In this work, we study contextual strongly convex simulation optimization and adopt an "optimize then predict" (OTP) approach for real-time decision making. In the offline stage, simulation optimization is conducted across a set of covariates to approximate the optimal-solution function; in the online stage, decisions are obtained by evaluating this approximation at the observed covariate. The central theoretical challenge is to understand how the inexactness of solutions generated by simulation-optimization algorithms affects the optimality gap, which is overlooked in existing studies. To address this, we develop a unified analysis framework that explicitly accounts for both solution bias and variance. Using Polyak-Ruppert averaging SGD as an illustrative simulation-optimization algorithm, we analyze the optimality gap of OTP under four representative smoothing techniques: $k$ nearest neighbor, kernel smoothing, linear regression, and kernel ridge regression. We establish convergence rates, derive the optimal allocation of the computational budget $Γ$ between the number of design covariates and the per-covariate simulation effort, and demonstrate the convergence rate can approximately achieve $Γ^{-1}$ under appropriate smoothing technique and sample-allocation rule. Finally, through a numerical study, we validate the theoretical findings and demonstrate the effectiveness and practical value of the proposed approach.

Semi-implicit variational inference (SIVI) constructs approximate posteriors of the form $q(θ) = \int k(θ| z) r(dz)$, where the conditional kernel is parameterized and the mixing base is fixed and tractable. This paper develops a unified "approximation-optimization-statistics'' theory for such families. On the approximation side, we show that under compact L1-universality and a mild tail-dominance condition, semi-implicit families are dense in L1 and can achieve arbitrarily small forward Kullback-Leibler (KL) error. We also identify two sharp obstructions to global approximation: (i) an Orlicz tail-mismatch condition that induces a strictly positive forward-KL gap, and (ii) structural restrictions, such as non-autoregressive Gaussian kernels, that force "branch collapse'' in conditional distributions. For each obstruction we give a minimal structural modification that restores approximability. On the optimization side, we establish finite-sample oracle inequalities and prove that the empirical SIVI objectives L(K,n) $Γ$-converge to their population limit as n and K tend to infinity. These results give consistency of empirical maximizers, quantitative control of finite-K surrogate bias, and stability of the resulting variational posteriors. Combining the approximation and optimization analyses yields the first general end-to-end statistical theory for SIVI: we characterize precisely when SIVI can recover the target distribution, when it cannot, and how architectural and algorithmic choices govern the attainable asymptotic behavior.

Semi-supervised learning (SSL) constructs classifiers from datasets in which only a subset of observations is labelled, a situation that naturally arises because obtaining labels often requires expert judgement or costly manual effort. This motivates methods that integrate labelled and unlabelled data within a learning framework. Most SSL approaches assume that label absence is harmless, typically treated as missing completely at random or ignored, but in practice, the missingness process can be informative, as the chances of an observation being unlabelled may depend on the ambiguity of its feature vector. In such cases, the missingness indicators themselves provide additional information that, if properly modelled, may improve estimation efficiency. The \textbf{SSLfmm} package for R is designed to capture this behaviour by estimating the Bayes' classifier under a finite mixture model in which each component corresponding to a class follows a multivariate normal distribution. It incorporates a mixed-missingness mechanism that combines a missing completely at random (MCAR) component with a (non-ignorable) missing at random (MAR) component, the latter modelling the probability of label missingness as a logistic function of the entropy based on the features. Parameters are estimated via an Expectation--Conditional Maximisation algorithm. In the two-class Gaussian setting with arbitrary covariance matrices, the resulting classifier trained on partially labelled data may, in some cases, achieve a lower misclassification rate than the supervised version in the case where all the labels are known. The package includes a practical tool for modelling and illustrates its performance through simulated examples.

Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1) bridge equation methods, which leverage solutions to integral equations to recover causal targets, and (2) array decomposition methods, which recover latent factors composing counterfactual quantities by exploiting unique determination of eigenspaces. We compare the model restrictions underlying these two approaches and provide insight into implications of the underlying assumptions, clarifying the scope of applicability for each method.

Clustering in stationary and nonstationary settings, where data distributions remain static or evolve over time, requires models that can adapt to distributional shifts while preserving previously learned cluster structures. This paper proposes an Adaptive Resonance Theory (ART)-based topological clustering algorithm that autonomously adjusts its recalculation interval and vigilance threshold through a diversity-driven adaptation mechanism. This mechanism enables hyperparameter-free learning that maintains cluster stability and continuity in dynamic environments. Experiments on 24 real-world datasets demonstrate that the proposed algorithm outperforms state-of-the-art methods in both clustering performance and continual learning capability. These results highlight the effectiveness of the proposed parameter adaptation in mitigating catastrophic forgetting and maintaining consistent clustering in evolving data streams. Source code is available at https://github.com/Masuyama-lab/IDAT

There exist various Software Development Kits (SDKs) tailored to different quantum computing platforms. These are known as Quantum SDKs (QSDKs). Examples include but are not limited to Qiskit, Cirq, and PennyLane. However, this diversity presents significant challenges for interoperability and cross-platform development of hybrid quantum-classical software systems. Traditional rule-based transpilers for translating code between QSDKs are time-consuming to design and maintain, requiring deep expertise and rigid mappings in the source and destination code. In this study, we explore the use of Large Language Models (LLMs) as a flexible and automated solution. Leveraging their pretrained knowledge and contextual reasoning capabilities, we position LLMs as programming language-agnostic transpilers capable of converting quantum programs from one QSDK to another while preserving functional equivalence. Our approach eliminates the need for manually defined transformation rules and offers a scalable solution to quantum software portability. This work represents a step toward enabling intelligent, general-purpose transpilation in the quantum computing ecosystem.

