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 consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices using only $T=\mathcal{O}(\log N)$ observations, irrespective of whether the matrix is sparse or dense. This estimator is based on the method of moments and does not rely on problem-specific regularization. This is especially important for applications such as structure discovery.

Understanding the robustness of a weather forecasting model with respect to input noise or different uncertainties is important in assessing its output reliability, particularly for extreme weather events like hurricanes. In this paper, we test sensitivity and robustness of an artificial intelligence (AI) weather forecasting model: NVIDIAs FourCastNetv2 (FCNv2). We conduct two experiments designed to assess model output under different levels of injected noise in the models initial condition. First, we perturb the initial condition of Hurricane Florence from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) dataset (September 13-16, 2018) with varying amounts of Gaussian noise and examine the impact on predicted trajectories and forecasted storm intensity. Second, we start FCNv2 with fully random initial conditions and observe how the model responds to nonsensical inputs. Our results indicate that FCNv2 accurately preserves hurricane features under low to moderate noise injection. Even under high levels of noise, the model maintains the general storm trajectory and structure, although positional accuracy begins to degrade. FCNv2 consistently underestimates storm intensity and persistence across all levels of injected noise. With full random initial conditions, the model generates smooth and cohesive forecasts after a few timesteps, implying the models tendency towards stable, smoothed outputs. Our approach is simple and portable to other data-driven AI weather forecasting models.

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.

Underwater images often suffer from severe color distortion, low contrast, and a hazy appearance due to wavelength-dependent light absorption and scattering. Simultaneously, existing deep learning models exhibit high computational complexity, which limits their practical deployment for real-time underwater applications. To address these challenges, this paper presents a novel underwater image enhancement model, called Adaptive Frequency Fusion and Illumination Aware Network (AQUA-Net). It integrates a residual encoder decoder with dual auxiliary branches, which operate in the frequency and illumination domains. The frequency fusion encoder enriches spatial representations with frequency cues from the Fourier domain and preserves fine textures and structural details. Inspired by Retinex, the illumination-aware decoder performs adaptive exposure correction through a learned illumination map that separates reflectance from lighting effects. This joint spatial, frequency, and illumination design enables the model to restore color balance, visual contrast, and perceptual realism under diverse underwater conditions. Additionally, we present a high-resolution, real-world underwater video-derived dataset from the Mediterranean Sea, which captures challenging deep-sea conditions with realistic visual degradations to enable robust evaluation and development of deep learning models. Extensive experiments on multiple benchmark datasets show that AQUA-Net performs on par with SOTA in both qualitative and quantitative evaluations while using less number of parameters. Ablation studies further confirm that the frequency and illumination branches provide complementary contributions that improve visibility and color representation. Overall, the proposed model shows strong generalization capability and robustness, and it provides an effective solution for real-world underwater imaging applications.

Vision-language models (VLMs) have achieved strong performance in visual question answering (VQA), yet they remain constrained by static training data. Retrieval-Augmented Generation (RAG) mitigates this limitation by enabling access to up-to-date, culturally grounded, and multilingual information; however, multilingual multimodal RAG remains largely underexplored. We introduce M4-RAG, a massive-scale benchmark covering 42 languages and 56 regional dialects and registers, comprising over 80,000 culturally diverse image-question pairs for evaluating retrieval-augmented VQA across languages and modalities. To balance realism with reproducibility, we build a controlled retrieval environment containing millions of carefully curated multilingual documents relevant to the query domains, approximating real-world retrieval conditions while ensuring consistent experimentation. Our systematic evaluation reveals that although RAG consistently benefits smaller VLMs, it fails to scale to larger models and often even degrades their performance, exposing a critical mismatch between model size and current retrieval effectiveness. M4-RAG provides a foundation for advancing next-generation RAG systems capable of reasoning seamlessly across languages, modalities, and cultural contexts.