This paper proposes a neural architecture search space using ResNet as a framework, with search objectives including parameters for convolution, pooling, fully connected layers, and connectivity of the residual network. In addition to recognition accuracy, this paper uses the loss value on the validation set as a secondary objective for optimization. The experimental results demonstrate that the search space of this paper together with the optimisation approach can find competitive network architectures on the MNIST, Fashion-MNIST and CIFAR100 datasets.

Database Management Systems (DBMSs) are fundamental for managing large-scale and heterogeneous data, and their performance is critically influenced by configuration parameters. Effective tuning of these parameters is essential for adapting to diverse workloads and maximizing throughput while minimizing latency. Recent research has focused on automated configuration optimization using machine learning; however, existing approaches still exhibit several key limitations. Most tuning frameworks disregard the dependencies among parameters, assuming that each operates independently. This simplification prevents optimizers from leveraging relational effects across parameters, limiting their capacity to capture performancesensitive interactions. Moreover, to reduce the complexity of the high-dimensional search space, prior work often selects only the top few parameters for optimization, overlooking others that contribute meaningfully to performance. Bayesian Optimization (BO), the most common method for automatic tuning, is also constrained by its reliance on surrogate models, which can lead to unstable predictions and inefficient exploration. To overcome these limitations, we propose RelTune, a novel framework that represents parameter dependencies as a Relational Graph and learns GNN-based latent embeddings that encode performancerelevant semantics. RelTune further introduces Hybrid-Score-Guided Bayesian Optimization (HBO), which combines surrogate predictions with an Affinity Score measuring proximity to previously high-performing configurations. Experimental results on multiple DBMSs and workloads demonstrate that RelTune achieves faster convergence and higher optimization efficiency than conventional BO-based methods, achieving state-of-the-art performance across all evaluated scenarios.

This thesis investigates how foundation models can be systematically leveraged to enhance robotic capabilities, enabling more effective localization, interaction, and manipulation in unstructured environments. The work is structured around four core lines of inquiry, each addressing a fundamental challenge in robotics while collectively contributing to a cohesive framework for semantics-aware robotic intelligence.

We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees and computational efficiency, its theoretical foundations for hypothesis testing remain limited. We address this gap by proposing a permutation-based SW test and analyzing its performance. The test inherits finite-sample Type I error control from the permutation principle. Moreover, we establish non-asymptotic power bounds and show that the procedure achieves the minimax separation rate $n^{-1/2}$ over multinomial and bounded-support alternatives, matching the optimal guarantees of kernel-based tests while building on the geometric foundations of Wasserstein distances. Our analysis further quantifies the trade-off between the number of projections and statistical power. Finally, numerical experiments demonstrate that the test combines finite-sample validity with competitive power and scalability, and -- unlike kernel-based tests, which require careful kernel tuning -- it performs consistently well across all scenarios we consider.

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack research on the effect of constraint tightness on the performance of NCO methods. This paper takes the capacity-constrained vehicle routing problem (CVRP) as an example to empirically analyze the NCO performance under different tightness degrees of the capacity constraint. Our analysis reveals that existing NCO methods overfit the capacity constraint, and they can only perform satisfactorily on a small range of the constraint values but poorly on other values. To tackle this drawback of existing NCO methods, we develop an efficient training scheme that explicitly considers varying degrees of constraint tightness and proposes a multi-expert module to learn a generally adaptable solving strategy. Experimental results show that the proposed method can effectively overcome the overfitting issue, demonstrating superior performances on the CVRP and CVRP with time windows (CVRPTW) with various constraint tightness degrees.

Neural Combinatorial Optimisation (NCO) is a promising learning-based approach for solving Vehicle Routing Problems (VRPs) without extensive manual design. While existing constructive NCO methods typically follow an appending-based paradigm that sequentially adds unvisited nodes to partial solutions, this rigid approach often leads to suboptimal results. To overcome this limitation, we explore the idea of insertion-based paradigm and propose Learning to Construct with Insertion-based Paradigm (L2C-Insert), a novel learning-based method for constructive NCO. Unlike traditional approaches, L2C-Insert builds solutions by strategically inserting unvisited nodes at any valid position in the current partial solution, which can significantly enhance the flexibility and solution quality. The proposed framework introduces three key components: a novel model architecture for precise insertion position prediction, an efficient training scheme for model optimization, and an advanced inference technique that fully exploits the insertion paradigm's flexibility. Extensive experiments on both synthetic and real-world instances of the Travelling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that L2C-Insert consistently achieves superior performance across various problem sizes.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

