Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage within the semantic feature space. We extend conformal prediction to this setting by introducing minimum-volume covering sets equipped with learnable generalized multi-norm constraints. We propose a method that constructs conformal sets guaranteeing user-specified coverage of positive samples while maximizing negative sample exclusion. We establish theoretically that volume minimization serves as a proxy for negative exclusion, enabling our approach to operate effectively even when negative pairs are unavailable. The positive inclusion guarantee inherits the distribution-free coverage property of conformal prediction, while negative exclusion is maximized through learned set geometry optimized on a held-out training split. Experiments on simulated and real-world image datasets demonstrate improved inclusion-exclusion trade-offs compared to standard distance-based conformal baselines.

Many causal discovery algorithms, including the celebrated FCI algorithm, output a Partial Ancestral Graph (PAG). PAGs serve as an abstract graphical representation of the underlying causal structure, modeled by directed acyclic graphs with latent and selection variables. This paper develops a characterization of the set of extended-type conditional independence relations that are invariant across all causal models represented by a PAG. This theory allows us to formulate a general measure-theoretic version of Pearl's causal calculus and a sound and complete identification algorithm for PAGs under selection bias. Our results also apply when PAGs are learned by certain algorithms that integrate observational data with experimental data and incorporate background knowledge.

Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers, which may be present in both the response and the predictor. It can be affected by casewise outliers, which are observations that deviate from the bulk of the data, as well as by cellwise outliers, which are individual anomalous cells within the tensors. The latter are particularly common due to the typically large number of cells in tensor data. This paper introduces a novel robust TOT regression method, named ROTOT, that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers in the response. The outliers in the predictor are handled using a robust Multilinear Principal Component Analysis method. Graphical diagnostic tools are also proposed to identify the different types of outliers detected. The performance of ROTOT is evaluated through extensive simulations and further illustrated using the Labeled Faces in the Wild dataset, where ROTOT is applied to predict facial attributes.

We propose SAHMM-VAE, a source-wise adaptive Hidden Markov prior variational autoencoder for unsupervised blind source separation. Instead of treating the latent prior as a single generic regularizer, the proposed framework assigns each latent dimension its own adaptive regime-switching prior, so that different latent dimensions are pulled toward different source-specific temporal organizations during training. Under this formulation, source separation is not implemented as an external post-processing step; it is embedded directly into variational learning itself. The encoder, decoder, posterior parameters, and source-wise prior parameters are optimized jointly, where the encoder progressively learns an inference map that behaves like an approximate inverse of the mixing transformation, while the decoder plays the role of the generative mixing model. Through this coupled optimization, the gradual alignment between posterior source trajectories and heterogeneous HMM priors becomes the mechanism through which different latent dimensions separate into different source components. To instantiate this idea, we develop three branches within one common framework: a Gaussian-emission HMM prior, a Markov-switching autoregressive HMM prior, and an HMM state-flow prior with state-wise autoregressive flow transformations. Experiments show that the proposed framework achieves unsupervised source recovery while also learning meaningful source-wise switching structures. More broadly, the method extends our structured-prior VAE line from smooth, mixture-based, and flow-based latent priors to adaptive switching priors, and provides a useful basis for future work on interpretable and potentially identifiable latent source modeling.

Efficiently aggregating spatial or temporal horizons to acquire compact representations has become a unifying principle in modern deep learning models, yet learning data-adaptive representations for long-horizon sequence data, especially continuous sequences like time series, remains an open challenge. While fixed-size patching has improved scalability and performance, discovering variable-sized, data-driven patches end-to-end often forces models to rely on soft discretization, specific backbones, or heuristic rules. In this work, we propose Reinforcement Patching (ReinPatch), the first framework to jointly optimize a sequence patching policy and its downstream sequence backbone model using reinforcement learning. By formulating patch boundary placement as a discrete decision process optimized via Group Relative Policy Gradient (GRPG), ReinPatch bypasses the need for continuous relaxations and performs dynamic patching policy optimization in a natural manner. Moreover, our method allows strict enforcement of a desired compression rate, freeing the downstream backbone to scale efficiently, and naturally supports multi-level hierarchical modeling. We evaluate ReinPatch on time-series forecasting datasets, where it demonstrates compelling performance compared to state-of-the-art data-driven patching strategies. Furthermore, our detached design allows the patching module to be extracted as a standalone foundation patcher, providing the community with visual and empirical insights into the segmentation behaviors preferred by a purely performance-driven neural patching strategy.

