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Scientific idea generation has been extensively studied in creativity theory and computational creativity research, providing valuable frameworks for understanding and implementing creative processes. However, recent work using Large Language Models (LLMs) for research idea generation often overlooks these theoretical foundations. We present a framework that explicitly implements combinatorial creativity theory using LLMs, featuring a generalization-level retrieval system for cross-domain knowledge discovery and a structured combinatorial process for idea generation. The retrieval system maps concepts across different abstraction levels to enable meaningful connections between disparate domains, while the combinatorial process systematically analyzes and recombines components to generate novel solutions. Experiments on the OAG-Bench dataset demonstrate our framework's effectiveness, consistently outperforming baseline approaches in generating ideas that align with real research developments (improving similarity scores by 7\%-10\% across multiple metrics). Our results provide strong evidence that LLMs can effectively realize combinatorial creativity when guided by appropriate theoretical frameworks, contributing both to practical advancement of AI-assisted research and theoretical understanding of machine creativity.

In this study, we address the central issue of statistical inference for Markov jump processes using discrete time observations. The primary problem at hand is to accurately estimate the infinitesimal generator of a Markov jump process, a critical task in various applications. To tackle this problem, we begin by reviewing established methods for generating sample paths from a Markov jump process conditioned to endpoints, known as Markov bridges. Additionally, we introduce a novel algorithm grounded in the concept of time-reversal, which serves as our main contribution. Our proposed method is then employed to estimate the infinitesimal generator of a Markov jump process. To achieve this, we use a combination of Markov Chain Monte Carlo techniques and the Monte Carlo Expectation-Maximization algorithm. The results obtained from our approach demonstrate its effectiveness in providing accurate parameter estimates. To assess the efficacy of our proposed method, we conduct a comprehensive comparative analysis with existing techniques (Bisection, Uniformization, Direct, Rejection, and Modified Rejection), taking into consideration both speed and accuracy. Notably, our method stands out as the fastest among the alternatives while maintaining high levels of precision.

This article methodologically reflects on how social media scholars can effectively engage with speech-based data in their analyses. While contemporary media studies have embraced textual, visual, and relational data, the aural dimension remained comparatively under-explored. Building on the notion of secondary orality and rejection towards purely visual culture, the paper argues that considering voice and speech at scale enriches our understanding of multimodal digital content. The paper presents the TikTok Subtitles Toolkit that offers accessible speech processing readily compatible with existing workflows. In doing so, it opens new avenues for large-scale inquiries that blend quantitative insights with qualitative precision. Two illustrative cases highlight both opportunities and limitations of speech research: while genres like #storytime on TikTok benefit from the exploration of spoken narratives, nonverbal or music-driven content may not yield significant insights using speech data. The article encourages researchers to integrate aural exploration thoughtfully to complement existing methods, rather than replacing them. I conclude that the expansion of our methodological repertoire enables richer interpretations of platformised content, and our capacity to unpack digital cultures as they become increasingly multimodal.

The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. This work is accompanied by open-source implementations of our methods to facilitate reproduction and broader adoption.

We design and investigate a variety of multigrid solvers for high-order local discontinuous Galerkin methods applied to elliptic interface and multiphase Stokes problems. Using the template of a standard multigrid V-cycle, we consider a variety of element-wise block smoothers, including Jacobi, multi-coloured Gauss-Seidel, processor-block Gauss-Seidel, and with special interest, smoothers based on sparse approximate inverse (SAI) methods. In particular, we develop SAI methods that: (i) balance the smoothing of velocity and pressure variables in Stokes problems; and (ii) robustly handles high-contrast viscosity coefficients in multiphase problems. Across a broad range of two- and three-dimensional test cases, including Poisson, elliptic interface, steady-state Stokes, and unsteady Stokes problems, we examine a multitude of multigrid smoother and solver combinations. In every case, there is at least one approach that matches the performance of classical geometric multigrid algorithms, e.g., 4 to 8 iterations to reduce the residual by 10 orders of magnitude. We also discuss their relative merits with regard to simplicity, robustness, computational cost, and parallelisation.