The application of Vision-Language Models (VLMs) in medicine is critically hampered by the scarcity of high-quality, expert-annotated data. Supervised Fine-Tuning (SFT) on existing datasets often leads to poor generalization on unseen modalities and tasks, while Reinforcement Learning (RL), a promising alternative, is stymied by the lack of reliable reward signals in this data-scarce domain. To break this impasse, we introduce Generative Reward Learning for Medical Reasoning (MedGR$^2$), a novel framework that creates a self-improving virtuous cycle. MedGR$^2$ co-develops a data generator and a reward model, enabling the automated, continuous creation of high-quality, multi-modal medical data that serves as both a superior training source for SFT and RL. Our experiments demonstrate that SFT with MedGR$^2$-produced data already surpasses baselines trained on large-scale, human-curated datasets. Crucially, when leveraging this data for RL via Group Relative Policy Optimization (GRPO), our model achieves state-of-the-art cross-modality and cross-task generalization, significantly outperforming specialized RL-based methods. Furthermore, our compact model, empowered by MedGR$^2$, achieves performance competitive with foundation models possessing over 10 times more parameters. MedGR$^2$ presents a new paradigm for data-efficient learning in high-stakes domains, transforming the problem from data scarcity to data generation and unlocking the full potential of RL for building truly generalizable medical AI.

Grasp synthesis is a fundamental task in robotic manipulation which usually has multiple feasible solutions. Multimodal grasp synthesis seeks to generate diverse sets of stable grasps conditioned on object geometry, making the robust learning of geometric features crucial for success. To address this challenge, we propose a framework for learning multimodal grasp distributions that leverages variational shape inference to enhance robustness against shape noise and measurement sparsity. Our approach first trains a variational autoencoder for shape inference using implicit neural representations, and then uses these learned geometric features to guide a diffusion model for grasp synthesis on the SE(3) manifold. Additionally, we introduce a test-time grasp optimization technique that can be integrated as a plugin to further enhance grasping performance. Experimental results demonstrate that our shape inference for grasp synthesis formulation outperforms state-of-the-art multimodal grasp synthesis methods on the ACRONYM dataset by 6.3%, while demonstrating robustness to deterioration in point cloud density compared to other approaches. Furthermore, our trained model achieves zero-shot transfer to real-world manipulation of household objects, generating 34% more successful grasps than baselines despite measurement noise and point cloud calibration errors.

Significant Others (SOs) stabilize identity, regulate emotion, and support narrative meaning-making, yet many people today lack access to such relational anchors. Recent advances in large language models and memory-augmented AI raise the question of whether artificial systems could support some of these functions. Existing empathic AIs, however, remain reactive and short-term, lacking autobiographical memory, identity modeling, predictive emotional regulation, and narrative coherence. This manuscript introduces Significant Other Artificial Intelligence (SO-AI) as a new domain of relational AI. It synthesizes psychological and sociological theory to define SO functions and derives requirements for SO-AI, including identity awareness, long-term memory, proactive support, narrative co-construction, and ethical boundary enforcement. A conceptual architecture is proposed, comprising an anthropomorphic interface, a relational cognition layer, and a governance layer. A research agenda outlines methods for evaluating identity stability, longitudinal interaction patterns, narrative development, and sociocultural impact. SO-AI reframes AI-human relationships as long-term, identity-bearing partnerships and provides a foundational blueprint for investigating whether AI can responsibly augment the relational stability many individuals lack today.

Large Language Models (LLMs) offer powerful capabilities, but their significant size and computational requirements hinder deployment on resource-constrained mobile devices. This paper investigates Post-Training Quantization (PTQ) for compressing LLMs for mobile execution. We apply 4-bit PTQ using the BitsAndBytes library with the Hugging Face Transformers framework to Meta's Llama 3.2 3B model. The quantized model is converted to GGUF format using llama.cpp tools for optimized mobile inference. The PTQ workflow achieves a 68.66% reduction in model size through 4-bit quantization, enabling the Llama 3.2 3B model to run efficiently on an Android device. Qualitative validation shows that the 4-bit quantized model can perform inference tasks successfully. We demonstrate the feasibility of running the quantized GGUF model on an Android device using the Termux environment and the Ollama framework. PTQ, especially at 4-bit precision combined with mobile-optimized formats like GGUF, provides a practical pathway for deploying capable LLMs on mobile devices, balancing model size and performance.