Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples come from the same distribution or not. Kernel-based procedures for hypothetical testing have been proposed to efficiently disentangle high-dimensional complex structures in data to obtain accurate results in a model-free way by embedding the data into the reproducing kernel Hilbert space (RKHS). While the choice of kernels plays a crucial role for their performance, little is understood about how to choose kernel especially for small datasets. Here we aim to construct a hypothetical test which is effective even for small datasets, based on the theoretical foundation of kernel-based tests using maximum mean discrepancy, which is called MMD-FUSE. To address this, we enhance the MMD-FUSE framework by incorporating quantum kernels and propose a novel hybrid testing strategy that fuses classical and quantum kernels. This approach creates a powerful and adaptive test by combining the domain-specific inductive biases of classical kernels with the unique expressive power of quantum kernels. We evaluate our method on various synthetic and real-world clinical datasets, and our experiments reveal two key findings: 1) With appropriate hyperparameter tuning, MMD-FUSE with quantum kernels consistently improves test power over classical counterparts, especially for small and high-dimensional data. 2) The proposed hybrid framework demonstrates remarkable robustness, adapting to different data characteristics and achieving high test power across diverse scenarios. These results highlight the potential of quantum-inspired and hybrid kernel strategies to build more effective statistical tests, offering a versatile tool for data analysis where sample sizes are limited.

Real-world systems ranging from airline routes to cryptocurrency transfers are naturally modelled as dynamic graphs whose topology changes over time. Conventional benchmarks judge dynamic-graph learners by a handful of task-specific scores, yet seldom ask whether the embeddings themselves remain a truthful, interpretable reflection of the evolving network. W e formalize this requirement as representation integrity and derive a family of indexes that measure how closely embedding changes follow graph changes. Three synthetic scenarios--Gradual Merge, Abrupt Move, and Periodic Re-wiring--are used to screen forty-two candidate indexes. Based on which we recommend one index that passes all of our theoretical and empirical tests. In particular, this validated metric consistently ranks the provably stable UASE and IPP models highest. W e then use this index to do a comparative study on representation integrity of common dynamic graph learning models. This study exposes the scenario-specific strengths of neural methods, and shows a strong positive rank correlation with one-step link-prediction AUC. The proposed integrity framework, therefore, offers a task-agnostic and interpretable evaluation tool for dynamic-graph representation quality, providing more explicit guidance for model selection and future architecture design.

We present Primal, a deterministic feature mapping framework that harnesses the number-theoretic independence of prime square roots to construct robust, tunable vector representations. Diverging from standard stochastic projections (e.g., Random Fourier Features), our method exploits the Besicovitch property to create irrational frequency modulations that guarantee infinite non-repeating phase trajectories. We formalize two distinct algorithmic variants: (1) StaticPrime, a sequence generation method that produces temporal position encodings empirically approaching the theoretical Welch bound for quasi-orthogonality; and (2) DynamicPrime, a tunable projection layer for input-dependent feature mapping. A central novelty of the dynamic framework is its ability to unify two disparate mathematical utility classes through a single scaling parameter σ. In the low-frequency regime, the method acts as an isometric kernel map, effectively linearizing non-convex geometries (e.g., spirals) to enable high-fidelity signal reconstruction and compressive sensing. Conversely, the high-frequency regime induces chaotic phase wrapping, transforming the projection into a maximum-entropy one-way hash suitable for Hyperdimensional Computing and privacy-preserving Split Learning. Empirical evaluations demonstrate that our framework yields superior orthogonality retention and distribution tightness compared to normalized Gaussian baselines, establishing it as a computationally efficient, mathematically rigorous alternative to random matrix projections. The code is available at https://github.com/VladimerKhasia/primal

