Interpretability is central to trustworthy machine learning, yet existing metrics rarely quantify how effectively data support an interpretive representation. We propose Interpretive Efficiency, a normalized, task-aware functional that measures the fraction of task-relevant information transmitted through an interpretive channel. The definition is grounded in five axioms ensuring boundedness, Blackwell-style monotonicity, data-processing stability, admissible invariance, and asymptotic consistency. We relate the functional to mutual information and derive a local Fisher-geometric expansion, then establish asymptotic and finite-sample estimation guarantees using standard empirical-process tools. Experiments on controlled image and signal tasks demonstrate that the measure recovers theoretical orderings, exposes representational redundancy masked by accuracy, and correlates with robustness, making it a practical, theory-backed diagnostic for representation design.

Chimpanzees' brutal battle for territory leads to a baby boom A rival chimp can die in less than 15 minutes during these deadly territorial fights. New research led by UCLA and the University of Michigan has shown that chimp communities that kill their neighbors to gain territory also gain reproductive advantages. Breakthroughs, discoveries, and DIY tips sent every weekday. Uganda's Ngogo chimpanzees are well known for their "chimpanzee warfare." Primatologists have observed their brutal, lethal fights between 10 or more chimpanzees for decades, deciphering what leads to such violence.

We propose a unified information-geometric framework that formalizes understanding in learning as a trade-off between informativeness and geometric simplicity. An encoder ϕ is evaluated by U(ϕ): = I(ϕ(X);Y) βC(ϕ), where C(ϕ) penalizes curvature and intrinsic dimensionality, enforcing smooth, low-complexity manifolds. Under mild manifold and regularity assumptions, we derive non-asymptotic bounds showing that generalization error scales with intrinsic dimension while curvature controls approximation stability, directly linking geometry to sample efficiency. To operationalize this theory, we introduce the Varia-tional Geometric Information Bottleneck (V-GIB); a varia-tional estimator that unifies mutual-information compression and curvature regularization through tractable geometric proxies (Hutchinson trace, Jacobian norms, and local PCA). Experiments across synthetic manifolds, few-shot settings, and real-world datasets (Fashion-MNIST, CIFAR-10) reveal a robust information-geometry Pareto frontier, stable estimators, and substantial gains in interpretive efficiency. Notably, fractional-data experiments on CIFAR-10 confirm that curvature-aware encoders maintain predictive power under data scarcity, validating the predicted efficiency-curvature law. Overall, V-GIB provides a principled and measurable route to representations that are geometrically coherent, data-efficient, and aligned with human-understandable structure. Keywords: geometry of understanding; information bottleneck; curvature regularization; few-shot learning; mutual information; Hutchinson trace estimator; inter-pretability; human-machine alignment.

We present a unified theoretical framework for analyzing the stability and consistency of Physics-Informed Neural Networks (PINNs), grounded in operator coercivity, variational formulations, and non-asymptotic perturbation theory. PINNs approximate solutions to partial differential equations (PDEs) by minimizing residual losses over sampled collocation and boundary points. We formalize both operator-level and variational notions of consistency, proving that residual minimization in Sobolev norms leads to convergence in energy and uniform norms under mild regularity. Deterministic stability bounds quantify how bounded perturbations to the network outputs propagate through the full composite loss, while probabilistic concentration results via McDiarmid's inequality yield sample complexity guarantees for residual-based generalization. A unified generalization bound links residual consistency, projection error, and perturbation sensitivity. Empirical results on elliptic, parabolic, and nonlinear PDEs confirm the predictive accuracy of our theoretical bounds across regimes. The framework identifies key structural principles, such as operator coercivity, activation smoothness, and sampling admissibility, that underlie robust and generalizable PINN training, offering principled guidance for the design and analysis of PDE-informed learning systems.

Clustering patient subgroups is essential for personalized care and efficient resource use. Traditional clustering methods struggle with high-dimensional, heterogeneous healthcare data and lack contextual understanding. This study evaluates Large Language Model (LLM) based clustering against classical methods using a pediatric sepsis dataset from a low-income country (LIC), containing 2,686 records with 28 numerical and 119 categorical variables. Patient records were serialized into text with and without a clustering objective. Embeddings were generated using quantized LLAMA 3.1 8B, DeepSeek-R1-Distill-Llama-8B with low-rank adaptation(LoRA), and Stella-En-400M-V5 models. K-means clustering was applied to these embeddings. Classical comparisons included K-Medoids clustering on UMAP and FAMD-reduced mixed data. Silhouette scores and statistical tests evaluated cluster quality and distinctiveness. Stella-En-400M-V5 achieved the highest Silhouette Score (0.86). LLAMA 3.1 8B with the clustering objective performed better with higher number of clusters, identifying subgroups with distinct nutritional, clinical, and socioeconomic profiles. LLM-based methods outperformed classical techniques by capturing richer context and prioritizing key features. These results highlight potential of LLMs for contextual phenotyping and informed decision-making in resource-limited settings.

