A Framework for Directed Acyclic Hypergraph Learning

Continuous optimization methods for learning Directed Acyclic Graphs (DAGs) operate on weighted adjacency matrices and are therefore limited to pairwise causal relationships. We propose a framework for learning Directed Acyclic Hypergraphs (DAHGs) from observational data, capturing joint parental influences that pairwise models cannot represent. Our approach rests on three components: (i) a generalized linear structural equation model (SEM) with multiplicative interaction terms whose non-zero weights correspond one-to-one with directed hyperedges; (ii) a weighted adjacency tensor representation whose acyclicity is characterized via nilpotency under the tensor t-product; and (iii) a differentiable acyclicity constraint derived through the Fourier decomposition of the t-product, which reduces tensor nilpotency to slice-wise matrix nilpotency and enables least-squares learning via the augmented Lagrangian method.

Towards Secure and Private Language Models for Nuclear Power Plants

This paper introduces a domain-specific Large Language Model for nuclear applications, built from the publicly accessible Essential CANDU textbook. Drawing on a compact Transformer-based architecture, the model is trained on a single GPU to protect the sensitive data inherent in nuclear operations. Despite relying on a relatively small dataset, it shows encouraging signs of capturing specialized nuclear vocabulary, though the generated text sometimes lacks syntactic coherence. By focusing exclusively on nuclear content, this approach demonstrates the feasibility of in-house LLM solutions that align with rigorous cybersecurity and data confidentiality standards. Early successes in text generation underscore the model's utility for specialized tasks, while also revealing the need for richer corpora, more sophisticated preprocessing, and instruction fine-tuning to enhance domain accuracy. Future directions include extending the dataset to cover diverse nuclear subtopics, refining tokenization to reduce noise, and systematically evaluating the model's readiness for real-world applications in nuclear domain.