Sparse Convolution (SpC) powers 3D point cloud networks widely used in autonomous driving and AR/VR. SpC builds a kernel map that stores mappings between input voxel coordinates, output coordinates, and weight offsets, then uses this map to compute feature vectors for output coordinates. Our work identifies three key properties of voxel coordinates: they are integer-valued, bounded within a limited spatial range, and geometrically continuous-neighboring voxels on the same object surface are highly likely to exist at small spatial offsets from each other. Prior SpC engines do not fully exploit these properties and suffer from high pre-processing and post-processing overheads during kernel map construction. To address this, we design Spira, the first voxel-property-aware SpC engine for GPUs. Spira proposes: (i) a high-performance one-shot search algorithm that builds the kernel map with no preprocessing and high memory locality, (ii) an effective packed-native processing scheme that accesses packed voxel coordinates at low cost, (iii) a flexible dual-dataflow execution mechanism that efficiently computes output feature vectors by adapting to layer characteristics, and (iv) a network-wide parallelization strategy that builds kernel maps for all SpC layers concurrently at network start. Our evaluation shows that Spira significantly outperforms prior SpC engines by 1.71x on average and up to 2.31x for end-to-end inference, and by 2.13x on average and up to 3.32x for layer-wise execution across diverse layer configurations.

The increasing availability of data and advancements in computational intelligence have accelerated the adoption of data-driven methods (DDMs) in product development. However, their integration into product development remains fragmented. This fragmentation stems from uncertainty, particularly the lack of clarity on what types of DDMs to use and when to employ them across the product development lifecycle. To address this, a necessary first step is to investigate the usage of DDM in engineering design by identifying which methods are being used, at which development stages, and for what application. This paper presents a PRISMA systematic literature review. The V-model as a product development framework was adopted and simplified into four stages: system design, system implementation, system integration, and validation. A structured search across Scopus, Web of Science, and IEEE Xplore (2014--2024) retrieved 1{,}689 records. After screening, 114 publications underwent full-text analysis. Findings show that machine learning (ML) and statistical methods dominate current practice, whereas deep learning (DL), though still less common, exhibits a clear upward trend in adoption. Additionally, supervised learning, clustering, regression analysis, and surrogate modeling are prevalent in design, implementation, and integration system stages but contributions to validation remain limited. Key challenges in existing applications include limited model interpretability, poor cross-stage traceability, and insufficient validation under real-world conditions. Additionally, it highlights key limitations and opportunities such as the need for interpretable hybrid models. This review is a first step toward design-stage guidelines; a follow-up synthesis should map computer science algorithms to engineering design problems and activities.

Its simple update, linear scalability with sample size, and compatibility with momentum, mini-batching, and learning-rate heuristics keep it dominant in both industry and academia. Current research continues to refine convergence rates, variance characterizations, and averaging schemes, while engineering efforts focus on hardware-aligned and distributed variants. B. Mini-Batch Stochastic Gradient Descent 1) Background and Development: Batch Gradient Descent (BGD) requires computing the gradient using the entire training dataset at each iteration. As dataset sizes expand to millions or even larger scales, the computational cost of a single iteration becomes extremely high, making it unsuitable for large-scale learning tasks. The convergence of SGD was proven by Robbins and Monro through the stochastic approximation method [1]. SGD uses one sample to update the gradient at each step, resulting in low computational cost but high gradient variance and unstable updates. The mini-batch strategy has gradually become the mainstream in practice, especially with the rise of large-scale machine learning and deep learning. Bottou emphasized the practical value of mini-batches in his research on large-scale learning [5], while systematic monographs and reviews on deep learning have further standardized this approach [6], [7]. Mini-batch SGD achieves an optimal balance between stability, high-frequency updates, and GPU parallel acceleration [2].

