Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these can be viewed as using Dirac delta distributions to model the relationships between shared factors and the low-rank tensor. However, such prior knowledge is rarely available in practical scenarios, particularly regarding the optimal rank structure and contraction rules. The optimization procedures based on fixed contraction rules are complex, and approximations made during these processes often lead to accuracy loss. To address this issue, we propose a score-based model that eliminates the need for predefined structural or distributional assumptions, enabling the learning of compatibility between tensors and shared factors. Specifically, a neural network is designed to learn the energy function, which is optimized via score matching to capture the gradient of the joint log-probability of tensor entries and shared factors. Our method allows for modeling structures and distributions beyond the Dirac delta assumption. Moreover, integrating the block coordinate descent (BCD) algorithm with the proposed smooth regularization enables the model to perform both tensor completion and denoising. Experimental results demonstrate significant performance improvements across various tensor types, including sparse and continuous-time tensors, as well as visual data.

Explicit density learners are becoming an increasingly popular technique for generative models because of their ability to better model probability distributions. They have advantages over Generative Adversarial Networks due to their ability to perform density estimation and having exact latent-variable inference. This has many advantages, including: being able to simply interpolate, calculate sample likelihood, and analyze the probability distribution. The downside of these models is that they are often more difficult to train and have lower sampling quality. Normalizing flows are explicit density models, that use composable bijective functions to turn an intractable probability function into a tractable one. In this work, we present novel knowledge distillation techniques to increase sampling quality and density estimation of smaller student normalizing flows. We seek to study the capacity of knowledge distillation in Compositional Normalizing Flows to understand the benefits and weaknesses provided by these architectures. Normalizing flows have unique properties that allow for a non-traditional forms of knowledge transfer, where we can transfer that knowledge within intermediate layers. We find that through this distillation, we can make students significantly smaller while making substantial performance gains over a non-distilled student. With smaller models there is a proportionally increased throughput as this is dependent upon the number of bijectors, and thus parameters, in the network.

This research addresses critical autonomous vehicle control challenges arising from road roughness variation, which induces course deviations and potential loss of road contact during steering operations. We present a novel real-time road roughness estimation system employing Bayesian calibration methodology that processes axle accelerations to predict terrain roughness with quantifiable confidence measures. The technical framework integrates a Gaussian process surrogate model with a simulated half-vehicle model, systematically processing vehicle velocity and road surface roughness parameters to generate corresponding axle acceleration responses. The Bayesian calibration routine performs inverse estimation of road roughness from observed accelerations and velocities, yielding posterior distributions that quantify prediction uncertainty for adaptive risk management. Training data generation utilizes Latin Hypercube sampling across comprehensive velocity and roughness parameter spaces, while the calibrated model integrates seamlessly with a Simplex controller architecture to dynamically adjust velocity limits based on real-time roughness predictions. Experimental validation on stochastically generated surfaces featuring varying roughness regions demonstrates robust real-time characterization capabilities, with the integrated Simplex control strategy effectively enhancing autonomous vehicle operational safety through proactive surface condition response. This innovative Bayesian framework establishes a comprehensive foundation for mitigating roughness-related operational risks while simultaneously improving efficiency and safety margins in autonomous vehicle systems.

The manifold hypothesis asserts that data of interest in high-dimensional ambient spaces, such as image data, lies on unknown low-dimensional submanifolds. Diffusion models (DMs) -- which operate by convolving data with progressively larger amounts of Gaussian noise and then learning to revert this process -- have risen to prominence as the most performant generative models, and are known to be able to learn distributions with low-dimensional support. For a given datum in one of these submanifolds, we should thus intuitively expect DMs to have implicitly learned its corresponding local intrinsic dimension (LID), i.e. the dimension of the submanifold it belongs to. Kamkari et al. (2024b) recently showed that this is indeed the case by linking this LID to the rate of change of the log marginal densities of the DM with respect to the amount of added noise, resulting in an LID estimator known as FLIPD. LID estimators such as FLIPD have a plethora of uses, among others they quantify the complexity of a given datum, and can be used to detect outliers, adversarial examples and AI-generated text. FLIPD achieves state-of-the-art performance at LID estimation, yet its theoretical underpinnings are incomplete since Kamkari et al. (2024b) only proved its correctness under the highly unrealistic assumption of affine submanifolds. In this work we bridge this gap by formally proving the correctness of FLIPD under realistic assumptions. Additionally, we show that an analogous result holds when Gaussian convolutions are replaced with uniform ones, and discuss the relevance of this result.

