The pseudo-code of plugging our method into the vanilla BO is summarised in Algorithm 1. Therefore, our method is applicable to any other variants of BO in a plug-in manner. In this section, we present the proofs associated with the theoretical assertions from Section 2. To Lemma 1. Assume the GP employs a stationary kernel Lemma 2. Given Lemma 1, determining Proposition 2. Leveraging Lemma 2, suppose Lemma 3. As per Srinivas et al., the optimization process in BO can be conceptualized as a sampling Pr null |f ( x) µ(x) | ωσ ( x) null > δ, (24) where δ > 0 signifies the confidence level adhered to by the UCB. This lemma is directly from Srinivas et al. . The proof can be found therein. Theorem 1. Leveraging Corollary 1, when employing the termination method proposed in this paper, As discussed in Remark 2 of Section 2.2 in the main manuscript, we suggest initializing L-BFGS Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's

The use of LLM-based applications as a means to accelerate and/or substitute human labor in the creation of language resources and dataset is a reality. Nonetheless, despite the potential of such tools for linguistic research, comprehensive evaluation of their performance and impact on the creation of annotated datasets, especially under a perspectivized approach to NLP, is still missing. This paper contributes to reduction of this gap by reporting on an extensive evaluation of the (semi-)automatization of FrameNet-like semantic annotation by the use of an LLM-based semantic role labeler. The methodology employed compares annotation time, coverage and diversity in three experimental settings: manual, automatic and semi-automatic annotation. Results show that the hybrid, semi-automatic annotation setting leads to increased frame diversity and similar annotation coverage, when compared to the human-only setting, while the automatic setting performs considerably worse in all metrics, except for annotation time.

This study presents an integrated approach to understanding epidemic dynamics through a stochastic spatio-temporal simulation model on a multiplex network, blending physical and informational layers. The physical layer maps the geographic movement of individuals, while the information layer tracks the spread of knowledge and health behavior via social interactions. We explore the interplay between physical mobility, information flow, and epidemic outcomes by simulating disease spread within this dual-structured network. Our model employs stochastic elements to mirror human behavior, mobility, and information dissemination uncertainties. Through simulations, we assess the impact of network structure, mobility patterns, and information spread speed on epidemic dynamics. The findings highlight the crucial role of effective communication in curbing disease transmission, even in highly mobile societies. Additionally, our agent-based simulation allows for real-time scenario analysis through a user interface, offering insights into leveraging physical and informational networks for epidemic control. This research sheds light on designing strategic interventions in complex social systems to manage disease outbreaks.

What should a function that extrapolates beyond known input/output examples look like? This is a tricky question to answer in general, as any function matching the outputs on those examples can in principle be a correct extrapolant. We argue that a "good" extrapolant should follow certain kinds of rules, and here we study a particularly appealing criterion for rule-following in list functions: that the function should behave predictably even when certain elements are removed. In functional programming, a standard way to express such removal operations is by using a filter function. Accordingly, our paper introduces a new semantic class of functions -- the filter equivariant functions. We show that this class contains interesting examples, prove some basic theorems about it, and relate it to the well-known class of map equivariant functions. We also present a geometric account of filter equivariants, showing how they correspond naturally to certain simplicial structures. Our highlight result is the amalgamation algorithm, which constructs any filter-equivariant function's output by first studying how it behaves on sublists of the input, in a way that extrapolates perfectly.

Accurate characterization of the equilibrium distributions of complex molecular systems and their dependence on environmental factors such as temperature is essential for understanding thermodynamic properties and transition mechanisms. Projecting these distributions onto meaningful low-dimensional representations enables interpretability and downstream analysis. Recent advances in generative AI, particularly flow models such as Normalizing Flows (NFs), have shown promise in modeling such distributions, but their scope is limited without tailored representation learning. In this work, we introduce Latent Thermodynamic Flows (LaTF), an end-to-end framework that tightly integrates representation learning and generative modeling. LaTF unifies the State Predictive Information Bottleneck (SPIB) with NFs to simultaneously learn low-dimensional latent representations, referred to as Collective Variables (CVs), classify metastable states, and generate equilibrium distributions across temperatures beyond the training data. The two components of representation learning and generative modeling are optimized jointly, ensuring that the learned latent features capture the system's slow, important degrees of freedom while the generative model accurately reproduces the system's equilibrium behavior. We demonstrate LaTF's effectiveness across diverse systems, including a model potential, the Chignolin protein, and cluster of Lennard Jones particles, with thorough evaluations and benchmarking using multiple metrics and extensive simulations. Finally, we apply LaTF to a RNA tetraloop system, where despite using simulation data from only two temperatures, LaTF reconstructs the temperature-dependent structural ensemble and melting behavior, consistent with experimental and prior extensive computational results.

