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In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

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In this project, we have investigated the use of advanced machine learning methods, specifically fine-tuned large language models, for pre-annotating data for a lexical extension task, namely adding descriptive words (verbs) to an existing (but incomplete, as of yet) ontology of event types. Several research questions have been focused on, from the investigation of a possible heuristics to provide at least hints to annotators which verbs to include and which are outside the current version of the ontology, to the possible use of the automatic scores to help the annotators to be more efficient in finding a threshold for identifying verbs that cannot be assigned to any existing class and therefore they are to be used as seeds for a new class. We have also carefully examined the correlation of the automatic scores with the human annotation. While the correlation turned out to be strong, its influence on the annotation proper is modest due to its near linearity, even though the mere fact of such pre-annotation leads to relatively short annotation times.

In this paper, we present an analytical framework to explore the interplay of signal interference and transmission queue management, and their impacts on the performance of unmanned aerial vehicles (UAVs) when operating in the unlicensed spectrum bands. In particular, we develop a comprehensive framework to investigate the impact of other interference links on the UAV as it communicates with the ground users. To this end, we provide closed-form expressions for packet drop probabilities in the queue due to buffer overflow or large queuing delay, which are expressed in terms of a transmission policy as a function of the channel fading threshold $\beta$. The overall packet loss caused either by interference signals or queuing packet drop is obtained, which, in turn, yields in obtaining the expected throughput performance. Through extensive numerical results, we investigate the impact of the channel fading threshold $\beta$, which plays an important role in balancing the trade-offs between packet loss due to queue drop or transmission error due to large interference levels.

In this work, we propose a new transformer-based regularization to better localize objects for Weakly supervised semantic segmentation (WSSS). In image-level WSSS, Class Activation Map (CAM) is adopted to generate object localization as pseudo segmentation labels. To address the partial activation issue of the CAMs, consistency regularization is employed to maintain activation intensity invariance across various image augmentations. However, such methods ignore pair-wise relations among regions within each CAM, which capture context and should also be invariant across image views. To this end, we propose a new all-pairs consistency regularization (ACR). Given a pair of augmented views, our approach regularizes the activation intensities between a pair of augmented views, while also ensuring that the affinity across regions within each view remains consistent. We adopt vision transformers as the self-attention mechanism naturally embeds pair-wise affinity. This enables us to simply regularize the distance between the attention matrices of augmented image pairs. Additionally, we introduce a novel class-wise localization method that leverages the gradients of the class token. Our method can be seamlessly integrated into existing WSSS methods using transformers without modifying the architectures. We evaluate our method on PASCAL VOC and MS COCO datasets. Our method produces noticeably better class localization maps (67.3% mIoU on PASCAL VOC train), resulting in superior WSSS performances.

In this work, we propose a methodology for investigating the application of semantic attention to enhance the explainability of Graph Neural Network (GNN)-based models, introducing semantically-informed perturbations and establishing a correlation between predicted feature-importance weights and model accuracy. Graph Deep Learning (GDL) has emerged as a promising field for tasks like scene interpretation, leveraging flexible graph structures to concisely describe complex features and relationships. As traditional explainability methods used in eXplainable AI (XAI) cannot be directly applied to such structures, graph-specific approaches are introduced. Attention mechanisms have demonstrated their efficacy in estimating the importance of input features in deep learning models and thus have been previously employed to provide feature-based explanations for GNN predictions. Building upon these insights, we extend existing attention-based graph-explainability methods investigating the use of attention weights as importance indicators of semantically sorted feature sets. Through analysing the behaviour of predicted attention-weights distribution in correlation with model accuracy, we gain valuable insights into feature importance with respect to the behaviour of the GNN model. We apply our methodology to a lidar pointcloud estimation model successfully identifying key semantic classes that contribute to enhanced performance effectively generating reliable post-hoc semantic explanations.

We consider a causal inference model in which individuals interact in a social network and they may not comply with the assigned treatments. In particular, we suppose that the form of network interference is unknown to researchers. To estimate meaningful causal parameters in this situation, we introduce a new concept of exposure mapping, which summarizes potentially complicated spillover effects into a fixed dimensional statistic of instrumental variables. We investigate identification conditions for the intention-to-treat effects and the average treatment effects for compliers, while explicitly considering the possibility of misspecification of exposure mapping. Based on our identification results, we develop nonparametric estimation procedures via inverse probability weighting. Their asymptotic properties, including consistency and asymptotic normality, are investigated using an approximate neighborhood interference framework. For an empirical illustration, we apply our method to experimental data on the anti-conflict intervention school program. The proposed methods are readily available with the companion R package latenetwork.

In this article, we study the whole theory of regularized learning for linear-functional data in Banach spaces including representer theorems, pseudo-approximation theorems, and convergence theorems. The input training data are composed of linear functionals in the predual space of the Banach space to represent the discrete local information of multimodel data and multiscale models. The training data and the multi-loss functions are used to compute the empirical risks to approximate the expected risks, and the regularized learning is to minimize the regularized empirical risks over the Banach spaces. The exact solutions of the original problems are approximated globally by the regularized learning even if the original problems are unknown or unformulated. In the convergence theorems, we show the convergence of the approximate solutions to the exact solutions by the weak* topology of the Banach space. Moreover, the theorems of the regularized learning are applied to solve many problems of machine learning such as support vector machines and artificial neural networks.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.

In order to answer natural language questions over knowledge graphs, most processing pipelines involve entity and relation linking. Traditionally, entity linking and relation linking has been performed either as dependent sequential tasks or independent parallel tasks. In this paper, we propose a framework called "EARL", which performs entity linking and relation linking as a joint single task. EARL uses a graph connection based solution to the problem. We model the linking task as an instance of the Generalised Travelling Salesman Problem (GTSP) and use GTSP approximate algorithm solutions. We later develop EARL which uses a pair-wise graph-distance based solution to the problem.The system determines the best semantic connection between all keywords of the question by referring to a knowledge graph. This is achieved by exploiting the "connection density" between entity candidates and relation candidates. The "connection density" based solution performs at par with the approximate GTSP solution.We have empirically evaluated the framework on a dataset with 5000 questions. Our system surpasses state-of-the-art scores for entity linking task by reporting an accuracy of 0.65 to 0.40 from the next best entity linker.

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