Recent surge in Large Language Model (LLM) availability has opened exciting avenues for research. However, efficiently interacting with these models presents a significant hurdle since LLMs often reside on proprietary or self-hosted API endpoints, each requiring custom code for interaction. Conducting comparative studies between different models can therefore be time-consuming and necessitate significant engineering effort, hindering research efficiency and reproducibility. To address these challenges, we present prompto, an open source Python library which facilitates asynchronous querying of LLM endpoints enabling researchers to interact with multiple LLMs concurrently, while maximising efficiency and utilising individual rate limits. Our library empowers researchers and developers to interact with LLMs more effectively and allowing faster experimentation, data generation and evaluation. prompto is released with an introductory video (//youtu.be/lWN9hXBOLyQ) under MIT License and is available via GitHub (//github.com/alan-turing-institute/prompto).

Adaptive gradient methods have been increasingly adopted by deep learning community due to their fast convergence and reduced sensitivity to hyper-parameters. However, these methods come with limitations, such as increased memory requirements for elements like moving averages and a poorly understood convergence theory. To overcome these challenges, we introduce F-CMA, a Fast-Controlled Mini-batch Algorithm with a random reshuffling method featuring a sufficient decrease condition and a line-search procedure to ensure loss reduction per epoch, along with its deterministic proof of global convergence to a stationary point. To evaluate the F-CMA, we integrate it into conventional training protocols for classification tasks involving both convolutional neural networks and vision transformer models, allowing for a direct comparison with popular optimizers. Computational tests show significant improvements, including a decrease in the overall training time by up to 68%, an increase in per-epoch efficiency by up to 20%, and in model accuracy by up to 5%.

Most of the scientific literature on causal modeling considers the structural framework of Pearl and the potential-outcome framework of Rubin to be formally equivalent, and therefore interchangeably uses do-interventions and the potential-outcome subscript notation to write counterfactual outcomes. In this paper, we agnostically superimpose the two causal models to specify under which mathematical conditions structural counterfactual outcomes and potential outcomes need to, do not need to, can, or cannot be equal (almost surely or law). Our comparison reminds that a structural causal model and a Rubin causal model compatible with the same observations do not have to coincide, and highlights real-world problems where they even cannot correspond. Then, we examine common claims and practices from the causal-inference literature in the light of these results. In doing so, we aim at clarifying the relationship between the two causal frameworks, and the interpretation of their respective counterfactuals.

This study presents a novel representation learning model tailored for dynamic networks, which describes the continuously evolving relationships among individuals within a population. The problem is encapsulated in the dimension reduction topic of functional data analysis. With dynamic networks represented as matrix-valued functions, our objective is to map this functional data into a set of vector-valued functions in a lower-dimensional learning space. This space, defined as a metric functional space, allows for the calculation of norms and inner products. By constructing this learning space, we address (i) attribute learning, (ii) community detection, and (iii) link prediction and recovery of individual nodes in the dynamic network. Our model also accommodates asymmetric low-dimensional representations, enabling the separate study of nodes' regulatory and receiving roles. Crucially, the learning method accounts for the time-dependency of networks, ensuring that representations are continuous over time. The functional learning space we define naturally spans the time frame of the dynamic networks, facilitating both the inference of network links at specific time points and the reconstruction of the entire network structure without direct observation. We validated our approach through simulation studies and real-world applications. In simulations, we compared our methods link prediction performance to existing approaches under various data corruption scenarios. For real-world applications, we examined a dynamic social network replicated across six ant populations, demonstrating that our low-dimensional learning space effectively captures interactions, roles of individual ants, and the social evolution of the network. Our findings align with existing knowledge of ant colony behavior.

This work is motivated by the following problem: Can we identify the disease-causing gene in a patient affected by a monogenic disorder? This problem is an instance of root cause discovery. In particular, we aim to identify the intervened variable in one interventional sample using a set of observational samples as reference. We consider a linear structural equation model where the causal ordering is unknown. We begin by examining a simple method that uses squared z-scores and characterize the conditions under which this method succeeds and fails, showing that it generally cannot identify the root cause. We then prove, without additional assumptions, that the root cause is identifiable even if the causal ordering is not. Two key ingredients of this identifiability result are the use of permutations and the Cholesky decomposition, which allow us to exploit an invariant property across different permutations to discover the root cause. Furthermore, we characterize permutations that yield the correct root cause and, based on this, propose a valid method for root cause discovery. We also adapt this approach to high-dimensional settings. Finally, we evaluate the performance of our methods through simulations and apply the high-dimensional method to discover disease-causing genes in the gene expression dataset that motivates this work.