A Theory of the Mechanics of Information: Generalization Through Measurement of Uncertainty (Learning is Measuring)

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and perform inferences from raw data, eliminating distribution modeling, reducing bias, and enabling efficient updates including direct edits and deletion of training data. By quantifying relevance through uncertainty, the approach enables generalizable inference across tasks including generative inference, causal discovery, anomaly detection, and time series forecasting. It emphasizes traceability, interpretability, and data-driven decision making, offering a unified, human-understandable framework for machine learning, and achieves at or near state-of-the-art performance across most common machine learning tasks. The mathematical foundations create a ``physics'' of information, which enable these techniques to apply effectively to a wide variety of complex data types, including missing data. Empirical results indicate that this may be a viable alternative path to neural networks with regard to scalable machine learning and artificial intelligence that can maintain human understandability of the underlying mechanics.

Combining Deep Learning and Explainable AI for Toxicity Prediction of Chemical Compounds

The task here is to predict the toxicological activity of chemical compounds based on the Tox21 dataset, a benchmark in computational toxicology. After a domain-specific overview of chemical toxicity, we discuss current computational strategies, focusing on machine learning and deep learning. Several architectures are compared in terms of performance, robustness, and interpretability. This research introduces a novel image-based pipeline based on DenseNet121, which processes 2D graphical representations of chemical structures. Additionally, we employ Grad-CAM visualizations, an explainable AI technique, to interpret the model's predictions and highlight molecular regions contributing to toxicity classification. The proposed architecture achieves competitive results compared to traditional models, demonstrating the potential of deep convolutional networks in cheminformatics. Our findings emphasize the value of combining image-based representations with explainable AI methods to improve both predictive accuracy and model transparency in toxicology.

Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains

Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive representations for traditional numerical methods and lead to difficult optimization landscapes for machine learning-based approaches. In this work, we introduce an enhanced Finite Expression Method (FEX) designed to address these challenges with improved accuracy, interpretability, and computational efficiency. The proposed framework incorporates three key innovations: a symbolic spectral composition module that enables FEX to learn and represent multiscale oscillatory behavior; a redesigned linear input layer that significantly expands the expressivity of the model; and an eigenvalue formulation that extends FEX to a new class of problems involving eigenvalue PDEs. Through extensive numerical experiments, we demonstrate that FEX accurately resolves oscillatory PDEs on domains containing multiple holes of varying shapes and sizes. Compared with existing neural network-based solvers, FEX achieves substantially higher accuracy while yielding interpretable, closed-form solutions that expose the underlying structure of the problem. These advantages, often absent in conventional finite element, finite difference, and black-box neural approaches, highlight FEX as a powerful and transparent framework for solving complex PDEs.

A Review of End-to-End Precipitation Prediction Using Remote Sensing Data: from Divination to Machine Learning

Precipitation prediction has undergone a profound transformation -- from early symbolic and empirical methods rooted in divination and observation, to modern technologies based on atmospheric physics and artificial intelligence. This review traces the historical and technological evolution of precipitation forecasting, presenting a survey about end-to-end precipitation prediction technologies that spans ancient practices, the foundations of meteorological science, the rise of numerical weather prediction (NWP), and the emergence of machine learning (ML) and deep learning (DL) models. We first explore traditional and indigenous forecasting methods, then describe the development of physical modeling and statistical frameworks that underpin contemporary operational forecasting. Particular emphasis is placed on recent advances in neural network-based approaches, including automated deep learning, interpretability-driven design, and hybrid physical-data models. By compositing research across multiple eras and paradigms, this review not only depicts the history of end-to-end precipitation prediction but also outlines future directions in next generation forecasting systems.

Machine Learning Enabled Early Warning System For Financial Distress Using Real-Time Digital Signals

The growing instability of both global and domestic economic environments has increased the risk of financial distress at the household level. However, traditional econometric models often rely on delayed and aggregated data, limiting their effectiveness. This study introduces a machine learning-based early warning system that utilizes real-time digital and macroeconomic signals to identify financial distress in near real-time. Using a panel dataset of 750 households tracked over three monitoring rounds spanning 13 months, the framework combines socioeconomic attributes, macroeconomic indicators (such as GDP growth, inflation, and foreign exchange fluctuations), and digital economy measures (including ICT demand and market volatility). Through data preprocessing and feature engineering, we introduce lagged variables, volatility measures, and interaction terms to capture both gradual and sudden changes in financial stability. We benchmark baseline classifiers, such as logistic regression and decision trees, against advanced ensemble models including random forests, XGBoost, and LightGBM. Our results indicate that the engineered features from the digital economy significantly enhance predictive accuracy. The system performs reliably for both binary distress detection and multi-class severity classification, with SHAP-based explanations identifying inflation volatility and ICT demand as key predictors. Crucially, the framework is designed for scalable deployment in national agencies and low-bandwidth regional offices, ensuring it is accessible for policymakers and practitioners. By implementing machine learning in a transparent and interpretable manner, this study demonstrates the feasibility and impact of providing near-real-time early warnings of financial distress. This offers actionable insights that can strengthen household resilience and guide preemptive intervention strategies.

