We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the "complete" loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive non-iterative maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.

In high-stakes applications, predictive models must not only produce accurate predictions but also quantify and communicate their uncertainty. Reject-option prediction addresses this by allowing the model to abstain when prediction uncertainty is high. Traditional reject-option approaches focus solely on aleatoric uncertainty, an assumption valid only when large training data makes the epistemic uncertainty negligible. However, in many practical scenarios, limited data makes this assumption unrealistic. This paper introduces the epistemic reject-option predictor, which abstains in regions of high epistemic uncertainty caused by insufficient data. Building on Bayesian learning, we redefine the optimal predictor as the one that minimizes expected regret -- the performance gap between the learned model and the Bayes-optimal predictor with full knowledge of the data distribution. The model abstains when the regret for a given input exceeds a specified rejection cost. To our knowledge, this is the first principled framework that enables learning predictors capable of identifying inputs for which the training data is insufficient to make reliable decisions.

In this work, we propose a new flow-matching Markov chain Monte Carlo (FM-MCMC) algorithm for estimating the orbital parameters of exoplanetary systems, especially for those only one exoplanet is involved. Compared to traditional methods that rely on random sampling within the Bayesian framework, our approach first leverages flow matching posterior estimation (FMPE) to efficiently constrain the prior range of physical parameters, and then employs MCMC to accurately infer the posterior distribution. For example, in the orbital parameter inference of beta Pictoris b, our model achieved a substantial speed-up while maintaining comparable accuracy-running 77.8 times faster than Parallel Tempered MCMC (PTMCMC) and 365.4 times faster than nested sampling. Moreover, our FM-MCMC method also attained the highest average log-likelihood among all approaches, demonstrating its superior sampling efficiency and accuracy. This highlights the scalability and efficiency of our approach, making it well-suited for processing the massive datasets expected from future exoplanet surveys. Beyond astrophysics, our methodology establishes a versatile paradigm for synergizing deep generative models with traditional sampling, which can be adopted to tackle complex inference problems in other fields, such as cosmology, biomedical imaging, and particle physics.

The loss function used to train a neural network is strongly connected to its output layer from a statistical point of view. This technical report analyzes common activation functions for a neural network output layer, like linear, sigmoid, ReLU, and softmax, detailing their mathematical properties and their appropriate use cases. A strong statistical justification exists for the selection of the suitable loss function for training a deep learning model. This report connects common loss functions such as Mean Squared Error (MSE), Mean Absolute Error (MAE), and various Cross-Entropy losses to the statistical principle of Maximum Likelihood Estimation (MLE). Choosing a specific loss function is equivalent to assuming a specific probability distribution for the model output, highlighting the link between these functions and the Generalized Linear Models (GLMs) that underlie network output layers. Additional scenarios of practical interest are also considered, such as alternative output encodings, constrained outputs, and distributions with heavy tails.

Simulating human reasoning in open-ended tasks has long been a central aspiration in AI and cognitive science. While large language models now approximate human responses at scale, they remain tuned to population-level consensus, often erasing the individuality of reasoning styles and belief trajectories. To advance the vision of more human-like reasoning in machines, we introduce HugAgent (Human-Grounded Agent Benchmark), which rethinks human reasoning simulation along three dimensions: (i) from averaged to individualized reasoning, (ii) from behavioral mimicry to cognitive alignment, and (iii) from vignette-based to open-ended data. The benchmark evaluates whether a model can predict a specific person's behavioral responses and the underlying reasoning dynamics in out-of-distribution scenarios, given partial evidence of their prior views. HugAgent adopts a dual-track design: a human track that automates and scales the think-aloud method to collect ecologically valid human reasoning data, and a synthetic track for further scalability and systematic stress testing. This architecture enables low-cost, extensible expansion to new tasks and populations. Experiments with state-of-the-art language models reveal persistent adaptation gaps, positioning HugAgent as the first extensible benchmark for aligning machine reasoning with the individuality of human thought. The benchmark, along with its complete data collection pipeline and companion chatbot, is open-sourced as HugAgent (https://anonymous.4open.science/r/HugAgent) and TraceYourThinking (https://anonymous.4open.science/r/trace-your-thinking).

Pedestrian inertial localization is key for mobile and IoT services because it provides infrastructure-free positioning. Yet most learning-based methods depend on fixed sliding-window integration, struggle to adapt to diverse motion scales and cadences, and yield inconsistent uncertainty, limiting real-world use. We present ReNiL, a Bayesian deep-learning framework for accurate, efficient, and uncertainty-aware pedestrian localization. ReNiL introduces Inertial Positioning Demand Points (IPDPs) to estimate motion at contextually meaningful waypoints instead of dense tracking, and supports inference on IMU sequences at any scale so cadence can match application needs. It couples a motion-aware orientation filter with an Any-Scale Laplace Estimator (ASLE), a dual-task network that blends patch-based self-supervision with Bayesian regression. By modeling displacements with a Laplace distribution, ReNiL provides homogeneous Euclidean uncertainty that integrates cleanly with other sensors. A Bayesian inference chain links successive IPDPs into consistent trajectories. On RoNIN-ds and a new WUDataset covering indoor and outdoor motion from 28 participants, ReNiL achieves state-of-the-art displacement accuracy and uncertainty consistency, outperforming TLIO, CTIN, iMoT, and RoNIN variants while reducing computation. Application studies further show robustness and practicality for mobile and IoT localization, making ReNiL a scalable, uncertainty-aware foundation for next-generation positioning.

