We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers.

Medical Lay Language Generation (MLLG) plays a vital role in improving the accessibility of complex scientific content for broader audiences. Recent literature to MLLG commonly employ parameter-efficient fine-tuning methods such as LowRank Adaptation (LoRA) to fine-tuning large language models (LLMs) using paired expert-lay language datasets. However, LoRA struggles with the challenges posed by multi-source heterogeneous MLLG datasets. Specifically, through a series of exploratory experiments, we reveal that standard LoRA fail to meet the requirement for semantic fidelity and diverse lay-style generation in MLLG task. To address these limitations, we propose Magical, an asymmetric LoRA architecture tailored for MLLG under heterogeneous data scenarios. Magical employs a shared matrix Afor abstractive summarization, along with multiple isolated matrices B for diverse lay-style generation. To preserve semantic fidelity during the lay language generation process, Magical introduces a Semantic Invariance Constraint to mitigate semantic subspace shifts on matrix A. Furthermore, to better adapt to diverse lay-style generation, Magical incorporates the Recommendation-guided Switch, an externally interface to prompt the LLM to switch between different matrices B. Experimental results on three real-world lay language generation datasets demonstrate that Magical consistently outperforms prompt-based methods, vanilla LoRA, and its recent variants, while also reducing trainable parameters by 31.66%.

The code for our experiments is available at https://github.com/AndyShih12/HyperSPN. To examine the merits of HyperSPNs as discussed in Section 3, we construct a hand-crafted dataset to test the three types of models described in Figure 4: SPN-Large, SPN-Small, and HyperSPN. The hand-crafted dataset is procedurally generated with 256 binary variables and 10000 instances, broken into train/valid/test splits at 70/10/20%. The generation procedure is designed such that the correlation between variable i and j is dependent on the path length between leaves i and j of a complete binary tree over the 256 variables. The exact details can be found in our code.

Coupled norms have emerged as a convex method to solve coupled tensor completion. A limitation with coupled norms is that they only induce low-rankness using the multilinear rank of coupled tensors. In this paper, we introduce a new set of coupled norms known as coupled nuclear norms by constraining the CP rank of coupled tensors. We propose new coupled completion models using the coupled nuclear norms as regularizers, which can be optimized using computationally efficient optimization methods. We derive excess risk bounds for proposed coupled completion models and show that proposed norms lead to better performance. Through simulation and real-data experiments, we demonstrate that proposed norms achieve better performance for coupled completion compared to existing coupled norms.

Recognizing that the language modality typically contains dense sentiment information, we consider it as the dominant modality and present an innovative Language-dominated Noise-resistant Learning Network (LNLN) to achieve robust MSA.