The 2-page upward book embedding (2UBE) problem, recently proven NP-complete, is a fundamental problem in graph theory with various applications. Given its computational intractability, SAT-based approaches offer a promising direction for efficiently determining embeddability. In this paper, we present two practical SAT encodings, SAT-1 (largely adopted from the literature) and SAT-2 (specifically tailored for 2UBE). We also introduce a Constraint Programming (CP) formulation as an alternative approach. Our empirical evaluation on benchmark datasets demonstrates that SAT solvers significantly outperform CP in solving 2UBE instances. Additionally, we analyze the scalability of these methods on large grid graphs, revealing that SAT-2 achieves up to a 40% speedup over SAT-1. Using SAT-2, we discovered a phase transition in 2UBE, which occurs when the edge-to-node ratio (m/n) ≈ 1.5. In general, we have established SAT-based approaches as both a practical and scalable solution for book embedding problems and a tool for evaluating their structural properties.

Image segmentation is a fundamental task in computer vision. Precise evaluation metrics are essential for assessing the performance of segmentation models, particularly in medical imaging. Intersection over Union (IoU) is commonly used to evaluate the performance of segmentation models. However, it has been reported to be biased based on object size, placing less emphasis on boundary regions. To address this issue, alternative IoU-based measures have been proposed, which are either asymmetric or completely ignore the inner regions of objects. In this study, we propose a Balanced Boundary IoU (BBIoU) to overcome the limitations of these metrics and provide a more accurate assessment of both the boundary and inner region of objects. BBIoU is a symmetric function that considers both the inner regions and boundaries of objects, providing a comprehensive measure for evaluating segmentation models. We evaluated BBIoU across six different medical imaging datasets for binary segmentation, covering a wide range of object sizes and shapes. Additionally, extensive analysis of synthetic and real predictions demonstrated that BBIoU is robust and consistent while avoiding biases such as erroneous penalization and sensitivity to object size. This study presents a comprehensive comparative analysis of IoU, alternative IoU-based metrics, and BBIoU, demonstrating the suitability of BBIoU for evaluating segmentation quality across diverse image segmentation tasks.

Games present sophisticated challenges and require intricate reasoning. Quantified Boolean Formulas enjoy a natural game-theoretic semantics and are therefore a promising representation for games. However, game solving with current QBF solvers is challenging. In this paper, we use QBF solvers’ reasoning capabilities to search for a specific kind of winning strategy, restricting the allowed moves. While this could, in principle, prevent the discovery of a winning strategy, when there are only more complex ones, we experimentally show that our method does indeed find a winning strategy when one is found by the current best QBF encoding. Furthermore, we also show that this reduction in available moves allows to reduce solving time across QBF solvers and preprocessors.

Large Language Models (LLMs) have demonstrated exceptional abilities across a broad range of language-related tasks, including generating solutions to complex reasoning problems. An effective technique to enhance LLM performance is in-context learning, which encourages a step-by-step reasoning process by including explanatory examples to guide the model's responses. However, selecting appropriate exemplars for the model poses a challenge, as each dataset demands a distinct set of exemplars to enable the LLM to learn effectively and perform well on the test set. Current studies often rely on uncertainty- or diversity-based selection strategies to select exemplars for annotation and to improve model learning. However, these studies typically employ a non-adaptive approach, selecting a set of exemplars all at once. We argue that this non-adaptive strategy may result in a set of exemplars with high redundancy in terms of the knowledge covered, ultimately reducing their overall informativeness. To address this limitation, we propose Adaptive-Prompt, a novel method that adaptively selects exemplars by leveraging model feedback from previously chosen exemplars. Experimental results show that Adaptive-Prompt significantly enhances LLM performance across a variety of reasoning tasks.

Meta-learning is originally developed for supervised learning to enable models to generalize across tasks by leveraging prior experience. However, its potential in the unsupervised learning domain remains largely underexplored. To demonstrate the feasibility of meta-learning in unsupervised settings, we apply it to Non-negative Matrix Factorization (NMF), a widely used technique for decomposing non-negative data matrices into interpretable, lower-dimensional representations. While NMF has found applications in topic modeling, image processing, bioinformatics, and recommendation systems, it faces persistent challenges such as rank selection, optimization stability, uniqueness, and computational efficiency. Traditional approaches primarily focus on improving initialization strategies to enhance convergence and generalization. However, these methods often fail to exploit structural similarities across tasks. In this paper, we introduce a meta-learning paradigm for NMF that systematically learns optimal factorization parameters from small-scale tasks and transfers this knowledge to improve learning on larger tasks. By discovering fine structures in small tasks and leveraging them to guide factorization on more complex datasets, our approach directs the search process toward a more optimal and structured search space, reducing the risk of suboptimal solutions and improving model robustness. This meta-unsupervised learning framework enhances NMF's ability to uncover meaningful patterns while maintaining adaptability across different domains. Additionally, we evaluate the model under noisy conditions and demonstrate its robustness by filtering noise over learning epochs, further enhancing its interpretability and stability. By integrating meta-learning principles, our method not only improves optimization stability but also enhances interpretability and generalizability, bridging the gap between NMF-based models and advanced autonomous (unsupervised) learning strategies.

