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We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The generalized CRDDME is obtained through two steps. We first derive an unstructured grid jump process approximation for reversible diffusions, enabling the simulation of drift-diffusion processes where the drift arises due to a conservative field that biases particle motion. Leveraging the Edge-Averaged Finite Element method, our approach preserves detailed balance of drift-diffusion fluxes at equilibrium, and preserves an equilibrium Gibbs-Boltzmann distribution for particles undergoing drift-diffusion on the unstructured mesh. We next formulate a spatially-continuous volume reactivity particle-based reaction-drift-diffusion model for reversible reactions of the form $\textrm{A} + \textrm{B} \leftrightarrow \textrm{C}$. A finite volume discretization is used to generate jump process approximations to reaction terms in this model. The discretization is developed to ensure the combined reaction-drift-diffusion jump process approximation is consistent with detailed balance of reaction fluxes holding at equilibrium, along with supporting a discrete version of the continuous equilibrium state. The new CRDDME model represents a continuous-time discrete-space jump process approximation to the underlying volume reactivity model. We demonstrate the convergence and accuracy of the new CRDDME through a number of numerical examples, and illustrate its use on an idealized model for membrane protein receptor dynamics in T cell signaling.

We introduce AdaMoLE, a novel method for fine-tuning large language models (LLMs) through an Adaptive Mixture of Low-Rank Adaptation (LoRA) Experts. Moving beyond conventional methods that employ a static top-k strategy for activating experts, AdaMoLE dynamically adjusts the activation threshold using a dedicated threshold network, adaptively responding to the varying complexities of different tasks. By replacing a single LoRA in a layer with multiple LoRA experts and integrating a gating function with the threshold mechanism, AdaMoLE effectively selects and activates the most appropriate experts based on the input context. Our extensive evaluations across a variety of commonsense reasoning and natural language processing tasks show that AdaMoLE exceeds baseline performance. This enhancement highlights the advantages of AdaMoLE's adaptive selection of LoRA experts, improving model effectiveness without a corresponding increase in the expert count. The experimental validation not only confirms AdaMoLE as a robust approach for enhancing LLMs but also suggests valuable directions for future research in adaptive expert selection mechanisms, potentially broadening the scope for optimizing model performance across diverse language processing tasks.

Code generation aims to synthesize code and fulfill functional requirements based on natural language (NL) specifications, which can greatly improve development efficiency. In the era of large language models (LLMs), large code models (LCMs) have been recently proposed to generate source code. LCMs can generate highly feasible solutions for programming problems described in natural language. Despite the effectiveness, we observe a noticeable multilingual bias in the generation performance of LCMs. Specifically, LCMs demonstrate proficiency in generating solutions when provided with instructions in English, yet may falter when faced with semantically equivalent instructions in other NLs such as Chinese. Moreover, the ability of LCMs to generate code exhibits variety across different programming languages (PLs), such as Python and C++. The observed phenomenon indicates the presence of multi-lingual bias within the generative capabilities of LCMs, which has remained unexplored. In this paper, we aim to investigate the multi-lingual bias that exists in current LCMs. First, we initiate our investigation by constructing the first multi-lingual evaluation benchmark X-HumanEval-X, enabling us to systematically evaluate the extent of multi-lingual bias that exists in current LCMs. In our large-scale experiments on nine popular LCMs, we observe a pronounced multi-lingual bias of LCMs in code generation, including multi-NL and multi-PL bias. Specifically, when using Chinese instructions, the code generation capabilities of LCMs decrease by at least 13% in terms of the Pass@1 metric. Furthermore, LCMs perform variously across different programming languages, e.g., the performance gap between Python and C++ reaches as high as 20.9%. ...

