In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory (LSTM) network estimates the key parameters $μ>0$ and $β\in(0,1)$ from sequences of inter-arrival times, effectively modeling their temporal dependencies. Our experiments on synthetic data show that the proposed approach reduces the mean squared error (MSE) by about 55.3\% compared to the traditional method of moments (MOM) and performs reliably across different training conditions. We tested the method on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. The results show that the LSTM can effectively track daily patterns and parameter changes, indicating its effectiveness on real-world data with complex time dependencies.

Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are operationalized by introducing states of the world, conditional on which the decision situation can be analyzed without any remaining uncertainty. Conversely, most classical decision-theoretic approaches are not applicable if the states of the world are inaccessible. We propose a decision model that retains the appeal and simplicity of the original theory, but completely overcomes the need to specify the states of the world explicitly. The main idea of our approach is to address decision problems in a radically empirical way: instead of specifying states and consequences prior to the decision analysis, we only assume a protocol of observed act--consequence pairs as model primitives. We show how optimality in such empirical decision problems can be addressed by using protocol-based empirical choice functions and discuss three approaches for deriving inferential guarantees: (I) consistent statistical estimation of choice sets, (II) consistent statistical testing of choice functions with robustness guarantees, and (III) direct inference for empirical choice functions using credal sets. We illustrate our theory with a proof-of-concept application comparing different prompting strategies in generative AI models.

The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive semi-supervised learning where the similarity metric between image samples is the Wasserstein distance. This metric is used in the label propagation mechanism during learning. We apply and demonstrate the effectiveness of the method on a GNSS real life application. More specifically, we address the problem of multi-path interference detection. Experiments are conducted under various signal conditions. The results show that for specific choices of hyperparameters controlling the amount of semi-supervision and the level of sensitivity to the metric, the classification accuracy can be significantly improved over the fully supervised training method.

As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g., rising costs, declining survey response rates), researchers increasingly use predictions from pre-trained algorithms as substitutes for missing or unobserved data. Though appealing for financial and logistical reasons, using standard tools for inference can misrepresent the association between independent variables and the outcome of interest when the true, unobserved outcome is replaced by a predicted value. In this paper, we characterize the statistical challenges inherent to drawing inference with predicted data (IPD) and show that high predictive accuracy does not guarantee valid downstream inference. We show that all such failures reduce to statistical notions of (i) bias, when predictions systematically shift the estimand or distort relationships among variables, and (ii) variance, when uncertainty from the prediction model and the intrinsic variability of the true data are ignored. We then review recent methods for conducting IPD and discuss how this framework is deeply rooted in classical statistical theory. We then comment on some open questions and interesting avenues for future work in this area, and end with some comments on how to use predicted data in scientific studies that is both transparent and statistically principled.

We develop a general theory of semantic dynamics for large language models by formalizing them as Continuous State Machines (CSMs): smooth dynamical systems whose latent manifolds evolve under probabilistic transition operators. The associated transfer operator $P: L^2(M,μ) \to L^2(M,μ)$ encodes the propagation of semantic mass. Under mild regularity assumptions (compactness, ergodicity, bounded Jacobian), $P$ is compact with discrete spectrum. Within this setting, we prove the Semantic Characterization Theorem (SCT): the leading eigenfunctions of $P$ induce finitely many spectral basins of invariant meaning, each definable in an o-minimal structure over $\mathbb{R}$. Thus spectral lumpability and logical tameness coincide. This explains how discrete symbolic semantics can emerge from continuous computation: the continuous activation manifold collapses into a finite, logically interpretable ontology. We further extend the SCT to stochastic and adiabatic (time-inhomogeneous) settings, showing that slowly drifting kernels preserve compactness, spectral coherence, and basin structure.

We formulate the Fast-Weights Homeostatic Reentry Network (FHRN) as a continuous-time neural-ODE system, revealing its role as a norm-regulated reentrant dynamical process. Starting from the discrete reentry rule $x_t = x_t^{(\mathrm{ex})} + γ\, W_r\, g(\|y_{t-1}\|)\, y_{t-1}$, we derive the coupled system $\dot{y}=-y+f(W_ry;\,x,\,A)+g_{\mathrm{h}}(y)$ showing that the network couples fast associative memory with global radial homeostasis. The dynamics admit bounded attractors governed by an energy functional, yielding a ring-like manifold. A Jacobian spectral analysis identifies a \emph{reflective regime} in which reentry induces stable oscillatory trajectories rather than divergence or collapse. Unlike continuous-time recurrent neural networks or liquid neural networks, FHRN achieves stability through population-level gain modulation rather than fixed recurrence or neuron-local time adaptation. These results establish the reentry network as a distinct class of self-referential neural dynamics supporting recursive yet bounded computation.

