The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called \textit{cold start} problem by using source data to aid in the optimization of a target problem. We present a method that leverages an ensemble of surrogate models using transfer learning and integrates it in a constrained Bayesian optimization framework. We identify challenges particular to aircraft design optimization related to heterogeneous design variables and constraints. We propose the use of a partial-least-squares dimension reduction algorithm to address design space heterogeneity, and a \textit{meta} data surrogate selection method to address constraint heterogeneity. Numerical benchmark problems and an aircraft conceptual design optimization problem are used to demonstrate the proposed methods. Results show significant improvement in convergence in early optimization iterations compared to standard Bayesian optimization, with improved prediction accuracy for both objective and constraint surrogate models.

Reasoning based on Large Language Models (LLMs) has garnered increasing attention due to outstanding performance of these models in mathematical and complex logical tasks. Beginning with the Chain-of-Thought (CoT) prompting technique, numerous reasoning methods have emerged that decompose problems into smaller, sequential steps (or thoughts). However, existing reasoning models focus on conventional problem-solving and do not necessarily generate creative solutions by ``creative reasoning''. In domains where the solution space is expansive and conventional solutions are suboptimal, such as drug discovery or business strategization, creative reasoning to discover innovative solutions is crucial. To address this gap, first we introduce a computational framework for creative reasoning inspired by established cognitive science principles. With this framework, we propose three core creative reasoning paradigms, namely, \textit{combinational}, \textit{exploratory}, and \textit{transformative} reasoning, where each offers specific directions for systematic exploration of the universe of thoughts to generate creative solutions. Next, to materialize this framework using LLMs, we introduce the \textit{Universe of Thoughts} (or \textit{UoT}, for short), a novel set of methods to implement the aforementioned three creative processes. Finally, we introduce three novel tasks that necessitate creative problem-solving, along with an evaluation benchmark to assess creativity from three orthogonal perspectives: feasibility as constraint, and utility and novelty as metrics. With a comparative analysis against the state-of-the-art (SOTA) reasoning techniques as well as representative commercial models with reasoning capability, we show that UoT demonstrates superior performance in creative reasoning.

Surrogate regret bounds, also called excess risk bounds, are a common tool to prove generalization rates for surrogate risk minimization.

This study investigates whether large language models, specifically GPT4, can match human capabilities in analogical reasoning within strategic decision making contexts. Using a novel experimental design involving source to target matching, we find that GPT4 achieves high recall by retrieving all plausible analogies but suffers from low precision, frequently applying incorrect analogies based on superficial similarities. In contrast, human participants exhibit high precision but low recall, selecting fewer analogies yet with stronger causal alignment. These findings advance theory by identifying matching, the evaluative phase of analogical reasoning, as a distinct step that requires accurate causal mapping beyond simple retrieval. While current LLMs are proficient in generating candidate analogies, humans maintain a comparative advantage in recognizing deep structural similarities across domains. Error analysis reveals that AI errors arise from surface level matching, whereas human errors stem from misinterpretations of causal structure. Taken together, the results suggest a productive division of labor in AI assisted organizational decision making where LLMs may serve as broad analogy generators, while humans act as critical evaluators, applying the most contextually appropriate analogies to strategic problems.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose \textbf{MetaLadder}, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (\textbf{10.3\%} accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

Knowledge tracing (KT) in programming education presents unique challenges due to the complexity of coding tasks and the diverse methods students use to solve problems. Although students' questions often contain valuable signals about their understanding and misconceptions, traditional KT models often neglect to incorporate these questions as inputs to address these challenges. This paper introduces SQKT (Students' Question-based Knowledge Tracing), a knowledge tracing model that leverages students' questions and automatically extracted skill information to enhance the accuracy of predicting students' performance on subsequent problems in programming education. Our method creates semantically rich embeddings that capture not only the surface-level content of the questions but also the student's mastery level and conceptual understanding. Experimental results demonstrate SQKT's superior performance in predicting student completion across various Python programming courses of differing difficulty levels. In in-domain experiments, SQKT achieved a 33.1\% absolute improvement in AUC compared to baseline models. The model also exhibited robust generalization capabilities in cross-domain settings, effectively addressing data scarcity issues in advanced programming courses. SQKT can be used to tailor educational content to individual learning needs and design adaptive learning systems in computer science education.

We define a digital twin (DT) of a physical system governed by partial differential equations (PDEs) as a model for real-time simulations and control of the system behavior under changing conditions. We construct DTs using the Karhunen-Lo\`{e}ve Neural Network (KL-NN) surrogate model and transfer learning (TL). The surrogate model allows fast inference and differentiability with respect to control parameters for control and optimization. TL is used to retrain the model for new conditions with minimal additional data. We employ the moment equations to analyze TL and identify parameters that can be transferred to new conditions. The proposed analysis also guides the control variable selection in DT to facilitate efficient TL. For linear PDE problems, the non-transferable parameters in the KL-NN surrogate model can be exactly estimated from a single solution of the PDE corresponding to the mean values of the control variables under new target conditions. Retraining an ML model with a single solution sample is known as one-shot learning, and our analysis shows that the one-shot TL is exact for linear PDEs. For nonlinear PDE problems, transferring of any parameters introduces errors. For a nonlinear diffusion PDE model, we find that for a relatively small range of control variables, some surrogate model parameters can be transferred without introducing a significant error, some can be approximately estimated from the mean-field equation, and the rest can be found using a linear residual least square problem or an ordinary linear least square problem if a small labeled dataset for new conditions is available. The former approach results in a one-shot TL while the latter approach is an example of a few-shot TL. Both methods are approximate for the nonlinear PDEs.

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still scaling limitations. In parallel, Graph Neural Networks (GNN) have been recently adapted to solve combinatorial problems, showing competitive results and potentially high scalability due to their distributed nature. We propose a merging approach that aims at retaining both the accuracy exhibited by AMs and the representational flexibility and scalability of GNNs. Our model considers a compression step, followed by a supervised interaction where partial solutions obtained from the AM are used to guide local GNNs from where node feature representations are obtained and combined to initialize an additional GNN-based solver that handles the original graph's target problem. Intuitively, the AM can solve the combinatorial problem indirectly by infusing its knowledge into the GNN. Experiments on canonical optimization problems show that the idea is feasible, effectively allowing the AM to solve size problems beyond its original limits.

Automated design of metaheuristic algorithms offers an attractive avenue to reduce human effort and gain enhanced performance beyond human intuition. Current automated methods design algorithms within a fixed structure and operate from scratch. This poses a clear gap towards fully discovering potentials over the metaheuristic family and fertilizing from prior design experience. To bridge the gap, this paper proposes an autoregressive learning-based designer for automated design of metaheuristic algorithms. Our designer formulates metaheuristic algorithm design as a sequence generation task, and harnesses an autoregressive generative network to handle the task. This offers two advances. First, through autoregressive inference, the designer generates algorithms with diverse lengths and structures, enabling to fully discover potentials over the metaheuristic family. Second, prior design knowledge learned and accumulated in neurons of the designer can be retrieved for designing algorithms for future problems, paving the way to continual design of algorithms for open-ended problem-solving. Extensive experiments on numeral benchmarks and real-world problems reveal that the proposed designer generates algorithms that outperform all human-created baselines on 24 out of 25 test problems. The generated algorithms display various structures and behaviors, reasonably fitting for different problem-solving contexts. Code will be released after paper publication.