Foundation models pre-trained with self-supervised learning (SSL) on large-scale datasets have become powerful general-purpose feature extractors. However, their immense size and computational cost make them prohibitive for deployment on edge devices such as robots and AR/VR headsets. Existing compression techniques like standard knowledge distillation create efficient 'specialist' models but sacrifice the crucial, downstream-agnostic generality that makes foundation models so valuable. In this paper, we introduce Foundation Model Distillation (FMD), a new paradigm for compressing large SSL models into compact, efficient, and faithful proxies that retain their general-purpose representational power. We present Foundry, the first implementation of FMD for 3D point clouds. Our approach, Foundry, trains a student to learn a compressed set of SuperTokens that reconstruct the teacher's token-level representations, capturing a compact basis of its latent space. A single distilled model maintains strong transferability across diverse downstream tasks-classification, part segmentation, and few-shot scenarios-approaching full foundation-model performance while using significantly fewer tokens and FLOPs, making such models more practical for deployment on resourceconstrained hardware.

Text classification with hierarchical taxonomies is a fundamental requirement in IT Service Management (ITSM) systems, where support tickets must be categorized into tree-structured taxonomies. We present a dual-embedding centroid-based classification framework that maintains separate semantic and lexical centroid representations per category, combining them through reciprocal rank fusion at inference time. The framework achieves performance competitive with Support Vector Machines (hierarchical F1: 0.731 vs 0.727) while providing interpretability through centroid representations. Evaluated on 8,968 ITSM tickets across 123 categories, this method achieves 5.9 times faster training and up to 152 times faster incremental updates. With 8.6-8.8 times speedup across batch sizes (100-1000 samples) when excluding embedding computation. These results make the method suitable for production ITSM environments prioritizing interpretability and operational efficiency.

Representation learning on multi-omics data is challenging due to extreme dimensionality, modality heterogeneity, and cohort-specific batch effects. While pre-trained transformer backbones have shown broad generalization capabilities in biological sequence modeling, their application to multi-omics integration remains underexplored. We present MoRE (Multi-Omics Representation Embedding), a framework that repurposes frozen pre-trained transformers to align heterogeneous assays into a shared latent space. Unlike purely generative approaches, MoRE employs a parameter-efficient fine-tuning (PEFT) strategy, prioritizing cross-sample and cross-modality alignment over simple sequence reconstruction. Specifically, MoRE attaches lightweight, modality-specific adapters and a task-adaptive fusion layer to the frozen backbone. It optimizes a masked modeling objective jointly with supervised contrastive and batch-invariant alignment losses, yielding structure-preserving embeddings that generalize across unseen cell types and platforms. We benchmark MoRE against established baselines, including scGPT, scVI, and Harmony with Scrublet, evaluating integration fidelity, rare population detection, and modality transfer. Our results demonstrate that MoRE achieves competitive batch robustness and biological conservation while significantly reducing trainable parameters compared to fully fine-tuned models. This work positions MoRE as a practical step toward general-purpose omics foundation models.

Quantum computing promises transformative advances, but remains constrained by recurring misconceptions and methodological pitfalls. This paper demonstrates a fundamental incompatibility between traditional agent-based modeling (ABM) implementations and quantum optimization frameworks like Quadratic Unconstrained Binary Optimization (QUBO). Using Schelling's segregation model as a case study, we show that the standard practice of directly translating ABM state observations into QUBO formulations not only fails to deliver quantum advantage, but actively undermines computational efficiency. The fundamental issue is architectural. Traditional ABM implementations entail observing the state of the system at each iteration, systematically destroying the quantum superposition required for computational advantage. Through analysis of Schelling's segregation dynamics on lollipop networks, we demonstrate how abandoning the QUBO reduction paradigm and instead reconceptualizing the research question, from "simulate agent dynamics iteratively until convergence" to "compute minimum of agent moves required for global satisfaction", enables a faster classical solution. This structural reconceptualization yields an algorithm that exploits network symmetries obscured in traditional ABM simulations and QUBO formulations. It establishes a new lower bound which quantum approaches must outperform to achieve advantage. Our work emphasizes that progress in quantum agent-based modeling does not require forcing classical ABM implementations into quantum frameworks. Instead, it should focus on clarifying when quantum advantage is structurally possible, developing best-in-class classical baselines through problem analysis, and fundamentally reformulating research questions rather than preserving classical iterative state change observation paradigms.