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[2601.13851] Inverting Self-Organizing Maps: A Unified Activation-Based Framework
Summary
This paper presents a novel framework for inverting Self-Organizing Maps (SOMs) to recover original inputs from activation patterns, introducing the MUSIC update rule for controlled transitions in high-dimensional data.
Why It Matters
The study addresses a significant gap in the application of Self-Organizing Maps as generative models, offering a new method that enhances interpretability and control in high-dimensional data analysis. This could have implications for various fields, including data visualization and machine learning.
Key Takeaways
- Introduces a method to invert Self-Organizing Maps to recover original inputs.
- Presents the MUSIC update rule for generating semantically meaningful trajectories.
- Demonstrates high classifier confidence and sharp intermediate images in experiments.
Computer Science > Machine Learning arXiv:2601.13851 (cs) [Submitted on 20 Jan 2026 (v1), last revised 23 Feb 2026 (this version, v2)] Title:Inverting Self-Organizing Maps: A Unified Activation-Based Framework Authors:Alessandro Londei, Matteo Benati, Denise Lanzieri, Vittorio Loreto View a PDF of the paper titled Inverting Self-Organizing Maps: A Unified Activation-Based Framework, by Alessandro Londei and 3 other authors View PDF HTML (experimental) Abstract:Self-Organizing Maps (SOMs) provide topology-preserving projections of high-dimensional data, yet their use as generative models remains largely unexplored. We show that the activation pattern of a SOM -- the squared distances to its prototypes -- can be \emph{inverted} to recover the exact input, following from a classical result in Euclidean distance geometry: a point in $D$ dimensions is uniquely determined by its distances to $D{+}1$ affinely independent references. We derive the corresponding linear system and characterize the conditions under which inversion is well-posed. Building on this mechanism, we introduce the \emph{Manifold-Aware Unified SOM Inversion and Control} (MUSIC) update rule, which modifies squared distances to selected prototypes while preserving others, producing controlled, semantically meaningful trajectories aligned with the SOM's piecewise-linear structure. Tikhonov regularization stabilizes the update and ensures smooth motion in high dimensions. Unlike variational or diffusion-based gen...