Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations

Accurately explaining hidden patterns in multi-aspect data has typically been done by leveraging labels and/or accompanying auxiliary metadata. However, labels and auxiliary data may be inaccurate (e.g. nonstandard, inconsistent), insufficient (e.g. static tabular metadata for time-dependent recordings), or unavailable. % We propose \fullmethod (\method), which leverages the knowledge of large language models (LLMs) to explain the hidden patterns in human narratives. \method uses task-agnostic and task-specific prompts to explain extracted co-clustered latent patterns from tensor decomposition. To evaluate these explanations, we test the LLMs on forward and backward inference tasks. % Our demo system is available at https://github.com/dawonahn/ECML_PKDD_AnTenA.

Many biomedical challenges can be posed as tensor completion problems where the observed entries of a multidimensional array (a tensor) are used to impute the missing values. In such settings, incorporating side information about the modes of the tensor, such as gene-gene similarity, can significantly enhance the solutions of the completion problem. Most existing tensor completion methods can only incorporate side information in the form of matrices. In this study, we introduce a novel framework to incorporate side information in the form of tensors. Our new approach, called Coupled Tensor-Tensor Completion (CTTC), leverages the hidden connections among multimodal tensors to improve tensor completion performance. In addition to practical utility, CTTC has theoretical foundations in distance metric learning and group theory. We derive an alternating algorithm to solve the CTTC optimization problem and establish its convergence to a stationary point. Finally, we show that CTTC outperforms state-of-the-art tensor completion methods at predicting drug effects. Results: Compared with other tensor completion methods, including HaLRTC, CTRC, Cell, and NTDDR, CTTC demonstrates superior run-time and RSE tensor completion accuracy on two benchmark datasets, DTD and LINCS.

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent parameters, meaning they disregard weight-space symmetries. To address these issues for the class of tensor-based models, we introduce a weight-based metric, tensor similarity, that is invariant to such symmetries. This metric captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. Empirically, tensor similarity tracks functional training dynamics, such as grokking and backdoor insertion, with higher fidelity than existing metrics. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.