Arithmetic circuits (ACs) have been empirically shown to be the state-of-the-art method for exact inference in discrete Bayesian networks (BNs). Although ACs are a compact and efficient computational model, they do not perform any optimization steps for a given query. Here, we introduce AC inference that exploits barren variables, a standard optimization step when conducting probabilistic inference directly within the BN itself. The main idea is to compute an AC node's value only if that node is relevant to a given query. Our experimental results on ACs compiled from well-known and randomly generated BNs evaluate the effectiveness of barren variable exploitation across varying elimination orders, query sizes, and query types. While the results are somewhat mixed, this work is the first to demonstrate AC inference without requiring probability propagation over the entire circuit and paves the way for future improvements.

Predictive coding networks (PCnets) provide a biologically inspired framework for classification and generative tasks. However, their generative performance is limited when handling multi-modal class distributions, as the standard weight decay method struggles to differentiate between multiple modes within a class effectively. To address this issue, we propose two extensions: (1) integrating an auto-encoder (AE) to enhance latent representations and (2) employing a predictive coding Hopfield network (PCHN) to capture attractor dynamics. We evaluate these models on synthetic multi-Gaussian datasets and a subset of MNIST, revealing that the AE-enhanced PCnet can generate samples representing distinct clusters. Meanwhile, the PCHN variant independently discovers and maintains cluster structures without explicit latent supervision. Our findings highlight the potential of predictive coding as a sturdy framework for learning multi-modal data distributions in a biologically plausible manner.

This study investigates how LLMs, specifically GPT-3.5 and GPT-4, can develop tailored questions for Grade 9 math, aligning with active learning principles. By utilizing an iterative method, these models adjust questions based on difficulty and content, responding to feedback from a simulated 'student' model. A novel aspect of the research involved using GPT-4 as a 'teacher' to create complex questions, with GPT-3.5 as the 'student' responding to these challenges. This setup mirrors active learning, promoting deeper engagement. The findings demonstrate GPT-4's superior ability to generate precise, challenging questions and notable improvements in GPT-3.5's ability to handle more complex problems after receiving instruction from GPT-4. These results underscore the potential of LLMs to mimic and enhance active learning scenarios, offering a promising path for AI in customized education. This research contributes to understanding how AI can support personalized learning experiences, highlighting the need for further exploration in various educational contexts.

Microplastic particle ingestion or inhalation by humans is a problem of growing concern. Unfortunately, current research methods that use machine learning to understand their potential harms are obstructed by a lack of available data. Deep learning techniques in particular are challenged by such domains where only small or imbalanced data sets are available. Overcoming this challenge often involves oversampling underrepresented classes or augmenting the existing data to improve model performance. This paper proposes GANsemble: a two-module framework connecting data augmentation with conditional generative adversarial networks (cGANs) to generate class-conditioned synthetic data. First, the data chooser module automates augmentation strategy selection by searching for the best data augmentation strategy. Next, the cGAN module uses this strategy to train a cGAN for generating enhanced synthetic data. We experiment with the GANsemble framework on a small and imbalanced microplastics data set. A Microplastic-cGAN (MPcGAN) algorithm is introduced, and baselines for synthetic microplastics (SYMP) data are established in terms of Fréchet Inception Distance (FID) and Inception Scores (IS). We also provide a synthetic microplastics filter (SYMP-Filter) algorithm to increase the quality of generated SYMP. Additionally, we show the best amount of oversampling with augmentation to fix class imbalance in small microplastics data sets. To our knowledge, this study is the first application of generative AI to synthetically create microplastics data.

At first glance, it would seem that modern LLMs can assiduously parrot back output based on data that has previously been given to them as inputs. However they are still a long way away from coherently generating long form narratives that match defined parameters, unless they are first given a certain amount of guidance. By combining Automated Planning with Natural Language Text Generation by LLMs we can create logical, believable, and coherent stories that can be used in a wide variety of domains, for a large range of applications.