Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions, derivations, and proofs, in contrast to the experimental sciences which rely on the modelling of data with error-bars. In this Perspective, we categorize the approaches to mathematical discovery as "top-down", "bottom-up" and "meta-mathematics", as inspired by historical examples. We review some of the progress over the last few years, comparing and contrasting both the advances and the short-comings in each approach. We argue that while the theorist is in no way in danger of being replaced by AI in the near future, the hybrid of human expertise and AI algorithms will become an integral part of theoretical discovery.

Cardiovascular disease is one of the chronic diseases that is on the rise. The complications occur when cardiovascular disease is not discovered early and correctly diagnosed at the right time. Various machine learning approaches, including ontology-based Machine Learning techniques, have lately played an essential role in medical science by building an automated system that can identify heart illness. This paper compares and reviews the most prominent machine learning algorithms, as well as ontology-based Machine Learning classification. Random Forest, Logistic regression, Decision Tree, Naive Bayes, k-Nearest Neighbours, Artificial Neural Network, and Support Vector Machine were among the classification methods explored. The dataset used consists of 70000 instances and can be downloaded from the Kaggle website. The findings are assessed using performance measures generated from the confusion matrix, such as F-Measure, Accuracy, Recall, and Precision. The results showed that the ontology outperformed all the machine learning algorithms.

Large foundation models have recently emerged as a prominent focus of interest, attaining superior performance in widespread scenarios. Due to the scarcity of 3D data, many efforts have been made to adapt pre-trained transformers from vision to 3D domains. However, such 2D-to-3D approaches are still limited, due to the potential loss of spatial geometries and high computation cost. More importantly, their frameworks are mainly designed for 2D models, lacking a general any-to-3D paradigm. In this paper, we introduce Any2Point, a parameter-efficient method to empower any-modality large models (vision, language, audio) for 3D understanding. Given a frozen transformer from any source modality, we propose a 3D-to-any (1D or 2D) virtual projection strategy that correlates the input 3D points to the original 1D or 2D positions within the source modality. This mechanism enables us to assign each 3D token with a positional encoding paired with the pre-trained model, which avoids 3D geometry loss caused by the true projection and better motivates the transformer for 3D learning with 1D/2D positional priors. Then, within each transformer block, we insert an any-to-3D guided adapter module for parameter-efficient fine-tuning. The adapter incorporates prior spatial knowledge from the source modality to guide the local feature aggregation of 3D tokens, compelling the semantic adaption of any-modality transformers. We conduct extensive experiments to showcase the effectiveness and efficiency of our method. Code and models are released at https://github.com/Ivan-Tang-3D/Any2Point.

Probabilities of causation (PoC) are valuable concepts for explainable artificial intelligence and practical decision-making. PoC are originally defined for scalar binary variables. In this paper, we extend the concept of PoC to continuous treatment and outcome variables, and further generalize PoC to capture causal effects between multiple treatments and multiple outcomes. In addition, we consider PoC for a sub-population and PoC with multi-hypothetical terms to capture more sophisticated counterfactual information useful for decision-making. We provide a nonparametric identification theorem for each type of PoC we introduce. Finally, we illustrate the application of our results on a real-world dataset about education.

Adapting large language models (LLMs) for specific tasks usually involves fine-tuning through reinforcement learning with human feedback (RLHF) on preference data. While these data often come from diverse labelers' groups (e.g., different demographics, ethnicities, company teams, etc.), traditional RLHF approaches adopt a "one-size-fits-all" approach, i.e., they indiscriminately assume and optimize a single preference model, thus not being robust to unique characteristics and needs of the various groups. To address this limitation, we propose a novel Group Robust Preference Optimization (GRPO) method to align LLMs to individual groups' preferences robustly. Our approach builds upon reward-free direct preference optimization methods, but unlike previous approaches, it seeks a robust policy which maximizes the worst-case group performance. To achieve this, GRPO adaptively and sequentially weights the importance of different groups, prioritizing groups with worse cumulative loss. We theoretically study the feasibility of GRPO and analyze its convergence for the log-linear policy class. By fine-tuning LLMs with GRPO using diverse group-based global opinion data, we significantly improved performance for the worst-performing groups, reduced loss imbalances across groups, and improved probability accuracies compared to non-robust baselines.

