In quantum mechanics, observation actively shapes the system, paralleling the statistical notion of Missing Not At Random (MNAR). This study introduces a unified framework for \textbf{robust causal directionality inference} in quantum engineering, determining whether relations are system$\to$observation, observation$\to$system, or bidirectional. The method integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization. It jointly addresses quantum and classical noise while uncovering causal directionality, with theoretical guarantees for double robustness, perturbation stability, and oracle inequalities. Simulation and real-data analyses (TCGA gene expression, proteomics) show that the proposed MNAR-stabilized CVAE+GEE+AIPW+PEL framework achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics. This establishes robust causal directionality inference as a key methodological advance for reliable quantum engineering.

This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large number of samples to achieve accurate results. We propose a novel estimator, \emph{BayesSum}, which is an extension of Bayesian quadrature to discrete domains. It is more sample efficient than alternatives due to its ability to make use of prior information about the integrand through a Gaussian process. We show this through theory, deriving a convergence rate significantly faster than Monte Carlo in a broad range of settings. We also demonstrate empirically that our proposed method does indeed require fewer samples on several synthetic settings as well as for parameter estimation for Conway-Maxwell-Poisson and Potts models.

During training, generative large language models (LLMs) are exposed to vast amounts of information, including data relevant to economic modelling, such as geospatial statistics and firm-level financial metrics. If LLMs can effectively retrieve and utilise this knowledge, they could reduce dependence on external data sources that are time-consuming to access, clean, and merge, or that incur financial costs. Moreover, if LLMs accurately represent data, they could support downstream tasks like data imputation and outlier detection. In this study, we evaluate whether and how LLMs can be used for typical economic data processes. Not all knowledge within an LLM may be explicit and retrievable in natural language by prompting the model.

Implicit Neural Representations (INRs) leverage neural networks to map coordinates to corresponding signals, enabling continuous and compact representations. This paradigm has driven significant advances in various vision tasks. However, existing INRs lack frequency selectivity and spatial localization, leading to an over-reliance on redundant signal components. Consequently, they exhibit spectral bias, tending to learn low-frequency components early while struggling to capture fine high-frequency details. To address these issues, we propose FLAIR (Frequency- and Locality-Aware Implicit Neural Representations), which incorporates two key innovations. The first is Band-Localized Activation (BLA), a novel activation designed for joint frequency selection and spatial localization under the constraints of the time-frequency uncertainty principle (TFUP). Through structured frequency control and spatially localized responses, BLA effectively mitigates spectral bias and enhances training stability. The second is Wavelet-Energy-Guided Encoding (WEGE), which leverages the discrete wavelet transform to compute energy scores and explicitly guide frequency information to the network, enabling precise frequency selection and adaptive band control. Our method consistently outperforms existing INRs in 2D image representation, as well as 3D shape reconstruction and novel view synthesis.

This paper develops the foundations of Quantum Granular Computing (QGC), extending classical granular computing including fuzzy, rough, and shadowed granules to the quantum regime. Quantum granules are modeled as effects on a finite dimensional Hilbert space, so granular memberships are given by Born probabilities. This operator theoretic viewpoint provides a common language for sharp (projective) and soft (nonprojective) granules and embeds granulation directly into the standard formalism of quantum information theory. We establish foundational results for effect based quantum granules, including normalization and monotonicity properties, the emergence of Boolean islands from commuting families, granular refinement under Luders updates, and the evolution of granules under quantum channels via the adjoint channel in the Heisenberg picture. We connect QGC with quantum detection and estimation theory by interpreting the effect operators realizing Helstrom minimum error measurement for binary state discrimination as Helstrom type decision granules, i.e., soft quantum counterparts of Bayes optimal decision regions. Building on these results, we introduce Quantum Granular Decision Systems (QGDS) with three reference architectures that specify how quantum granules can be defined, learned, and integrated with classical components while remaining compatible with near term quantum hardware. Case studies on qubit granulation, two qubit parity effects, and Helstrom style soft decisions illustrate how QGC reproduces fuzzy like graded memberships and smooth decision boundaries while exploiting noncommutativity, contextuality, and entanglement. The framework thus provides a unified and mathematically grounded basis for operator valued granules in quantum information processing, granular reasoning, and intelligent systems.

Large Language Models (LLMs) have demonstrated remarkable potential in hardware front-end design using hardware description languages (HDLs). However, their inherent tendency toward hallucination often introduces functional errors into the generated HDL designs. To address this issue, we propose the framework CorrectHDL that leverages high-level synthesis (HLS) results as functional references to correct potential errors in LLM-generated HDL designs.The input to the proposed framework is a C/C++ program that specifies the target circuit's functionality. The program is provided to an LLM to directly generate an HDL design, whose syntax errors are repaired using a Retrieval-Augmented Generation (RAG) mechanism. The functional correctness of the LLM-generated circuit is iteratively improved by comparing its simulated behavior with an HLS reference design produced by conventional HLS tools, which ensures the functional correctness of the result but can lead to suboptimal area and power efficiency. Experimental results demonstrate that circuits generated by the proposed framework achieve significantly better area and power efficiency than conventional HLS designs and approach the quality of human-engineered circuits. Meanwhile, the correctness of the resulting HDL implementation is maintained, highlighting the effectiveness and potential of agentic HDL design leveraging the generative capabilities of LLMs and the rigor of traditional correctness-driven IC design flows.

We consider the problem of learning a low dimensional representation for compositional data.

We consider the problem of learning a low dimensional representation for compositional data.