In many-task optimization scenarios, surrogate models are valuable for mitigating the computational burden of repeated fitness evaluations across tasks. This study proposes a novel meta-surrogate framework to assist many-task optimization, by leveraging the knowledge transfer strengths and emergent capabilities of large language models (LLMs). We formulate a unified framework for many-task fitness prediction, by defining a universal model with metadata to fit a group of problems. Fitness prediction is performed on metadata and decision variables, enabling efficient knowledge sharing across tasks and adaptability to new tasks. The LLM-based meta-surrogate treats fitness prediction as conditional probability estimation, employing a unified token sequence representation for task metadata, inputs, and outputs. This approach facilitates efficient inter-task knowledge sharing through shared token embeddings and captures complex task dependencies via multi-task model training. Experimental results demonstrate the model's emergent generalization ability, including zero-shot performance on problems with unseen dimensions. When integrated into evolutionary transfer optimization (ETO), our framework supports dual-level knowledge transfer -- at both the surrogate and individual levels -- enhancing optimization efficiency and robustness. This work establishes a novel foundation for applying LLMs in surrogate modeling, offering a versatile solution for many-task optimization.

Despite the remarkable generative capabilities of language models in producing naturalistic language, their effectiveness on explicit manipulation and generation of linguistic structures remain understudied. In this paper, we investigate the task of generating new sentences preserving a given semantic structure, following the FrameNet formalism. We propose a framework to produce novel frame-semantically annotated sentences following an overgenerate-and-filter approach. Our results show that conditioning on rich, explicit semantic information tends to produce generations with high human acceptance, under both prompting and finetuning. Our generated frame-semantic structured annotations are effective at training data augmentation for frame-semantic role labeling in low-resource settings; however, we do not see benefits under higher resource settings. Our study concludes that while generating high-quality, semantically rich data might be within reach, the downstream utility of such generations remains to be seen, highlighting the outstanding challenges with automating linguistic annotation tasks.

Machine learning potentials (MLPs) offer the potential to accurately model the energy and free energy landscapes of molecules with the precision of quantum mechanics and an efficiency similar to classical simulations. This research focuses on using equivariant graph neural networks MLPs due to their proven effectiveness in modeling equilibrium molecular trajectories. A key issue addressed is the capability of MLPs to accurately predict free energies and transition states by considering both the energy and the diversity of molecular configurations. We examined how the distribution of collective variables (CVs) in the training data affects MLP accuracy in determining the free energy surface (FES) of systems, using Metadynamics simulations for butane and alanine dipeptide (ADP). The study involved training forty-three MLPs, half based on classical molecular dynamics data and the rest on ab initio computed energies. The MLPs were trained using different distributions that aim to replicate hypothetical scenarios of sampled CVs obtained if the underlying FES of the system was unknown. Findings for butane revealed that training data coverage of key FES regions ensures model accuracy regardless of CV distribution. However, missing significant FES regions led to correct potential energy predictions but failed free energy reconstruction. For ADP, models trained on classical dynamics data were notably less accurate, while ab initio-based MLPs predicted potential energy well but faltered on free energy predictions. These results emphasize the challenge of assembling an all-encompassing training set for accurate FES prediction and highlight the importance of understanding the FES in preparing training data. The study points out the limitations of MLPs in free energy calculations, stressing the need for comprehensive data that encompasses the system's full FES for effective model training.

Cooperative co-evolution (CC) algorithms, based on the divide-and-conquer strategy, have emerged as the predominant approach to solving large-scale global optimization (LSGO) problems. The efficiency and accuracy of the grouping stage significantly impact the performance of the optimization process. While the general separability grouping (GSG) method has overcome the limitation of previous differential grouping (DG) methods by enabling the decomposition of non-additively separable functions, it suffers from high computational complexity. To address this challenge, this article proposes a composite separability grouping (CSG) method, seamlessly integrating DG and GSG into a problem decomposition framework to utilize the strengths of both approaches. CSG introduces a step-by-step decomposition framework that accurately decomposes various problem types using fewer computational resources. By sequentially identifying additively, multiplicatively and generally separable variables, CSG progressively groups non-separable variables by recursively considering the interactions between each non-separable variable and the formed non-separable groups. Furthermore, to enhance the efficiency and accuracy of CSG, we introduce two innovative methods: a multiplicatively separable variable detection method and a non-separable variable grouping method. These two methods are designed to effectively detect multiplicatively separable variables and efficiently group non-separable variables, respectively. Extensive experimental results demonstrate that CSG achieves more accurate variable grouping with lower computational complexity compared to GSG and state-of-the-art DG series designs.

This report presents the test results Python library BaumEvA, which implements evolutionary algorithms for optimizing various types of problems, including computer vision tasks accompanied by the search for optimal model architectures. Testing was carried out to evaluate the effectiveness and reliability of the pro-posed methods, as well as to determine their applicability in various fields. Dur-ing testing, various test functions and parameters of evolutionary algorithms were used, which made it possible to evaluate their performance in a wide range of conditions. Test results showed that the library provides effective and reliable methods for solving optimization problems. However, some limitations were identified related to computational resources and execution time of algorithms on problems with large dimensions. The report includes a detailed description of the tests performed, the results obtained and conclusions about the applicability of the genetic algorithm in various tasks. Recommendations for choosing algorithm pa-rameters and using the library to achieve the best results are also provided. The report may be useful to developers involved in the optimization of complex com-puting systems, as well as to researchers studying the possibilities of using evo-lutionary algorithms in various fields of science and technology.