consider the problem of estimating a multivariate function $f_0$ of bounded variation (BV), from noisy observations $y_i = f_0(x_i) + z_i$ made at random design points $x_i \in \mathbb{R}^d$, $i=1,\ldots,n$. We study an estimator that forms the Voronoi diagram of the design points, and then solves an optimization problem that regularizes according to a certain discrete notion of total variation (TV): the sum of weighted absolute differences of parameters $\theta_i,\theta_j$ (which estimate the function values $f_0(x_i),f_0(x_j)$) at all neighboring cells $i,j$ in the Voronoi diagram. This is seen to be equivalent to a variational optimization problem that regularizes according to the usual continuum (measure-theoretic) notion of TV, once we restrict the domain to functions that are piecewise constant over the Voronoi diagram. The regression estimator under consideration hence performs (shrunken) local averaging over adaptively formed unions of Voronoi cells, and we refer to it as the Voronoigram, following the ideas in Koenker (2005), and drawing inspiration from Tukey's regressogram (Tukey, 1961). Our contributions in this paper span both the conceptual and theoretical frontiers: we discuss some of the unique properties of the Voronoigram in comparison to TV-regularized estimators that use other graph-based discretizations; we derive the asymptotic limit of the Voronoi TV functional; and we prove that the Voronoigram is minimax rate optimal (up to log factors) for estimating BV functions that are essentially bounded.

In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph. HNN derives multiple embeddings per node in the hypergraph where each embedding for a node is dependent on a specific hyperedge of that node. Notably, HNN is accurate, data-efficient, flexible with many interchangeable components, and useful for a wide range of hypergraph learning tasks. We evaluate the effectiveness of the HNN framework for hyperedge prediction and hypergraph node classification. We find that HNN achieves an overall mean gain of 7.72% and 11.37% across all baseline models and graphs for hyperedge prediction and hypergraph node classification, respectively.

Graph Neural Networks (GNNs) have become increasingly important in recent years due to their state-of-the-art performance on many important downstream applications. Existing GNNs have mostly focused on learning a single node representation, despite that a node often exhibits polysemous behavior in different contexts. In this work, we develop a persona-based graph neural network framework called PersonaSAGE that learns multiple persona-based embeddings for each node in the graph. Such disentangled representations are more interpretable and useful than a single embedding. Furthermore, PersonaSAGE learns the appropriate set of persona embeddings for each node in the graph, and every node can have a different number of assigned persona embeddings. The framework is flexible enough and the general design helps in the wide applicability of the learned embeddings to suit the domain. We utilize publicly available benchmark datasets to evaluate our approach and against a variety of baselines. The experiments demonstrate the effectiveness of PersonaSAGE for a variety of important tasks including link prediction where we achieve an average gain of 15% while remaining competitive for node classification. Finally, we also demonstrate the utility of PersonaSAGE with a case study for personalized recommendation of different entity types in a data management platform.

Traditionally, data analysis and theory have been viewed as separate disciplines, each feeding into fundamentally different types of models. Modern deep learning technology is beginning to unify these two disciplines and will produce a new class of predictively powerful space weather models that combine the physical insights gained by data and theory. We call on NASA to invest in the research and infrastructure necessary for the heliophysics' community to take advantage of these advances.

Learning fair graph representations for downstream applications is becoming increasingly important, but existing work has mostly focused on improving fairness at the global level by either modifying the graph structure or objective function without taking into account the local neighborhood of a node. In this work, we formally introduce the notion of neighborhood fairness and develop a computational framework for learning such locally fair embeddings. We argue that the notion of neighborhood fairness is more appropriate since GNN-based models operate at the local neighborhood level of a node. Our neighborhood fairness framework has two main components that are flexible for learning fair graph representations from arbitrary data: the first aims to construct fair neighborhoods for any arbitrary node in a graph and the second enables adaption of these fair neighborhoods to better capture certain application or data-dependent constraints, such as allowing neighborhoods to be more biased towards certain attributes or neighbors in the graph.Furthermore, while link prediction has been extensively studied, we are the first to investigate the graph representation learning task of fair link classification. We demonstrate the effectiveness of the proposed neighborhood fairness framework for a variety of graph machine learning tasks including fair link prediction, link classification, and learning fair graph embeddings. Notably, our approach achieves not only better fairness but also increases the accuracy in the majority of cases across a wide variety of graphs, problem settings, and metrics.

We introduce a language generation task grounded in a popular video game environment. KNUDGE (KNowledge Constrained User-NPC Dialogue GEneration) involves generating dialogue trees conditioned on an ontology captured in natural language passages providing quest and entity specifications. KNUDGE is constructed from side quest dialogues drawn directly from game data of Obsidian Entertainment's The Outer Worlds, leading to real-world complexities in generation: (1) dialogues are branching trees as opposed to linear chains of utterances; (2) utterances must remain faithful to the game lore--character personas, backstories, and entity relationships; and (3) a dialogue must accurately reveal new quest-related details to the human player. We report results for supervised and in-context learning techniques, finding there is significant room for future work on creating realistic game-quality dialogues.

Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases, probability mass can ``leak'' onto the set of infinite sequences. In order to characterize the notion of leakage more precisely, this paper offers a measure-theoretic treatment of language modeling. We prove that many popular language model families are in fact tight, meaning that they will not leak in this sense. We also generalize characterizations of tightness proposed in previous works.

We present a machine-learning framework to accurately characterize morphologies of Active Galactic Nucleus (AGN) host galaxies within $z<1$. We first use PSFGAN to decouple host galaxy light from the central point source, then we invoke the Galaxy Morphology Network (GaMorNet) to estimate whether the host galaxy is disk-dominated, bulge-dominated, or indeterminate. Using optical images from five bands of the HSC Wide Survey, we build models independently in three redshift bins: low $(0<z<0.25)$, medium $(0.25<z<0.5)$, and high $(0.5<z<1.0)$. By first training on a large number of simulated galaxies, then fine-tuning using far fewer classified real galaxies, our framework predicts the actual morphology for $\sim$ $60\%-70\%$ host galaxies from test sets, with a classification precision of $\sim$ $80\%-95\%$, depending on redshift bin. Specifically, our models achieve disk precision of $96\%/82\%/79\%$ and bulge precision of $90\%/90\%/80\%$ (for the 3 redshift bins), at thresholds corresponding to indeterminate fractions of $30\%/43\%/42\%$. The classification precision of our models has a noticeable dependency on host galaxy radius and magnitude. No strong dependency is observed on contrast ratio. Comparing classifications of real AGNs, our models agree well with traditional 2D fitting with GALFIT. The PSFGAN+GaMorNet framework does not depend on the choice of fitting functions or galaxy-related input parameters, runs orders of magnitude faster than GALFIT, and is easily generalizable via transfer learning, making it an ideal tool for studying AGN host galaxy morphology in forthcoming large imaging survey.