While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and multiclass classification problems. For Chipclass, a hyperparameter-less and optimization-less GG-based binary classifier, we discuss how activation functions and support edge (SE)-centered neurons affect the classification, proposing smoother functions and structural SV (SSV)-centered neurons to achieve margins with low probabilities and smoother classification contours. We extend the neural network architecture, which can be trained with backpropagation with a softmax function and a cross-entropy loss, or by solving a system of linear equations. A new subgraph-/distance-based membership function for graph regularization is also proposed, along with a new GG recomputation algorithm that is less computationally expensive than the standard approach. Experimental results with the Friedman test show that our method was better than previous GG-based classifiers and statistically equivalent to tree-based models.

This paper proposes a novel neuro-symbolic approach for sensor signal-based knowledge discovery, focusing on identifying latent subclasses in time series classification tasks. The approach leverages gradient-based saliency maps derived from trained neural networks to guide the discovery process. Multiclass time series classification problems are transformed into binary classification problems through label subsumption, and classifiers are trained for each of these to yield saliency maps. The input signals, grouped by predicted class, are clustered under three distinct configurations. The centroids of the final set of clusters are provided as input to an LLM for symbolic approximation and fuzzy knowledge graph matching to discover the underlying subclasses of the original multiclass problem. Experimental results on well-established time series classification datasets demonstrate the effectiveness of our saliency map-driven method for knowledge discovery, outperforming signal-only baselines in both clustering and subclass identification.

Section A provides more details about our algorithms. In particular, Section A.1 describes the Section A.2 describes the REx implementation of invariance in Section A.3 discusses the two implementation of the self-training used in our experiments: Section B gives the preliminaries of group theory. Section C gives the full proof of our theorem. Section E shows more comparisons and standard deviations on WILDS 2.0 benchmark [ The setup instructions and commands used in our experiments are included in the README.md Self-training loss α Self-training loss weight β Invariance loss weight Symbol in Theory G Group of semantics X Feature space H Subgroup of G that transforms environmental feature e g x Group action Table A1: List of abbreviations and symbols used in the paper. 1 A Additional Details on Algorithm REx circumvents the challenging bi-level optimization from line 2 of Eq. (2) by adding the following Please refer to [8] for a theoretical explanation.

We present a theoretical analysis of F -measures for binary, multiclass and mul-tilabel classification. These performance measures are non-linear, but in many scenarios they are pseudo-linear functions of the per-class false negative/false positive rate. Based on this observation, we present a general reduction of F - measure maximization to cost-sensitive classification with unknown costs. We then propose an algorithm with provable guarantees to obtain an approximately optimal classifier for the F -measure by solving a series of cost-sensitive classification problems. The strength of our analysis is to be valid on any dataset and any class of classifiers, extending the existing theoretical results on F -measures, which are asymptotic in nature. We present numerical experiments to illustrate the relative importance of cost asymmetry and thresholding when learning linear classifiers on various F -measure optimization tasks.

A free-form shape is generated in the following steps: 1) Decide what length of action programs a shape has.

Scientific information expresses human understanding of nature. This knowledge is largely disseminated in different forms of text, including scientific papers, news articles, and discourse among people on social media. While important for accelerating our pursuit of knowledge, not all scientific text is faithful to the underlying science. As the volume of this text has burgeoned online in recent years, it has become a problem of societal importance to be able to identify the faithfulness of a given piece of scientific text automatically. This thesis is concerned with the cultivation of datasets, methods, and tools for machine understanding of scientific language, in order to analyze and understand science communication at scale. To arrive at this, I present several contributions in three areas of natural language processing and machine learning: automatic fact checking, learning with limited data, and scientific text processing. These contributions include new methods and resources for identifying check-worthy claims, adversarial claim generation, multi-source domain adaptation, learning from crowd-sourced labels, cite-worthiness detection, zero-shot scientific fact checking, detecting exaggerated scientific claims, and modeling degrees of information change in science communication. Critically, I demonstrate how the research outputs of this thesis are useful for effectively learning from limited amounts of scientific text in order to identify misinformative scientific statements and generate new insights into the science communication process