Self-induced stochastic resonance: A physics-informed machine learning approach

Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

Modeling Hierarchical Thinking in Large Reasoning Models

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities when they generate step-by-step solutions, known as chain-of-thought (CoT) reasoning. When trained to using chain-of-thought reasoning examples, the resulting models (called Large Reasoning Models, or LRMs) appear to learn hierarchical thinking strategies similar to those used by humans. However, understanding LRMs emerging reasoning capabilities remains a difficult open problem, with many potential important applications including improving training and understanding robustness. In this paper, we adopt a memoryless Finite State Machine formulation to approximate LRM's emerging hierarchical reasoning dynamics as a structured, interpretable abstraction. We identify a small set of discrete reasoning states including - initialization, deduction, augmentation-strategy, uncertainty-estimation, backtracking, and final-conclusion that capture the high-level states present in the model's reasoning process. By annotating each step of a model's CoT with these states, we can represent the reasoning trajectory as a transition sequence through the state graph. This FSM formulation provides a systematic way to analyze, interpret and visualize how different models approach problems. We describe the FSM model, provide examples of CoT annotations under this scheme, and discuss how it can shed light on differences between available models in their approach to reasoning. Our results demonstrate that this FSM-based analysis reveals distinct reasoning patterns and potential shortcomings, offering a new lens to evaluate and improve LLM reasoning.

Predicting Metabolic Dysfunction-Associated Steatotic Liver Disease using Machine Learning Methods

Background: Metabolic Dysfunction-Associated Steatotic Liver Disease (MASLD) affects ~33% of U.S. adults and is the most common chronic liver disease. Although often asymptomatic, progression can lead to cirrhosis. Early detection is important, as lifestyle interventions can prevent disease progression. We developed a fair, rigorous, and reproducible MASLD prediction model and compared it to prior methods using a large electronic health record database. Methods: We evaluated LASSO logistic regression, random forest, XGBoost, and a neural network for MASLD prediction using clinical feature subsets, including the top 10 SHAP-ranked features. To reduce disparities in true positive rates across racial and ethnic subgroups, we applied an equal opportunity postprocessing method. Results: This study included 59,492 patients in the training data, 24,198 in the validating data, and 25,188 in the testing data. The LASSO logistic regression model with the top 10 features was selected for its interpretability and comparable performance. Before fairness adjustment, the model achieved AUROC of 0.84, accuracy of 78%, sensitivity of 72%, specificity of 79%, and F1-score of 0.617. After equal opportunity postprocessing, accuracy modestly increased to 81% and specificity to 94%, while sensitivity decreased to 41% and F1-score to 0.515, reflecting the fairness trade-off. Conclusions: We developed the MASER prediction model (MASLD Static EHR Risk Prediction), a LASSO logistic regression model which achieved competitive performance for MASLD prediction (AUROC 0.836, accuracy 77.6%), comparable to previously reported ensemble and tree-based models. Overall, this approach demonstrates that interpretable models can achieve a balance of predictive performance and fairness in diverse patient populations.

Subliminal Corruption: Mechanisms, Thresholds, and Interpretability

As machine learning models are increasingly fine-tuned on synthetic data, there is a critical risk of subtle misalignments spreading through interconnected AI systems. This paper investigates subliminal corruption, which we define as undesirable traits are transmitted through semantically neutral data, bypassing standard safety checks. While this phenomenon has been identified, a quantitative understanding of its dynamics is missing. To address this gap, we present a systematic study of the scaling laws, thresholds, and mechanisms of subliminal corruption using a teacher-student setup with GPT-2. Our experiments reveal three key findings: (1) subliminal corruption causes behavioral crossover, degrading the model's overall alignment, not just the targeted trait; (2) alignment fails in a sharp phase transition at a critical threshold of poisoned data, rather than degrading gradually; and (3) interpretability analysis shows the corruption mechanism mimics the model's natural fine-tuning process, making it difficult to detect. These results demonstrate a critical vulnerability in AI systems that rely on synthetic data and highlight the need for new safety protocols that can account for latent threats.

PSO-XAI: A PSO-Enhanced Explainable AI Framework for Reliable Breast Cancer Detection

Breast cancer is considered the most critical and frequently diagnosed cancer in women worldwide, leading to an increase in cancer-related mortality. Early and accurate detection is crucial as it can help mitigate possible threats while improving survival rates. In terms of prediction, conventional diagnostic methods are often limited by variability, cost, and, most importantly, risk of misdiagnosis. To address these challenges, machine learning (ML) has emerged as a powerful tool for computer-aided diagnosis, with feature selection playing a vital role in improving model performance and interpretability. This research study proposes an integrated framework that incorporates customized Particle Swarm Optimization (PSO) for feature selection. This framework has been evaluated on a comprehensive set of 29 different models, spanning classical classifiers, ensemble techniques, neural networks, probabilistic algorithms, and instance-based algorithms. To ensure interpretability and clinical relevance, the study uses cross-validation in conjunction with explainable AI methods. Experimental evaluation showed that the proposed approach achieved a superior score of 99.1\% across all performance metrics, including accuracy and precision, while effectively reducing dimensionality and providing transparent, model-agnostic explanations. The results highlight the potential of combining swarm intelligence with explainable ML for robust, trustworthy, and clinically meaningful breast cancer diagnosis.