Modern observatories are designed to deliver increasingly detailed views of astrophysical signals. To fully realize the potential of these observations, principled data-analysis methods are required to effectively separate and reconstruct the underlying astrophysical components from data corrupted by noise and instrumental effects. In this work, we introduce a novel multi-frequency Bayesian model of the sky emission field that leverages latent-space tension as an indicator of model misspecification, enabling automated separation of diffuse, point-like, and extended astrophysical emission components across wavelength bands. Deviations from latent-space prior expectations are used as diagnostics for model misspecification, thus systematically guiding the introduction of new sky components, such as point-like and extended sources. We demonstrate the effectiveness of this method on synthetic multi-frequency imaging data and apply it to observational X-ray data from the eROSITA Early Data Release (EDR) of the SN1987A region in the Large Magellanic Cloud (LMC). Our results highlight the method's capability to reconstruct astrophysical components with high accuracy, achieving sub-pixel localization of point sources, robust separation of extended emission, and detailed uncertainty quantification. The developed methodology offers a general and well-founded framework applicable to a wide variety of astronomical datasets, and is therefore well suited to support the analysis needs of next-generation multi-wavelength and multi-messenger surveys.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Modern cyberattacks in cyber-physical systems (CPS) rapidly evolve and cannot be deterred effectively with most current methods which focused on characterizing past threats. Adaptive anomaly detection (AAD) is among the most promising techniques to detect evolving cyberattacks focused on fast data processing and model adaptation. AAD has been researched in the literature extensively; however, to the best of our knowledge, our work is the first systematic literature review (SLR) on the current research within this field. We present a comprehensive SLR, gathering 397 relevant papers and systematically analyzing 65 of them (47 research and 18 survey papers) on AAD in CPS studies from 2013 to 2023 (November). We introduce a novel taxonomy considering attack types, CPS application, learning paradigm, data management, and algorithms. Our analysis indicates, among other findings, that reviewed works focused on a single aspect of adaptation (either data processing or model adaptation) but rarely in both at the same time. We aim to help researchers to advance the state of the art and help practitioners to become familiar with recent progress in this field. We identify the limitations of the state of the art and provide recommendations for future research directions.

Despite their widespread use, large language models (LLMs) are known to hallucinate incorrect information and be poorly calibrated. This makes the uncertainty quantification of these models of critical importance, especially in high-stakes domains, such as autonomy and healthcare. Prior work has made Bayesian deep learning-based approaches to this problem more tractable by performing inference over the low-rank adaptation (LoRA) parameters of a fine-tuned model. While effective, these approaches struggle to scale to larger LLMs due to requiring further additional parameters compared to LoRA. In this work we present $\textbf{Scala}$ble $\textbf{B}$ayesian $\textbf{L}$ow-Rank Adaptation via Stochastic Variational Subspace Inference (ScalaBL). We perform Bayesian inference in an $r$-dimensional subspace, for LoRA rank $r$. By repurposing the LoRA parameters as projection matrices, we are able to map samples from this subspace into the full weight space of the LLM. This allows us to learn all the parameters of our approach using stochastic variational inference. Despite the low dimensionality of our subspace, we are able to achieve competitive performance with state-of-the-art approaches while only requiring ${\sim}1000$ additional parameters. Furthermore, it allows us to scale up to the largest Bayesian LLM to date, with four times as a many base parameters as prior work.

Current approaches for question answering (QA) over tabular data, such as NL2SQL systems, perform well for factual questions where answers are directly retrieved from tables. However, they fall short on probabilistic questions requiring reasoning under uncertainty. In this paper, we introduce a new benchmark LUCARIO and a framework for probabilistic QA over large tabular data. Our method induces Bayesian Networks from tables, translates natural language queries into probabilistic queries, and uses large language models (LLMs) to generate final answers. Empirical results demonstrate significant improvements over baselines, highlighting the benefits of hybrid symbolic-neural reasoning.

Deep learning models, despite their popularity, face challenges such as long training times and a lack of interpretability. In contrast, fuzzy inference systems offer a balance of accuracy and transparency. This paper addresses the limitations of traditional Takagi-Sugeno-Kang fuzzy models by extending the recently proposed New Takagi-Sugeno-Kang model to a new Mamdani-based regressor. These models are data-driven, allowing users to define the number of rules to balance accuracy and interpretability. To handle the complexity of large datasets, this research integrates wrapper and ensemble techniques. A Genetic Algorithm is used as a wrapper for feature selection, creating genetic versions of the models. Furthermore, ensemble models, including the Random New Mamdani Regressor, Random New Takagi-Sugeno-Kang, and Random Forest New Takagi-Sugeno-Kang, are introduced to improve robustness. The proposed models are validated on photovoltaic energy forecasting datasets, a critical application due to the intermittent nature of solar power. Results demonstrate that the genetic and ensemble fuzzy models, particularly the Genetic New Takagi-Sugeno-Kang and Random Forest New Takagi-Sugeno-Kang, achieve superior performance. They often outperform both traditional machine learning and deep learning models while providing a simpler and more interpretable rule-based structure. The models are available online in a library called nfisis (https://pypi.org/project/nfisis/).