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Inverting Self-Organizing Maps: A Unified Activation-Based Framework
Londei, Alessandro, Benati, Matteo, Lanzieri, Denise, Loreto, Vittorio
Self-Organizing Maps provide topology-preserving projections of high-dimensional data and have been widely used for visualization, clustering, and vector quantization. In this work, we show that the activation pattern of a SOM - the squared distances to its prototypes - can be inverted to recover the exact input under mild geometric conditions. This follows from a classical fact 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 the inversion is well-posed. Building upon this mechanism, we introduce the Manifold-Aware Unified SOM Inversion and Control (MUSIC) update rule, which enables controlled, semantically meaningful trajectories in latent space. MUSIC modifies squared distances to selected prototypes while preserving others, resulting in a deterministic geometric flow aligned with the SOM's piecewise-linear structure. Tikhonov regularization stabilizes the update rule and ensures smooth motion on high-dimensional datasets. Unlike variational or probabilistic generative models, MUSIC does not rely on sampling, latent priors, or encoder-decoder architectures. If no perturbation is applied, inversion recovers the exact input; when a target cluster or prototype is specified, MUSIC produces coherent semantic variations while remaining on the data manifold. This leads to a new perspective on data augmentation and controllable latent exploration based solely on prototype geometry. We validate the approach using synthetic Gaussian mixtures, the MNIST and the Faces in the Wild dataset. Across all settings, MUSIC produces smooth, interpretable trajectories that reveal the underlying geometry of the learned manifold, illustrating the advantages of SOM-based inversion over unsupervised clustering.
Is this man the future of music – or its executioner? AI evangelist Mikey Shulman says he's making pop, not slop
'Music is not a problem to solve' Mikey Shulman, co-founder and CEO of Suno. 'Music is not a problem to solve' Mikey Shulman, co-founder and CEO of Suno. Is this man the future of music - or its executioner? AI evangelist Mikey Shulman says he's making pop, not slop Worth a staggering $2.45bn, Suno is an AI music company that can create a track with just a few prompts. Why is its CEO happy to see it called'the Ozempic of the music industry'?
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Socks, salsa and stand-up comedy... easy ways to find joy in January
Socks, salsa and stand-up comedy... easy ways to find joy in January There is a reason it is called Blue Monday. Slap-bang in the middle of a month that is all about freezing drizzle and self-denial, the third Monday in January is notoriously the gloomiest day of the year. But some of us are fighting back. Here are some ways to find joy among the January gloom. Laughter is a great tonic.
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The mysterious singer with millions of streams - but who (or what) is she?
The mysterious singer with millions of streams - but who (or what) is she? Sienna Rose is having a good month. Three of her dusky, jazz-infused soul songs are in Spotify's Viral Top 50. The most popular, a dreamy ballad called Into The Blue, has been played more than five million times. If she continues on this trajectory, Rose could become one of the year's hottest new stars.
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Bandcamp prohibits music made 'wholly or in substantial part' by AI
Apple's Siri AI will be powered by Gemini Bandcamp prohibits music made'wholly or in substantial part' by AI It added that impersonating other artists or styles using AI is'strictly prohibited.' Bandcamp has addressed the AI slop problem vexing musicians and their fans of late. The company is banning any music or audio on its platform that is wholly or in substantial part made by generative AI, according to its blog . It also clarified that the use of AI tools to impersonate other artists or styles is "strictly prohibited" by policies already in place. Any music suspected to be AI generated may be removed by the Bandcamp team and the company is giving users reporting tools to flag such content. We believe that the human connection found through music is a vital part of our society and culture, and that music is much more than a product to be consumed, the company wrote.
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Music in 2026: Who's releasing new albums and will Oasis play Knebworth?
Music in 2026: Who's releasing new albums and will Oasis play Knebworth? As the sun sets on 2025, all the year-end lists have been published and it's time to look forward to what 2026 has in store. In many ways, the last 12 months have felt transitional. With relatively few A-list releases, and a Brat-shaped hole in the summer, music seemed to split in two. The charts were agonisingly static: Just three songs held the number one spot hostage for half the year: Taylor Swift's Fate of Ophelia, Huntr/x's Golden, and Alex Warren's Ordinary (never has a song been so aptly titled).
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