We develop a principled framework for discovering causal structure in partial differential equations (PDEs) using physics-informed neural networks and counterfactual perturbations. Unlike classical residual minimization or sparse regression methods, our approach quantifies operator-level necessity through functional interventions on the governing dynamics. We introduce causal sensitivity indices and structural deviation metrics to assess the influence of candidate differential operators within neural surrogates. Theoretically, we prove exact recovery of the causal operator support under restricted isometry or mutual coherence conditions, with residual bounds guaranteeing identifiability. Empirically, we validate the framework on both synthetic and real-world datasets across climate dynamics, tumor diffusion, and ocean flows. Our method consistently recovers governing operators even under noise, redundancy, and data scarcity, outperforming standard PINNs and DeepONets in structural fidelity. This work positions causal PDE discovery as a tractable and interpretable inference task grounded in structural causal models and variational residual analysis.

We introduce the $D$-decomposition, a non-orthogonal matrix factorization of the form $A \approx P D Q$, where $P \in \mathbb{R}^{n \times k}$, $D \in \mathbb{R}^{k \times k}$, and $Q \in \mathbb{R}^{k \times n}$. The decomposition is defined variationally by minimizing a regularized Frobenius loss, allowing control over rank, sparsity, and conditioning. Unlike algebraic factorizations such as LU or SVD, it is computed by alternating minimization. We establish existence and perturbation stability of the solution and show that each update has complexity $\mathcal{O}(n^2k)$. Benchmarks against truncated SVD, CUR, and nonnegative matrix factorization show improved reconstruction accuracy on MovieLens, MNIST, Olivetti Faces, and gene expression matrices, particularly under sparsity and noise.

In this paper,we explore the application of Back translation (BT) as a semi-supervised technique to enhance Neural Machine Translation(NMT) models for the English-Luganda language pair, specifically addressing the challenges faced by low-resource languages. The purpose of our study is to demonstrate how BT can mitigate the scarcity of bilingual data by generating synthetic data from monolingual corpora. Our methodology involves developing custom NMT models using both publicly available and web-crawled data, and applying Iterative and Incremental Back translation techniques. We strategically select datasets for incremental back translation across multiple small datasets, which is a novel element of our approach. The results of our study show significant improvements, with translation performance for the English-Luganda pair exceeding previous benchmarks by more than 10 BLEU score units across all translation directions. Additionally, our evaluation incorporates comprehensive assessment metrics such as SacreBLEU, ChrF2, and TER, providing a nuanced understanding of translation quality. The conclusion drawn from our research confirms the efficacy of BT when strategically curated datasets are utilized, establishing new performance benchmarks and demonstrating the potential of BT in enhancing NMT models for low-resource languages.

Tuberculosis (TB) is a infectious global health challenge. Chest X-rays are a standard method for TB screening, yet many countries face a critical shortage of radiologists capable of interpreting these images. Machine learning offers an alternative, as it can automate tasks such as disease diagnosis, and report generation. However, traditional approaches rely on task-specific models, which cannot utilize the interdependence between tasks. Building a multi-task model capable of performing multiple tasks poses additional challenges such as scarcity of multimodal data, dataset imbalance, and negative transfer. To address these challenges, we propose PaliGemma-CXR, a multi-task multimodal model capable of performing TB diagnosis, object detection, segmentation, report generation, and VQA. Starting with a dataset of chest X-ray images annotated with TB diagnosis labels and segmentation masks, we curated a multimodal dataset to support additional tasks. By finetuning PaliGemma on this dataset and sampling data using ratios of the inverse of the size of task datasets, we achieved the following results across all tasks: 90.32% accuracy on TB diagnosis and 98.95% on close-ended VQA, 41.3 BLEU score on report generation, and a mAP of 19.4 and 16.0 on object detection and segmentation, respectively. These results demonstrate that PaliGemma-CXR effectively leverages the interdependence between multiple image interpretation tasks to enhance performance.

Deep Reinforcement Learning (RL) is remarkably effective in addressing sequential resource allocation problems in domains such as healthcare, public policy, and resource management. However, deep RL policies often lack transparency and adaptability, challenging their deployment alongside human decision-makers. In contrast, Language Agents, powered by large language models (LLMs), provide human-understandable reasoning but may struggle with effective decision making. To bridge this gap, we propose Rule-Bottleneck Reinforcement Learning (RBRL), a novel framework that jointly optimizes decision and explanations. At each step, RBRL generates candidate rules with an LLM, selects among them using an attention-based RL policy, and determines the environment action with an explanation via chain-of-thought reasoning. The RL rule selection is optimized using the environment rewards and an explainability metric judged by the LLM. Evaluations in real-world scenarios highlight RBRL's competitive performance with deep RL and efficiency gains over LLM fine-tuning. A survey further confirms the enhanced quality of its explanations.