In this paper, we generate conceptual engineering designs of electric vertical take-off and landing (eVTOL) aircraft. We follow the paradigm of simulation-based inference (SBI), whereby we look to learn a posterior distribution over the full eVTOL design space. To learn this distribution, we sample over discrete aircraft configurations (topologies) and their corresponding set of continuous parameters. Therefore, we introduce a hierarchical probabilistic model consisting of two diffusion models. The first model leverages recent work on Riemannian Diffusion Language Modeling (RDLM) and Unified World Models (UWMs) to enable us to sample topologies from a discrete and continuous space. For the second model we introduce a masked diffusion approach to sample the corresponding parameters conditioned on the topology. Our approach rediscovers known trends and governing physical laws in aircraft design, while significantly accelerating design generation.

Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably classically hard in certain regimes. Recent proposals focus on training IQP-QCBMs using Maximum Mean Discrepancy (MMD) losses built from low-body Pauli-$Z$ correlators, but the effect of initialization on the resulting optimization landscape remains poorly understood. In this work, we address this by first proving that the MMD loss landscape suffers from barren plateaus for random full-angle-range initializations of IQP circuits. We then establish lower bounds on the loss variance for identity and an unbiased data-agnostic initialization. We then additionally consider a data-dependent initialization that is better aligned with the target distribution and, under suitable assumptions, yields provable gradients and generally converges quicker to a good minimum (as indicated by our training of circuits with 150 qubits on genomic data). Finally, as a by-product, the developed variance lower bound framework is applicable to a general class of non-linear losses, offering a broader toolset for analyzing warm-starts in quantum machine learning.

Scaling laws for neural networks, in which the loss decays as a power-law in the number of parameters, data, and compute, depend fundamentally on the spectral structure of the data covariance, with power-law eigenvalue decay appearing ubiquitously in vision and language tasks. A central question is whether this spectral structure is preserved or destroyed when data passes through the basic building block of a neural network: a random linear projection followed by a nonlinear activation. We study this question for the random feature model: given data $x \sim N(0,H)\in \mathbb{R}^v$ where $H$ has $α$-power-law spectrum ($λ_j(H ) \asymp j^{-α}$, $α> 1$), a Gaussian sketch matrix $W \in \mathbb{R}^{v\times d}$, and an entrywise monomial $f(y) = y^{p}$, we characterize the eigenvalues of the population random-feature covariance $\mathbb{E}_{x }[\frac{1}{d}f(W^\top x )^{\otimes 2}]$. We prove matching upper and lower bounds: for all $1 \leq j \leq c_1 d \log^{-(p+1)}(d)$, the $j$-th eigenvalue is of order $\left(\log^{p-1}(j+1)/j\right)^α$. For $ c_1 d \log^{-(p+1)}(d)\leq j\leq d$, the $j$-th eigenvalue is of order $j^{-α}$ up to a polylog factor. That is, the power-law exponent $α$ is inherited exactly from the input covariance, modified only by a logarithmic correction that depends on the monomial degree $p$. The proof combines a dyadic head-tail decomposition with Wick chaos expansions for higher-order monomials and random matrix concentration inequalities.

Asynchronous Bayesian optimization is widely used for gradient-free optimization in domains with independent parallel experiments and varying evaluation times. Existing methods posit that standard acquisitions lead to redundant and repeated queries, proposing complex solutions to enforce diversity in queries. Challenging this fundamental premise, we show that methods, like the Upper Confidence Bound, can in fact achieve theoretical guarantees essentially equivalent to those of sequential Thompson sampling. A conceptual analysis of asynchronous Bayesian optimization reveals that existing works neglect intermediate posterior updates, which we find to be generally sufficient to avoid redundant queries. Further investigation shows that by penalizing busy locations, diversity-enforcing methods can over-explore in asynchronous settings, reducing their performance. Our extensive experiments demonstrate that simple standard acquisition functions match or outperform purpose-built asynchronous methods across synthetic and real-world tasks.

Functional magnetic resonance imaging (fMRI) enables noninvasive investigation of brain function, while short clinical scan durations, arising from human and non-human factors, usually lead to reduced data quality and limited statistical power for neuroimaging research. In this paper, we propose BrainCast, a novel spatio-temporal forecasting framework specifically tailored for whole-brain fMRI time series forecasting, to extend informative fMRI time series without additional data acquisition. It formulates fMRI time series forecasting as a multivariate time series prediction task and jointly models temporal dynamics within regions of interest (ROIs) and spatial interactions across ROIs. Specifically, BrainCast integrates a Spatial Interaction Awareness module to characterize inter-ROI dependencies via embedding every ROI time series as a token, a Temporal Feature Refinement module to capture intrinsic neural dynamics within each ROI by enhancing both low- and high-energy temporal components of fMRI time series at the ROI level, and a Spatio-temporal Pattern Alignment module to combine spatial and temporal representations for producing informative whole-brain features. Experimental results on resting-state and task fMRI datasets from the Human Connectome Project demonstrate the superiority of BrainCast over state-of-the-art time series forecasting baselines. Moreover, fMRI time series extended by BrainCast improve downstream cognitive ability prediction, highlighting the clinical and neuroscientific impact brought by whole-brain fMRI time series forecasting in scenarios with restricted scan durations.

Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold and learns dynamics via Riemannian flow matching. RMG factorizes motion into several manifold factors, yielding a scale-free representation with intrinsic normalization, and uses geodesic interpolation, tangent-space supervision, and manifold-preserving ODE integration for training and sampling. On HumanML3D, RMG achieves state-of-the-art FID in the HumanML3D format (0.043) and ranks first on all reported metrics under the MotionStreamer format. On MotionMillion, it also surpasses strong baselines (FID 5.6, R@1 0.86). Ablations show that the compact $\mathscr{T}+\mathscr{R}$ (translation + rotations) representation is the most stable and effective, highlighting geometry-aware modeling as a practical and scalable route to high-fidelity motion generation.

Label noise - incorrect labels assigned to observations - can substantially degrade the performance of supervised classifiers. This paper proposes a label noise cleaning method based on Bernoulli random sampling. We show that the mean label noise levels of subsets generated by Bernoulli random sampling containing a given observation are identically distributed for all clean observations, and identically distributed, with a different distribution, for all noisy observations. Although the mean label noise levels are not independent across observations, by introducing an independent coupling we further prove that they converge to a mixture of two well-separated distributions corresponding to clean and noisy observations. By establishing a linear model between cross-validated classification errors and label noise levels, we are able to approximate this mixture distribution and thereby separate clean and noisy observations without any prior label information. The proposed method is classifier-agnostic, theoretically justified, and demonstrates strong performance on both simulated and real datasets.

Masked diffusion language models (MDLMs) have recently emerged as a new paradigm in language modeling, offering flexible generation dynamics and enabling efficient parallel decoding. However, existing decoding strategies for pre-trained MDLMs predominantly rely on token-level uncertainty criteria, while largely overlooking sequence-level information and inter-token dependencies. To address this limitation, we propose Dependency-Oriented Sampler (DOS), a training-free decoding strategy that leverages inter-token dependencies to inform token updates during generation. Specifically, DOS exploits attention matrices from transformer blocks to approximate inter-token dependencies, emphasizing information from unmasked tokens when updating masked positions. Empirical results demonstrate that DOS consistently achieves superior performance on both code generation and mathematical reasoning tasks. Moreover, DOS can be seamlessly integrated with existing parallel sampling methods, leading to improved generation efficiency without sacrificing generation quality.

Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on variables and does not account for differences in variable importance, which may lead to unstable performance in highly noisy or structurally complex settings. We propose SP-SPCA, a method that introduces a single equilibrium parameter into the regularization framework to adaptively adjust variable penalties. This modification of the L2 penalty provides flexible control over the trade-off between sparsity and explained variance while maintaining computational efficiency. Simulation studies show that the proposed method consistently outperforms standard sparse principal component methods in identifying sparse loading patterns, filtering noise variables, and preserving cumulative variance, especially in high-dimensional and noisy settings. Empirical applications to crime and financial market data further demonstrate its practical utility. In real data analyses, the method selects fewer but more relevant variables, thereby reducing model complexity while maintaining explanatory power. Overall, the proposed approach offers a robust and efficient alternative for sparse modeling in complex high-dimensional data, with clear advantages in stability, feature selection, and interpretability

We introduce the Integrated Tsallis Combination (ITC), a hybrid impurity measure for decision tree learning that combines normalized Tsallis entropy with an exponential polarization component. While many existing measures sacrifice theoretical soundness for computational efficiency or vice versa, ITC provides a mathematically principled framework that balances both aspects. The core innovation lies in the complementarity between Tsallis entropy's information-theoretic foundations and the polarization component's sensitivity to distributional asymmetry. We establish key theoretical properties-concavity under explicit parameter conditions, proper boundary conditions, and connections to classical measures-and provide a rigorous justification for the hybridization strategy. Through an extensive comparative evaluation on seven benchmark datasets comparing 23 impurity measures with five-fold repetition, we show that simple parametric measures (Tsallis $α=0.5$) achieve the highest average accuracy ($91.17\%$), while ITC variants yield competitive results ($88.38-89.16\%$) with strong theoretical guarantees. Statistical analysis (Friedman test: $χ^2=3.89$, $p=0.692$) reveals no significant global differences among top performers, indicating practical equivalence for many applications. ITC's value resides in its solid theoretical grounding-proven concavity under suitable conditions, flexible parameterization ($α$, $β$, $γ$), and computational efficiency $O(K)$-making it a rigorous, generalizable alternative when theoretical guarantees are paramount. We provide guidelines for measure selection based on application priorities and release an open-source implementation to foster reproducibility and further research.