A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very successful since it was shown that any weighted tree can be embedded in that geometry with arbitrary low distortion. Various optimization methods for hyperbolic embeddings based on common models of hyperbolic geometry have been studied. In this paper, we consider Hilbert geometry for the standard simplex which is isometric to a vector space equipped with the variation polytope norm. We study the representation power of this Hilbert simplex geometry by embedding distance matrices of graphs. Our findings demonstrate that Hilbert simplex geometry is competitive to alternative geometries such as the Poincar\'e hyperbolic ball or the Euclidean geometry for embedding tasks while being fast and numerically robust.

Data scarcity has been the main factor that hinders the progress of event extraction. To overcome this issue, we propose a Self-Training with Feedback (STF) framework that leverages the large-scale unlabeled data and acquires feedback for each new event prediction from the unlabeled data by comparing it to the Abstract Meaning Representation (AMR) graph of the same sentence. Specifically, STF consists of (1) a base event extraction model trained on existing event annotations and then applied to large-scale unlabeled corpora to predict new event mentions as pseudo training samples, and (2) a novel scoring model that takes in each new predicted event trigger, an argument, its argument role, as well as their paths in the AMR graph to estimate a compatibility score indicating the correctness of the pseudo label. The compatibility scores further act as feedback to encourage or discourage the model learning on the pseudo labels during self-training. Experimental results on three benchmark datasets, including ACE05-E, ACE05-E+, and ERE, demonstrate the effectiveness of the STF framework on event extraction, especially event argument extraction, with significant performance gain over the base event extraction models and strong baselines. Our experimental analysis further shows that STF is a generic framework as it can be applied to improve most, if not all, event extraction models by leveraging large-scale unlabeled data, even when high-quality AMR graph annotations are not available.

Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces $\mathcal{X}$ and $\mathcal{Y}$ using elementary functions between Euclidean spaces as building blocks. Earlier results assume that the target space $\mathcal{Y}$ is a topological vector space. We overcome this limitation by ``randomization'': our approximators output discrete probability measures over $\mathcal{Y}$. When $\mathcal{X}$ and $\mathcal{Y}$ are Polish without additional structure, we prove very general qualitative guarantees; when they have suitable combinatorial structure, we prove quantitative guarantees for H\"{o}lder-like maps, including maps between finite graphs, solution operators to rough differential equations between certain Carnot groups, and continuous non-linear operators between Banach spaces arising in inverse problems. In particular, we show that the required number of Dirac measures is determined by the combinatorial structure of $\mathcal{X}$ and $\mathcal{Y}$. For barycentric $\mathcal{Y}$, including Banach spaces, $\mathbb{R}$-trees, Hadamard manifolds, or Wasserstein spaces on Polish metric spaces, our approximators reduce to $\mathcal{Y}$-valued functions. When the Euclidean approximators are neural networks, our constructions generalize transformer networks, providing a new probabilistic viewpoint of geometric deep learning.

IRS Agent Joseph Ziegler joins'Special Report' to respond to critiques of hearing, letters from Del. prosecutor. The IRS special agent-turned-whistleblower formerly known as "Mr. X." spoke out to Fox News on Friday following an at-times contentious congressional hearing earlier this week. Joseph Ziegler, who came forward to Congress along with his colleague, Gary Shapley, said his team uncovered "a ton of evidence" that proved Hunter Biden allegedly willfully evaded or fraudulently filed his taxes, which set him apart from a typical IRS investigatory subject that would be faced with civil fines. Ziegler also told "Special Report" the ultimate reason he came forward as a whistleblower was that he saw many instances where federal officials were not following proper procedures.

Fox News correspondent Matt Finn reports the defense team is asking the state to share the evidence given to the grand jury that indicted Bryan Kohberger. Lawyers for Idaho murder suspect Bryan Kohberger won a small victory this week when a judge granted his request to access training records of three police officers involved in the investigation of the murders of four University of Idaho students. The defense team argued that they wanted to understand the methods the officers utilized, citing their critical role in the probe against their client, News Idaho 6 reported. Bryan Kohberger enters the courtroom for his arraignment hearing in Latah County District Court on May 22. His lawyers have been granted access to officer training records for those involved in his murder case. Kohberger, 28, is accused of fatally stabbing the college students four University of Idaho students in a 4 a.m.

