KAN-Matrix: Visualizing Nonlinear Pairwise and Multivariate Contributions for Physical Insight

• URL: http://arxiv.org/abs/2512.15755v1
• Date: Fri, 12 Dec 2025 02:04:53 GMT
• Title: KAN-Matrix: Visualizing Nonlinear Pairwise and Multivariate Contributions for Physical Insight
• Authors: Luis A. De la Fuente, Hernan A. Moreno, Laura V. Alvarez, Hoshin V. Gupta,
• Abstract summary: We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance interpretability and parsimony.<n>We present two interpretable, color-coded visualization tools: the Pairwise KAN Matrix (PKAN) and the Multivariable KAN Contribution Matrix (MKAN)
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Interpreting complex datasets remains a major challenge for scientists, particularly due to high dimensionality and collinearity among variables. We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance interpretability and parsimony beyond what traditional correlation analyses offer. We present two interpretable, color-coded visualization tools: the Pairwise KAN Matrix (PKAN) and the Multivariate KAN Contribution Matrix (MKAN). PKAN characterizes nonlinear associations between pairs of variables, while MKAN serves as a nonlinear feature-ranking tool that quantifies the relative contributions of inputs in predicting a target variable. These tools support pre-processing (e.g., feature selection, redundancy analysis) and post-processing (e.g., model explanation, physical insights) in model development workflows. Through experimental comparisons, we demonstrate that PKAN and MKAN yield more robust and informative results than Pearson Correlation and Mutual Information. By capturing the strength and functional forms of relationships, these matrices facilitate the discovery of hidden physical patterns and promote domain-informed model development.

Related papers

• Platform for Representation and Integration of multimodal Molecular Embeddings [43.54912893426355]
  Existing machine learning methods for molecular embeddings are restricted to specific tasks or data modalities.<n>Existing embeddings capture largely non-overlapping molecular signals, highlighting the value of embedding integration.<n>We propose Platform for Representation and Integration of multimodal Molecular Embeddings (PRISME) to integrate heterogeneous embeddings into a unified multimodal representation.
  arXiv  Detail & Related papers  (2025-07-10T01:18:50Z)
• Information-theoretic Quantification of High-order Feature Effects in Classification Problems [0.19791587637442676]
  We present an information-theoretic extension of the High-order interactions for Feature importance (Hi-Fi) method.<n>Our framework decomposes feature contributions into unique, synergistic, and redundant components.<n>Results indicate that the proposed estimator accurately recovers theoretical and expected findings.
  arXiv  Detail & Related papers  (2025-07-06T11:50:30Z)
• Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models [3.0040661953201475]
  This paper studies the task of estimating heterogeneous treatment effects in causal panel data models.<n>We propose a novel CoAdjusted Deep Causal Learning (Co) for panel data models, that employs flexible model structures and powerful neural network architectures.
  arXiv  Detail & Related papers  (2025-05-26T21:45:43Z)
• LLM Enhancers for GNNs: An Analysis from the Perspective of Causal Mechanism Identification [19.389891710579022]
  We study the use of large language models (LLMs) as feature enhancers to optimize node representations, which are then used as inputs for graph neural networks (GNNs)<n>Building on the analytical results, we design a plug-and-play optimization module to improve the information transfer between LLM enhancers and GNNs.
  arXiv  Detail & Related papers  (2025-05-13T06:29:25Z)
• Beyond DAGs: A Latent Partial Causal Model for Multimodal Learning [80.44084021062105]
  We propose a novel latent partial causal model for multimodal data, featuring two latent coupled variables, connected by an undirected edge, to represent the transfer of knowledge across modalities.<n>Under specific statistical assumptions, we establish an identifiability result, demonstrating that representations learned by multimodal contrastive learning correspond to the latent coupled variables up to a trivial transformation.<n>Experiments on a pre-trained CLIP model embodies disentangled representations, enabling few-shot learning and improving domain generalization across diverse real-world datasets.
  arXiv  Detail & Related papers  (2024-02-09T07:18:06Z)
• Role of Structural and Conformational Diversity for Machine Learning Potentials [4.608732256350959]
  We investigate the relationship between data biases and model generalization in Quantum Mechanics. Our results reveal nuanced patterns in generalization metrics. These findings provide valuable insights and guidelines for QM data generation efforts.
  arXiv  Detail & Related papers  (2023-10-30T19:33:12Z)
• Leveraging Diffusion Disentangled Representations to Mitigate Shortcuts in Underspecified Visual Tasks [92.32670915472099]
  We propose an ensemble diversification framework exploiting the generation of synthetic counterfactuals using Diffusion Probabilistic Models (DPMs) We show that diffusion-guided diversification can lead models to avert attention from shortcut cues, achieving ensemble diversity performance comparable to previous methods requiring additional data collection.
  arXiv  Detail & Related papers  (2023-10-03T17:37:52Z)
• Latent Variable Multi-output Gaussian Processes for Hierarchical Datasets [0.8057006406834466]
  Multi-output Gaussian processes (MOGPs) have been introduced to deal with multiple tasks by exploiting the correlations between different outputs. This paper proposes an extension of MOGPs for hierarchical datasets.
  arXiv  Detail & Related papers  (2023-08-31T15:52:35Z)
• Causal Inference via Nonlinear Variable Decorrelation for Healthcare Applications [60.26261850082012]
  We introduce a novel method with a variable decorrelation regularizer to handle both linear and nonlinear confounding. We employ association rules as new representations using association rule mining based on the original features to increase model interpretability.
  arXiv  Detail & Related papers  (2022-09-29T17:44:14Z)
• coVariance Neural Networks [119.45320143101381]
  Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. We propose a GNN architecture, called coVariance neural network (VNN), that operates on sample covariance matrices as graphs. We show that VNN performance is indeed more stable than PCA-based statistical approaches.
  arXiv  Detail & Related papers  (2022-05-31T15:04:43Z)
• Learning from few examples with nonlinear feature maps [68.8204255655161]
  We explore the phenomenon and reveal key relationships between dimensionality of AI model's feature space, non-degeneracy of data distributions, and the model's generalisation capabilities. The main thrust of our present analysis is on the influence of nonlinear feature transformations mapping original data into higher- and possibly infinite-dimensional spaces on the resulting model's generalisation capabilities.
  arXiv  Detail & Related papers  (2022-03-31T10:36:50Z)
• Variational Interpretable Learning from Multi-view Data [2.687817337319978]
  DICCA is designed to disentangle both the shared and view-specific variations for multi-view data. Empirical results on real-world datasets show that our methods are competitive across domains.
  arXiv  Detail & Related papers  (2022-02-28T01:56:44Z)
• Model-agnostic multi-objective approach for the evolutionary discovery of mathematical models [55.41644538483948]
  In modern data science, it is more interesting to understand the properties of the model, which parts could be replaced to obtain better results. We use multi-objective evolutionary optimization for composite data-driven model learning to obtain the algorithm's desired properties.
  arXiv  Detail & Related papers  (2021-07-07T11:17:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.