In the realm of globalized financial markets, commercial banks are confronted with an escalating magnitude of credit risk, thereby imposing heightened requisites upon the security of bank assets and financial stability. This study harnesses advanced neural network techniques, notably the Backpropagation (BP) neural network, to pioneer a novel model for preempting credit risk in commercial banks. The discourse initially scrutinizes conventional financial risk preemptive models, such as ARMA, ARCH, and Logistic regression models, critically analyzing their real-world applications. Subsequently, the exposition elaborates on the construction process of the BP neural network model, encompassing network architecture design, activation function selection, parameter initialization, and objective function construction. Through comparative analysis, the superiority of neural network models in preempting credit risk in commercial banks is elucidated. The experimental segment selects specific bank data, validating the model's predictive accuracy and practicality. Research findings evince that this model efficaciously enhances the foresight and precision of credit risk management.

Most previous studies conduct factor analysis within the framework of incident-related label prediction, where the developed models can be categorized into short-term and long-term prediction models. The long-term models offer a more strategic approach, enabling more proactive risk management, compared to the short-term ones. Nevertheless, few studies have devoted to rigorously identifying the key factors for the long-term prediction and undertaking comprehensive factor analysis. Hence, this study aims to delve into the key factors for predicting the incident risk levels in the subsequent year given a specific datestamp. The majority of candidate factors potentially contributing to the incident risk are collected from vessels' historical safety performance data spanning up to five years. An improved embedded feature selection method, which integrates Random Forest classifier with a feature filtering process, is proposed to identify key risk-contributing factors from the candidate pool. A dataset with information of 131,652 vessels collected from 2015 to 2023 is utilized for case study. The results demonstrate superior performances of the proposed method in incident prediction and factor interpretability. Comprehensive analysis is conducted upon the key factors, which could help maritime stakeholders formulate management strategies for incident prevention.

Text clustering is an important approach for organising the growing amount of digital content, helping to structure and find hidden patterns in uncategorised data. However, the effectiveness of text clustering heavily relies on the choice of textual embeddings and clustering algorithms. We argue that recent advances in large language models (LLMs) can potentially improve this task. In this research, we investigated how different textual embeddings -- particularly those used in LLMs -- and clustering algorithms affect how text datasets are clustered. A series of experiments were conducted to assess how embeddings influence clustering results, the role played by dimensionality reduction through summarisation, and model size adjustment. Findings reveal that LLM embeddings excel at capturing subtleties in structured language, while BERT leads the lightweight options in performance. In addition, we observe that increasing model dimensionality and employing summarization techniques do not consistently lead to improvements in clustering efficiency, suggesting that these strategies require careful analysis to use in real-life models. These results highlight a complex balance between the need for refined text representation and computational feasibility in text clustering applications. This study extends traditional text clustering frameworks by incorporating embeddings from LLMs, providing a path for improved methodologies, while informing new avenues for future research in various types of textual analysis.

Out-of-distribution (OOD) generalisation is challenging because it involves not only learning from empirical data, but also deciding among various notions of generalisation, e.g., optimising the average-case risk, worst-case risk, or interpolations thereof. While this choice should in principle be made by the model operator like medical doctors, this information might not always be available at training time. The institutional separation between machine learners and model operators leads to arbitrary commitments to specific generalisation strategies by machine learners due to these deployment uncertainties. We introduce the Imprecise Domain Generalisation framework to mitigate this, featuring an imprecise risk optimisation that allows learners to stay imprecise by optimising against a continuous spectrum of generalisation strategies during training, and a model framework that allows operators to specify their generalisation preference at deployment. Supported by both theoretical and empirical evidence, our work showcases the benefits of integrating imprecision into domain generalisation.

In this paper, our goal is to generate synthetic data for heterogeneous (mixed-type) tabular datasets with high machine learning utility (MLu). Given that the MLu performance relies on accurately approximating the conditional distributions, we focus on devising a synthetic data generation method based on conditional distribution estimation. We propose a novel synthetic data generation method, MaCoDE, by redefining the multi-class classification task of Masked Language Modeling (MLM) as histogram-based non-parametric conditional density estimation. Our proposed method enables estimating conditional densities across arbitrary combinations of target and conditional variables. Furthermore, we demonstrate that our proposed method bridges the theoretical gap between distributional learning and MLM. To validate the effectiveness of our proposed model, we conduct synthetic data generation experiments on 10 real-world datasets. Given the analogy between predicting masked input tokens in MLM and missing data imputation, we also evaluate the performance of multiple imputations on incomplete datasets with various missing data mechanisms. Moreover, our proposed model offers the advantage of enabling adjustments to data privacy levels without requiring re-training.