We present a transfer-learning generative downscaling framework to reconstruct fine resolution satellite images from coarse scale inputs. Our approach combines a lightweight U-Net transfer encoder with a diffusion-based generative model. The simpler U-Net is first pretrained on a long time series of coarse resolution data to learn spatiotemporal representations; its encoder is then frozen and transferred to a larger downscaling model as physically meaningful latent features. Our application uses NASA's MERRA-2 reanalysis as the low resolution source domain (50 km) and the GEOS-5 Nature Run (G5NR) as the high resolution target (7 km). Our study area included a large area in Asia, which was made computationally tractable by splitting into two subregions and four seasons. We conducted domain similarity analysis using Wasserstein distances confirmed minimal distributional shift between MERRA-2 and G5NR, validating the safety of parameter frozen transfer. Across seasonal regional splits, our model achieved excellent performance (R2 = 0.65 to 0.94), outperforming comparison models including deterministic U-Nets, variational autoencoders, and prior transfer learning baselines. Out of data evaluations using semivariograms, ACF/PACF, and lag-based RMSE/R2 demonstrated that the predicted downscaled images preserved physically consistent spatial variability and temporal autocorrelation, enabling stable autoregressive reconstruction beyond the G5NR record. These results show that transfer enhanced diffusion models provide a robust and physically coherent solution for downscaling a long time series of coarse resolution images with limited training periods. This advancement has significant implications for improving environmental exposure assessment and long term environmental monitoring.

EEG recordings are inherently contaminated by artifacts such as ocular, muscular, and environmental noise, which obscure neural activity and complicate preprocessing. Artifact classification offers advantages in stability and transparency, providing a viable alternative to ICA-based methods that enable flexible use alongside human inspections and across various applications. However, artifact classification is limited by its training data as it requires extensive manual labeling, which cannot fully cover the diversity of real-world EEG. Semi-synthetic data (SSD) methods have been proposed to address this limitation, but prior approaches typically injected single artifact types using ICA components or required separately recorded artifact signals, reducing both the realism of the generated data and the applicability of the method. To overcome these issues, we introduce SSDLabeler, a framework that generates realistic, annotated SSDs by decomposing real EEG with ICA, epoch-level artifact verification using RMS and PSD criteria, and reinjecting multiple artifact types into clean data. When applied to train a multi-label artifact classifier, it improved accuracy on raw EEG across diverse conditions compared to prior SSD and raw EEG training, establishing a scalable foundation for artifact handling that captures the co-occurrence and complexity of real EEG.

In the era of Large Language Models (LLMs), Retrieval-Augmented Generation (RAG) architectures are gaining significant attention for their ability to ground language generation in reliable knowledge sources. Despite their impressive effectiveness in many areas, RAG systems based solely on semantic similarity often fail to ensure factual accuracy in specialized domains, where terminological ambiguity can affect retrieval relevance. This study proposes an enhanced RAG architecture that integrates a factual signal derived from Entity Linking to improve the accuracy of educational question-answering systems in Italian. The system includes a Wikidata-based Entity Linking module and implements three re-ranking strategies to combine semantic and entity-based information: a hybrid score weighting model, reciprocal rank fusion, and a cross-encoder re-ranker. Experiments were conducted on two benchmarks: a custom academic dataset and the standard SQuAD-it dataset. Results show that, in domain-specific contexts, the hybrid schema based on reciprocal rank fusion significantly outperforms both the baseline and the cross-encoder approach, while the cross-encoder achieves the best results on the general-domain dataset. These findings confirm the presence of an effect of domain mismatch and highlight the importance of domain adaptation and hybrid ranking strategies to enhance factual precision and reliability in retrieval-augmented generation. They also demonstrate the potential of entity-aware RAG systems in educational environments, fostering adaptive and reliable AI-based tutoring tools.

Reinforcement Learning (RL) has become the de facto standard for tuning LLMs to solve tasks involving reasoning. However, growing evidence shows that models trained in such way often suffer from a significant loss in diversity. We argue that this arises because RL implicitly optimizes the "mode-seeking" or "zero-forcing" Reverse KL to a target distribution causing the model to concentrate mass on certain high-probability regions of the target while neglecting others. In this work, we instead begin from an explicit target distribution, obtained by filtering out incorrect answers while preserving the relative probabilities of correct ones. Starting from a pre-trained LLM, we approximate this target distribution using the $α$-divergence family, which unifies prior approaches and enables direct control of the precision-diversity trade-off by interpolating between mode-seeking and mass-covering divergences. On a Lean theorem-proving benchmark, our method achieves state-of-the-art performance along the coverage-precision Pareto frontier, outperforming all prior methods on the coverage axis.