Designing efficient quantum circuits is a central bottleneck to exploring the potential of quantum computing, particularly for noisy intermediate-scale quantum (NISQ) devices, where circuit efficiency and resilience to errors are paramount. The search space of gate sequences grows combinatorially, and handcrafted templates often waste scarce qubit and depth budgets. We introduce \textsc{FlowQ-Net} (Flow-based Quantum design Network), a generative framework for automated quantum circuit synthesis based on Generative Flow Networks (GFlowNets). This framework learns a stochastic policy to construct circuits sequentially, sampling them in proportion to a flexible, user-defined reward function that can encode multiple design objectives such as performance, depth, and gate count. This approach uniquely enables the generation of a diverse ensemble of high-quality circuits, moving beyond single-solution optimization. We demonstrate the efficacy of \textsc{FlowQ-Net} through an extensive set of simulations. We apply our method to Variational Quantum Algorithm (VQA) ansatz design for molecular ground state estimation, Max-Cut, and image classification, key challenges in near-term quantum computing. Circuits designed by \textsc{FlowQ-Net} achieve significant improvements, yielding circuits that are 10$\times$-30$\times$ more compact in terms of parameters, gates, and depth compared to commonly used unitary baselines, without compromising accuracy. This trend holds even when subjected to error profiles from real-world quantum devices. Our results underline the potential of generative models as a general-purpose methodology for automated quantum circuit design, offering a promising path towards more efficient quantum algorithms and accelerating scientific discovery in the quantum domain.

We address finance-native collateral optimization under ISDA Credit Support Annexes (CSAs), where integer lots, Schedule A haircuts, RA/MTA gating, and issuer/currency/class caps create rugged, legally bounded search spaces. We introduce a certifiable hybrid pipeline purpose-built for this domain: (i) an evidence-gated LLM that extracts CSA terms to a normalized JSON (abstain-by-default, span-cited); (ii) a quantum-inspired explorer that interleaves simulated annealing with micro higher order QAOA (HO-QAOA) on binding sub-QUBOs (subset size n <= 16, order k <= 4) to coordinate multi-asset moves across caps and RA-induced discreteness; (iii) a weighted risk-aware objective (Movement, CVaR, funding-priced overshoot) with an explicit coverage window U <= Reff+B; and (iv) CP-SAT as single arbiter to certify feasibility and gaps, including a U-cap pre-check that reports the minimal feasible buffer B*. Encoding caps/rounding as higher-order terms lets HO-QAOA target the domain couplings that defeat local swaps. On government bond datasets and multi-CSA inputs, the hybrid improves a strong classical baseline (BL-3) by 9.1%, 9.6%, and 10.7% across representative harnesses, delivering better cost-movement-tail frontiers under governance settings. We release governance grade artifacts-span citations, valuation matrix audit, weight provenance, QUBO manifests, and CP-SAT traces-to make results auditable and reproducible.

Large language models (LLMs) are catalyzing the development of autonomous AI research agents for scientific and engineering discovery. We present FM Agent, a novel and general-purpose multi-agent framework that leverages a synergistic combination of LLM-based reasoning and large-scale evolutionary search to address complex real-world challenges. The core of FM Agent integrates several key innovations: 1) a cold-start initialization phase incorporating expert guidance, 2) a novel evolutionary sampling strategy for iterative optimization, 3) domain-specific evaluators that combine correctness, effectiveness, and LLM-supervised feedback, and 4) a distributed, asynchronous execution infrastructure built on Ray. Demonstrating broad applicability, our system has been evaluated across diverse domains, including operations research, machine learning, GPU kernel optimization, and classical mathematical problems. FM Agent reaches state-of-the-art results autonomously, without human interpretation or tuning -- 1976.3 on ALE-Bench (+5.2\%), 43.56\% on MLE-Bench (+4.0pp), up to 20x speedups on KernelBench, and establishes new state-of-the-art(SOTA) results on several classical mathematical problems. Beyond academic benchmarks, FM Agent shows considerable promise for both large-scale enterprise R\&D workflows and fundamental scientific research, where it can accelerate innovation, automate complex discovery processes, and deliver substantial engineering and scientific advances with broader societal impact.