We study the problem of model selection in causal inference, specifically for conditional average treatment effect (CATE) estimation. Unlike machine learning, there is no perfect analogue of cross-validation for model selection as we do not observe the counterfactual potential outcomes. Towards this, a variety of surrogate metrics have been proposed for CATE model selection that use only observed data. However, we do not have a good understanding regarding their effectiveness due to limited comparisons in prior studies. We conduct an extensive empirical analysis to benchmark the surrogate model selection metrics introduced in the literature, as well as the novel ones introduced in this work. We ensure a fair comparison by tuning the hyperparameters associated with these metrics via AutoML, and provide more detailed trends by incorporating realistic datasets via generative modeling. Our analysis suggests novel model selection strategies based on careful hyperparameter selection of CATE estimators and causal ensembling.

This research explores the application of Large Language Models (LLMs) for automating the extraction of requirement-related legal content in the food safety domain and checking legal compliance of regulatory artifacts. With Industry 4.0 revolutionizing the food industry and with the General Data Protection Regulation (GDPR) reshaping privacy policies and data processing agreements, there is a growing gap between regulatory analysis and recent technological advancements. This study aims to bridge this gap by leveraging LLMs, namely BERT and GPT models, to accurately classify legal provisions and automate compliance checks. Our findings demonstrate promising results, indicating LLMs' significant potential to enhance legal compliance and regulatory analysis efficiency, notably by reducing manual workload and improving accuracy within reasonable time and financial constraints.

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three general algorithms that allow to reconstruct a wide spectrum of random fields having a covariance function that depends on a specific metric, called resistance metric, and proposed in recent literature. The algorithms are applied to a synthetic case study consisting of a street network. They prove to be fast and accurate in that they reproduce the target covariance function and provide random fields whose finite-dimensional distributions are approximately Gaussian.

To guide the design of better iterative optimisation heuristics, it is imperative to understand how inherent structural biases within algorithm components affect the performance on a wide variety of search landscapes. This study explores the impact of structural bias in the modular Covariance Matrix Adaptation Evolution Strategy (modCMA), focusing on the roles of various modulars within the algorithm. Through an extensive investigation involving 435,456 configurations of modCMA, we identified key modules that significantly influence structural bias of various classes. Our analysis utilized the Deep-BIAS toolbox for structural bias detection and classification, complemented by SHAP analysis for quantifying module contributions. The performance of these configurations was tested on a sequence of affine-recombined functions, maintaining fixed optimum locations while gradually varying the landscape features. Our results demonstrate an interplay between module-induced structural bias and algorithm performance across different landscape characteristics.

Low-rank matrix approximation play a ubiquitous role in various applications such as image processing, signal processing, and data analysis. Recently, random algorithms of low-rank matrix approximation have gained widespread adoption due to their speed, accuracy, and robustness, particularly in their improved implementation on modern computer architectures. Existing low-rank approximation algorithms often require prior knowledge of the rank of the matrix, which is typically unknown. To address this bottleneck, we propose a low-rank approximation algorithm termed efficient orthogonal decomposition with automatic basis extraction (EOD-ABE) tailored for the scenario where the rank of the matrix is unknown. Notably, we introduce a randomized algorithm to automatically extract the basis that reveals the rank. The efficacy of the proposed algorithms is theoretically and numerically validated, demonstrating superior speed, accuracy, and robustness compared to existing methods. Furthermore, we apply the algorithms to image reconstruction, achieving remarkable results.

EEG-based brainprint recognition with deep learning models has garnered much attention in biometric identification. Yet, studies have indicated vulnerability to adversarial attacks in deep learning models with EEG inputs. In this paper, we introduce a novel adversarial attack method that jointly attacks time-domain and frequency-domain EEG signals by employing wavelet transform. Different from most existing methods which only target time-domain EEG signals, our method not only takes advantage of the time-domain attack's potent adversarial strength but also benefits from the imperceptibility inherent in frequency-domain attack, achieving a better balance between attack performance and imperceptibility. Extensive experiments are conducted in both white- and grey-box scenarios and the results demonstrate that our attack method achieves state-of-the-art attack performance on three datasets and three deep-learning models. In the meanwhile, the perturbations in the signals attacked by our method are barely perceptible to the human visual system.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.