In a hall with a hundred instruments, a symphony is playing, but the conductor is hidden behind a screen. The scientist hears only the notes played by the instruments and wants to understand who sets the rhythm. Scientific data resembles such an orchestra: we record instrument readings but do not see the hidden mechanisms that drive them. MOSAIC learns from these recordings to find the conductors and explain which instruments they influence.

Previously, it was unclear how to transfer the interpretability of observed variables to hidden factors without losing identifiability. MOSAIC solves this in two steps. First, a variational autoencoder compresses the data and extracts hidden factors, ensuring they are recovered uniquely. Then, the dense decoder is replaced with an additive sparse one: for each hidden factor, the model finds a small set of observed variables it influences. This is like saying after listening to the symphony: "The conductor raises the baton, the flutes come in, and the violins stay silent."

The method has been tested on different systems. In RNA molecular dynamics, MOSAIC found a factor related to the tetraloop, matching a known folding mechanism. On solar wind, climate data, a chemical process, and a tokamak, the method correctly identified expected variable groups in 12 out of 12 runs. This means MOSAIC not only finds hidden factors but also explains them through understandable physical quantities.

Today, MOSAIC can be applied to space weather, fusion diagnostics, climate monitoring, and chemical process safety. Where manual labeling is impossible, the method automatically detects mechanisms. In the future, it is planned to extend it to multi-class regimes and integrate it with causal discovery methods within modules. The symphony of complex systems becomes more audible when we know who is conducting.