Current wildfire risk assessments rely on coarse hazard maps and opaque machine learning models that optimize regional accuracy while sacrificing interpretability at the decision scale. WildfireGenome addresses these gaps through three components: (1) fusion of seven federal wildfire indicators into a sign-aligned, PCA-based composite risk label at H3 Level-8 resolution; (2) Random Forest classification of local wildfire risk; and (3) SHAP and ICE/PDP analyses to expose county-specific nonlinear driver relationships. Across seven ecologically diverse U.S. counties, models achieve accuracies of 0.755-0.878 and Quadratic Weighted Kappa up to 0.951, with principal components explaining 87-94% of indicator variance. Transfer tests show reliable performance between ecologically similar regions but collapse across dissimilar contexts. Explanations consistently highlight needleleaf forest cover and elevation as dominant drivers, with risk rising sharply at 30-40% needleleaf coverage. WildfireGenome advances wildfire risk assessment from regional prediction to interpretable, decision-scale analytics that guide vegetation management, zoning, and infrastructure planning.

Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associations miss context-dependent patterns, reducing statistical power and interpretability. We develop a geometric decomposition framework offering two strategies for partitioning inference problems into regional analyses on data-derived Riemannian graphs. Gradient flow decomposition uses path-monotonicity-validated discrete Morse theory to partition samples into gradient flow cells where outcomes exhibit monotonic behavior. Co-monotonicity decomposition utilizes vertex-level coefficients that provide context-dependent versions of the classical Pearson correlation: these coefficients measure edge-based directional concordance between outcome and features, or between feature pairs, defining embeddings of samples into association space. These embeddings induce Riemannian k-NN graphs on which biclustering identifies co-monotonicity cells (coherent regions) and feature modules. This extends naturally to multi-modal integration across multiple feature sets. Both strategies apply independently or jointly, with Bayesian posterior sampling providing credible intervals.

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In this paper, we fill the missing parts by investigating different perspectives of the "node similarity". Conventional homophily metrics quantify the "similarity" as an indicator function of whether

Such assumptions allow for identification of causal target parameters. For instance, one may be interested in the average variance-weighted treatment effects (Robins et al., 2008; Li et al., 2011),

MI can lead to the disclosure of highly sensitive information about the individual, e.g. that

However, two significant challenges hinder its research and application. First, existing datasets lack comprehensive visual information from various pose angles.

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty from perception to planning, providing a principled connection between these two abstraction levels. Our approach couples a transformer-based perceptual front-end with graph neural network (GNN) relational reasoning to extract probabilistic symbolic states from visual observations, and an uncertainty-aware symbolic planner that actively gathers information when confidence is low. We demonstrate the framework's effectiveness on tabletop robotic manipulation as a concrete application: the translator processes 10,047 PyBullet-generated scenes (3--10 objects) and outputs probabilistic predicates with calibrated confidences (overall F1=0.68). When embedded in the planner, the system achieves 94\%/90\%/88\% success on Simple Stack, Deep Stack, and Clear+Stack benchmarks (90.7\% average), exceeding the strongest POMDP baseline by 10--14 points while planning within 15\,ms. A probabilistic graphical-model analysis establishes a quantitative link between calibrated uncertainty and planning convergence, providing theoretical guarantees that are validated empirically. The framework is general-purpose and can be applied to any domain requiring uncertainty-aware reasoning from perceptual input to symbolic planning.