Toward a Unified Statistical Theory of Unsupervised Pretraining and Supervised Neural Knowledge Graph Learning

Knowledge graph learning provides a powerful framework for representing and inferring structured knowledge, with broad practical applications. However, the scarcity of relation-specific labeled triples per entity hinders the training of expressive models, and the ad hoc design of scoring functions limits generalizability and lacks theoretical grounding. We address both issues with a theoretically grounded, end-to-end training framework that extends and subsumes existing methods. Our framework is a two-stage procedure: unsupervised pretraining over heterogeneous corpora followed by supervised learning with multiple relation types. We establish a nonasymptotic risk bound that disentangles pretraining representation error from labeled-sample complexity, formally quantifying the benefit of large-scale unlabeled data for downstream knowledge prediction. Synthetic experiments validate each theoretical component, and real-world experiments confirm the effectiveness of our approach on large-scale knowledge graph benchmarks.

KnowsTFM: Knowledge-Informed Fine-Tuning of Small Tabular Foundation Models

Tabular foundation models have advanced deep learning for tabular data by delivering strong default performance across many small and medium tasks. Yet in niche domains, where data is scarce, high-dimensional, and shifted from the pretraining distribution, they may still fail to outperform carefully designed domain-specific methods. Many such domains also provide curated relational knowledge in the form of knowledge graphs and knowledge banks, but how to use this knowledge to improve and steer \textit{small} specialist tabular foundation models remains unclear. We address this problem through \textbf{Know}ledge-informed fine-tuning of \textbf{s}mall \textbf{T}abular \textbf{F}oundation \textbf{M}odels (\modelname). Specifically, we study nanoscale TabPFN- and TabICL-style variants, pretrained under controlled synthetic prior families and adapted using two complementary mechanisms: structural attention priors derived from knowledge graphs and parameter-efficient low-rank updates. We show that injecting domain-specific structural knowledge during fine-tuning yields meaningful gains over vanilla variants in specialist settings, whereas gains on general-domain tasks are marginal. We further observe that continual fine-tuning of frontier models can trigger collapse of pretrained knowledge and mechanisms.

Beyond Accuracy: Measuring Logical Compliance of Predictive Models

Machine learning models are predominantly evaluated through predictive performance metrics such as ranking quality, prediction error, or classification accuracy. While these metrics effectively quantify how closely predictions match the ground truth, they do not assess whether model outputs respect predefined logical or domain-specific constraints. In high-stakes applications, including healthcare, finance, and autonomous systems, logical consistency can be as critical as predictive accuracy, yet no standard metric captures this dimension. We introduce the Rule Violation Score (RVS), a complementary evaluation metric that quantifies the extent to which a predictive model respects a given set of logical rules, independently of predictive accuracy. RVS treats hard rules (strict constraints) and soft rules (statistical regularities) differently, can be evaluated on any dataset and on any predictive model expressed over a relational vocabulary, and can be computed using SQL queries that are automatically generated for Horn rules. Beyond evaluating models, RVS can also evaluate the logical consistency of training datasets and help identify poorly defined rules. We evaluate RVS on three benchmarks covering knowledge graph link prediction and relational regression, including rule-based, embedding-based, and neuro-symbolic predictive models. Our results demonstrate that two models achieving comparable predictive accuracy can exhibit substantially different levels of logical compliance, revealing differences in model behavior that standard metrics fail to capture.