For real-world applications, robots will need to continually learn in their environments through limited interactions with their users. Toward this, previous works in few-shot class incremental learning (FSCIL) and active class selection (ACS) have achieved promising results but were tested in constrained setups. Therefore, in this paper, we combine ideas from FSCIL and ACS to develop a novel framework that can allow an autonomous agent to continually learn new objects by asking its users to label only a few of the most informative objects in the environment. To this end, we build on a state-of-the-art (SOTA) FSCIL model and extend it with techniques from ACS literature. We further integrate a potential field-based navigation technique with our model to develop a complete framework that can allow an agent to process and reason on its sensory data through the FIASco model, navigate towards the most informative object in the environment, gather data about the object through its sensors and incrementally update the FIASco model. A primary challenge faced by robots deployed in the real world is continual adaptation to dynamic environments. Central to this challenge is object recognition (Ayub & Wagner, 2020d), a task typically requiring labeled examples. In this work, we address the problem of parsimonious object labelling wherein a robot may request labels for a small number of objects about which it knows least. In recent years, several works have been directed toward the problem of Few-Shot Class Incremental Learning (FSCIL) (Tao et al., 2020; Ayub & Wagner, 2020c) to develop models of incremental object learning that can learn from limited training data for each object class. The literature has made significant progress toward developing robots that can continually learn new objects from limited training data while preserving knowledge of previous objects. However, existing methods make strong assumptions about the training data that are rarely true in the real world. For example, FSCIL assumes that in each increment the robot will receive a fully labeled image dataset for the object classes in that increment, and the robot will not receive more data for these classes again (Tao et al., 2020; Ayub & Wagner, 2020c;d). In real world environments, however, robots will most likely encounter many unlabeled objects in their environment, and they will have to direct their learning toward a smaller subset of those unknown objects. Active learning is a subfield of machine learning that focuses on improving the learning efficiency of models by selectively seeking labels from within a large unlabeled data pool (Settles, 2009; Ayub & Fendley, 2022). Related to active learning is active class selection (ACS) in which a model seeks labels for specific object classes (Lomasky et al., 2007).

In this paper, we consider the sequential decision problem where the goal is to minimize the general dynamic regret on a complete Riemannian manifold. The task of offline optimization on such a domain, also known as a geodesic metric space, has recently received significant attention. The online setting has received significantly less attention, and it has remained an open question whether the body of results that hold in the Euclidean setting can be transplanted into the land of Riemannian manifolds where new challenges (e.g., curvature) come into play. In this paper, we show how to get optimistic regret bound on manifolds with non-positive curvature whenever improper learning is allowed and propose an array of adaptive no-regret algorithms. To the best of our knowledge, this is the first work that considers general dynamic regret and develops "optimistic" online learning algorithms which can be employed on geodesic metric spaces.

This paper revisits an adaptation of the random forest algorithm for Fr\'echet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we introduce a new splitting rule that circumvents the computationally expensive operation of Fr\'echet means by substituting with a medoid-based approach. We validate this approach by demonstrating its asymptotic equivalence to Fr\'echet mean-based procedures and establish the consistency of the associated regression estimator. The paper provides a sound theoretical framework and a more efficient computational approach to Fr\'echet regression, broadening its application to non-standard data types and complex use cases.

Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigenvectors of the graph Laplacian. One attractive application of ER is to point clouds, i.e. graphs whose vertices correspond to IID samples from a distribution over a metric space. Unfortunately, it was shown that the ER between any two points converges to a trivial quantity that holds no information about the graph's structure as the size of the sample increases to infinity. In this study, we show that this trivial solution can be circumvented by considering a region-based ER between pairs of small regions rather than pairs of points and by scaling the edge weights appropriately with respect to the underlying density in each region. By keeping the regions fixed, we show analytically that the region-based ER converges to a non-trivial limit as the number of points increases to infinity. Namely the ER on a metric space. We support our theoretical findings with numerical experiments.

Fake news detection has been a critical task for maintaining the health of the online news ecosystem. However, very few existing works consider the temporal shift issue caused by the rapidly-evolving nature of news data in practice, resulting in significant performance degradation when training on past data and testing on future data. In this paper, we observe that the appearances of news events on the same topic may display discernible patterns over time, and posit that such patterns can assist in selecting training instances that could make the model adapt better to future data. Specifically, we design an effective framework FTT (Forecasting Temporal Trends), which could forecast the temporal distribution patterns of news data and then guide the detector to fast adapt to future distribution. Experiments on the real-world temporally split dataset demonstrate the superiority of our proposed framework. The code is available at https://github.com/ICTMCG/FTT-ACL23.