Classical machine learning classifiers tend to be overconfident can be unreliable outside of the laboratory benchmarks. Properly assessing the reliability of the output of the model per sample is instrumental for real-life scenarios where these systems are deployed. Because of this, different techniques have been employed to properly quantify the quality of prediction for a given model. These are most commonly Bayesian statistics and, more recently, conformal learning. Given a calibration set, conformal learning can produce outputs that are guaranteed to cover the target class with a desired significance level, and are more reliable than the standard confidence intervals used by Bayesian methods. In this work, we propose to use conformal learning with fuzzy rule-based systems in classification and show some metrics of their performance. Then, we discuss how the use of type 2 fuzzy sets can improve the quality of the output of the system compared to both fuzzy and crisp rules. Finally, we also discuss how the fine-tuning of the system can be adapted to improve the quality of the conformal prediction.

A fundamental challenge in developing general learning algorithms is their tendency to forget past knowledge when adapting to new data. Addressing this problem requires a principled understanding of forgetting; yet, despite decades of study, no unified definition has emerged that provides insights into the underlying dynamics of learning. We propose an algorithm- and task-agnostic theory that characterises forgetting as a lack of self-consistency in a learner's predictive distribution over future experiences, manifesting as a loss of predictive information. Our theory naturally yields a general measure of an algorithm's propensity to forget. To validate the theory, we design a comprehensive set of experiments that span classification, regression, generative modelling, and reinforcement learning. We empirically demonstrate how forgetting is present across all learning settings and plays a significant role in determining learning efficiency. Together, these results establish a principled understanding of forgetting and lay the foundation for analysing and improving the information retention capabilities of general learning algorithms.

Steering cooperative multi-agent reinforcement learning (MARL) towards desired outcomes is challenging, particularly when the global guidance from a human on the whole multi-agent system is impractical in a large-scale MARL. On the other hand, designing external mechanisms (e.g., intrinsic rewards and human feedback) to coordinate agents mostly relies on empirical studies, lacking a easy-to-use research tool. In this work, we employ multi-agent influence diagrams (MAIDs) as a graphical framework to address the above issues. First, we introduce the concept of MARL interaction paradigms (orthogonal to MARL learning paradigms), using MAIDs to analyze and visualize both unguided self-organization and global guidance mechanisms in MARL. Then, we design a new MARL interaction paradigm, referred to as the targeted intervention paradigm that is applied to only a single targeted agent, so the problem of global guidance can be mitigated. In implementation, we introduce a causal inference technique, referred to as Pre-Strategy Intervention (PSI), to realize the targeted intervention paradigm. Since MAIDs can be regarded as a special class of causal diagrams, a composite desired outcome that integrates the primary task goal and an additional desired outcome can be achieved by maximizing the corresponding causal effect through the PSI. Moreover, the bundled relevance graph analysis of MAIDs provides a tool to identify whether an MARL learning paradigm is workable under the design of an MARL interaction paradigm. In experiments, we demonstrate the effectiveness of our proposed targeted intervention, and verify the result of relevance graph analysis.

Data-driven approaches using deep learning are emerging as powerful techniques to extract non-Gaussian information from cosmological large-scale structure. This work presents the first simulation-based inference (SBI) pipeline that combines weak lensing and galaxy clustering maps in a realistic Dark Energy Survey Year 3 (DES Y3) configuration and serves as preparation for a forthcoming analysis of the survey data. We develop a scalable forward model based on the CosmoGridV1 suite of N-body simulations to generate over one million self-consistent mock realizations of DES Y3 at the map level. Leveraging this large dataset, we train deep graph convolutional neural networks on the full survey footprint in spherical geometry to learn low-dimensional features that approximately maximize mutual information with target parameters. These learned compressions enable neural density estimation of the implicit likelihood via normalizing flows in a ten-dimensional parameter space spanning cosmological $w$CDM, intrinsic alignment, and linear galaxy bias parameters, while marginalizing over baryonic, photometric redshift, and shear bias nuisances. To ensure robustness, we extensively validate our inference pipeline using synthetic observations derived from both systematic contaminations in our forward model and independent Buzzard galaxy catalogs. Our forecasts yield significant improvements in cosmological parameter constraints, achieving $2-3\times$ higher figures of merit in the $Ω_m - S_8$ plane relative to our implementation of baseline two-point statistics and effectively breaking parameter degeneracies through probe combination. These results demonstrate the potential of SBI analyses powered by deep learning for upcoming Stage-IV wide-field imaging surveys.