The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding near-optimal ESPP, enabled by an unsupervised graph neural network that jointly learns node value estimates and edge-selection probabilities via a surrogate loss function. The loss provides a high probability certificate of finding near-optimal ESPP solutions by simultaneously reducing negative-cost cycles and embedding the desired algorithmic alignment. At inference time, a decoding algorithm transforms the learned edge probabilities into an elementary path. Experiments on graphs of up to 100 nodes show that the proposed method surpasses both unsupervised baselines and classical heuristics, while exhibiting high performance in cross-size and cross-topology generalization on unseen synthetic graphs.

Quantum computing holds significant potential to accelerate machine learning algorithms, especially in solving optimization problems like those encountered in Support Vector Machine (SVM) training. However, current QUBO-based Quantum SVM (QSVM) methods rely solely on binary optimal solutions, limiting their ability to identify fuzzy boundaries in data. Additionally, the limited qubit count in contemporary quantum devices constrains training on larger datasets. In this paper, we propose a probabilistic quantum SVM training framework suitable for Coherent Ising Machines (CIMs). By formulating the SVM training problem as a QUBO model, we leverage CIMs' energy minimization capabilities and introduce a Boltzmann distribution-based probabilistic approach to better approximate optimal SVM solutions, enhancing robustness. To address qubit limitations, we employ batch processing and multi-batch ensemble strategies, enabling small-scale quantum devices to train SVMs on larger datasets and support multi-class classification tasks via a one-vs-one approach. Our method is validated through simulations and real-machine experiments on binary and multi-class datasets. On the banknote binary classification dataset, our CIM-based QSVM, utilizing an energy-based probabilistic approach, achieved up to 20% higher accuracy compared to the original QSVM, while training up to $10^4$ times faster than simulated annealing methods. Compared with classical SVM, our approach either matched or reduced training time. On the IRIS three-class dataset, our improved QSVM outperformed existing QSVM models in all key metrics. As quantum technology advances, increased qubit counts are expected to further enhance QSVM performance relative to classical SVM.

In the end (from the proof of Theorem 3) I conclude that in all cases f_p(x) P(Y 1 X x) . This should be stated explicitly!

Representation learning of Text-Attributed Graphs (TAGs) has garnered significant attention due to its applications in various domains, including recommendation systems and social networks. Despite advancements in TAG learning methodologies, challenges remain in explainability due to the black-box nature of existing TAG representation learning models. This paper presents TAGExplainer, the first method designed to generate natural language explanations for TAG learning. TAGExplainer employs a generative language model that maps input-output pairs to explanations reflecting the model's decision-making process. To address the lack of annotated ground truth explanations in real-world scenarios, we propose first generating pseudo-labels that capture the model's decisions from saliency-based explanations, then the pseudo-label generator is iteratively trained based on three training objectives focusing on faithfulness and brevity via Expert Iteration, to improve the quality of generated pseudo-labels. The high-quality pseudo-labels are finally utilized to train an end-to-end explanation generator model. Extensive experiments are conducted to demonstrate the effectiveness of TAGExplainer in producing faithful and concise natural language explanations.

Representation learning on text-attributed graphs (TAGs) has attracted significant interest due to its wide-ranging real-world applications, particularly through Graph Neural Networks (GNNs). Traditional GNN methods focus on encoding the structural information of graphs, often using shallow text embeddings for node or edge attributes. This limits the model to understand the rich semantic information in the data and its reasoning ability for complex downstream tasks, while also lacking interpretability. With the rise of large language models (LLMs), an increasing number of studies are combining them with GNNs for graph representation learning and downstream tasks. While these approaches effectively leverage the rich semantic information in TAGs datasets, their main drawback is that they are only partially interpretable, which limits their application in critical fields. In this paper, we propose a verbalized graph representation learning (VGRL) method which is fully interpretable. In contrast to traditional graph machine learning models, which are usually optimized within a continuous parameter space, VGRL constrains this parameter space to be text description which ensures complete interpretability throughout the entire process, making it easier for users to understand and trust the decisions of the model. We conduct several studies to empirically evaluate the effectiveness of VGRL and we believe these method can serve as a stepping stone in graph representation learning.

Large Language Models (LLMs) have been widely employed in programming language analysis to enhance human productivity. Yet, their reliability can be compromised by various code distribution shifts, leading to inconsistent outputs. While probabilistic methods are known to mitigate such impact through uncertainty calibration and estimation, their efficacy in the language domain remains underexplored compared to their application in image-based tasks. In this work, we first introduce a large-scale benchmark dataset, incorporating three realistic patterns of code distribution shifts at varying intensities. Then we thoroughly investigate state-of-the-art probabilistic methods applied to CodeLlama using these shifted code snippets. We observe that these methods generally improve the uncertainty awareness of CodeLlama, with increased calibration quality and higher uncertainty estimation~(UE) precision. However, our study further reveals varied performance dynamics across different criteria (e.g., calibration error vs misclassification detection) and trade-off between efficacy and efficiency, highlighting necessary methodological selection tailored to specific contexts.

Practitioners building classifiers often start with a smaller pilot dataset and plan to grow to larger data in the near future. Such projects need a toolkit for extrapolating how much classifier accuracy may improve from a 2x, 10x, or 50x increase in data size. While existing work has focused on finding a single "best-fit" curve using various functional forms like power laws, we argue that modeling and assessing the uncertainty of predictions is critical yet has seen less attention. In this paper, we propose a Gaussian process model to obtain probabilistic extrapolations of accuracy or similar performance metrics as dataset size increases. We evaluate our approach in terms of error, likelihood, and coverage across six datasets. Though we focus on medical tasks and image modalities, our open source approach generalizes to any kind of classifier.

Modern deep models for summarization attains impressive benchmark performance, but they are prone to generating miscalibrated predictive uncertainty. This means that they assign high confidence to low-quality predictions, leading to compromised reliability and trustworthiness in real-world applications. Probabilistic deep learning methods are common solutions to the miscalibration problem. However, their relative effectiveness in complex autoregressive summarization tasks are not well-understood. In this work, we thoroughly investigate different state-of-the-art probabilistic methods' effectiveness in improving the uncertainty quality of the neural summarization models, across three large-scale benchmarks with varying difficulty. We show that the probabilistic methods consistently improve the model's generation and uncertainty quality, leading to improved selective generation performance (i.e., abstaining from low-quality summaries) in practice. We also reveal notable failure patterns of probabilistic methods widely-adopted in NLP community (e.g., Deep Ensemble and Monte Carlo Dropout), cautioning the importance of choosing appropriate method for the data setting.

I describe a framework for interpreting Support Vector Machines (SVMs) as maximum a posteriori (MAP) solutions to inference problems with Gaussian Process priors. This can provide intuitive guidelines for choosing a'good' SVM kernel. It can also assign (by evidence maximization) optimal values to parameters such as the noise level C which cannot be determined unambiguously from properties of the MAP solution alone (such as cross-validation er(cid:173) ror) . I illustrate this using a simple approximate expression for the SVM evidence. Once C has been determined, error bars on SVM predictions can also be obtained. Support Vector Machines (SVMs) have recently been the subject of intense re(cid:173) search activity within the neural networks community; for tutorial introductions and overviews of recent developments see [1, 2, 3].