Machine learning models of chemical bioactivity are increasingly used for prioritizing a small number of compounds in virtual screening libraries for experimental follow-up. In these applications, assessing model accuracy by early hit enrichment such as Positive Predicted Value (PPV) calculated for top N hits (PPV@N) is more appropriate and actionable than traditional global metrics such as AUC. We present KANEL, an ensemble workflow that combines interpretable Kolmogorov-Arnold Networks (KANs) with XGBoost, random forest, and multilayer perceptron models trained on complementary molecular representations (LillyMol descriptors, RDKit-derived descriptors, and Morgan fingerprints). Across five public PubChem BioAssay datasets (AIDs 485314, 485341, 504466, 624202, and 651820), Optuna-optimized weighted ensembles consistently outperformed the best single model in PPV@128 by 0.06-0.12

The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude characteristics observed in individual source signals. On the other hand, many existing non-Gaussian amplitude distributions derived from hyperspherical models achieve good empirical fit due to their power-law structures, while they do not explicitly account for the complex-plane geometry inherent in complex-valued observations. In this paper, we propose a new probabilistic model for complex-valued random variables, which can be interpreted as a power-weighted noncentral complex Gaussian distribution. Unlike conventional hyperspherical amplitude models, the proposed model is formulated directly on the complex plane and preserves the geometric structure of complex-valued observations while retaining a higher-dimensional interpretation. The model introduces a nonlinear phase diffusion through a single shape parameter, enabling continuous control of the distributional geometry from arc-shaped diffusion along the phase direction to concentration of probability mass toward the origin. We formulate the proposed distribution and analyze the statistical properties of the induced amplitude distribution. The derived amplitude and power distributions provide a unified framework encompassing several widely used distributions in signal modeling, including the Rice, Nakagami, and gamma distributions. Experimental results on speech power spectra demonstrate that the proposed model consistently outperforms conventional distributions in terms of log-likelihood.

Accurate uncertainty quantification is crucial for making reliable decisions in various supervised learning scenarios, particularly when dealing with complex, multimodal data such as images and text. Current approaches often face notable limitations, including rigid assumptions and limited generalizability, constraining their effectiveness across diverse supervised learning tasks. To overcome these limitations, we introduce Generative Score Inference (GSI), a flexible inference framework capable of constructing statistically valid and informative prediction and confidence sets across a wide range of multimodal learning problems. GSI utilizes synthetic samples generated by deep generative models to approximate conditional score distributions, facilitating precise uncertainty quantification without imposing restrictive assumptions about the data or tasks. We empirically validate GSI's capabilities through two representative scenarios: hallucination detection in large language models and uncertainty estimation in image captioning. Our method achieves state-of-the-art performance in hallucination detection and robust predictive uncertainty in image captioning, and its performance is positively influenced by the quality of the underlying generative model. These findings underscore the potential of GSI as a versatile inference framework, significantly enhancing uncertainty quantification and trustworthiness in multimodal learning.

Transformer architectures have achieved remarkable empirical success in modeling contextual relationships in natural language, yet a precise mathematical characterization of their expressive power remains incomplete. In this work, we introduce a measure-theoretic framework for contextual representations in which texts are modeled as probability measures over a semantic embedding space, and contextual relations between words, are represented as coupling measures between them. Within this setting, we introduce Sinkhorn Transformer, a transformer-like architecture. Our main result is a universal approximation theorem: any continuous coupling function between probability measures, that encodes the semantic relation coupling measure, can be uniformly approximated by a Sinkhorn Transformer with appropriate parameters.

Motifs often recur in musical works in altered forms, preserving aspects of their identity while undergoing local variation. This paper investigates how such motivic transformations occur within their musical context in symbolic music. To support this analysis, we develop a probabilistic framework for modeling motivic transformations and apply it to Beethoven's piano sonatas by integrating multiple datasets that provide melodic, rhythmic, harmonic, and motivic information within a unified analytical representation. Motif transformations are represented as multilabel variables by comparing each motif instance to a designated reference occurrence within its local context, ensuring consistent labeling across transformation families. We introduce a multilabel Conditional Random Field to model how motif-level musical features influence the occurrence of transformations and how different transformation families tend to co-occur. Our goal is to provide an interpretable, distributional analysis of motivic transformation patterns, enabling the study of their structural relationships and stylistic variation. By linking computational modeling with music-theoretical interpretation, the proposed framework supports quantitative investigation of musical structure and complexity in symbolic corpora and may facilitate the analysis of broader compositional patterns and writing practices.