A long conversation between two people can be condensed into a few key phrases that preserve the essence. That is exactly how a macrovariable works: temperature stands in for billions of moving molecules, and sea level for thousands of waves. But how do you find such phrases in a vast stream of data without relying on intuition?

Scientists have built a causal autoencoder: a pair of neural networks that learn simultaneously. The first network compresses ocean temperature data into a few numbers. The second does the same with air pressure data. Then each network tries to predict the full dataset of the other from its own compressed numbers. This approach is like a translator who listens to a long conversation and produces a short note, from which another person can reconstruct the entire meaning.

After training, the algorithm checks whether a causal relationship can be established between the discovered variables. To do this, it looks for a transformation such that one variable becomes a simple function of the other plus random noise. If the noise is independent of the cause, then the link is directed from the first variable to the second. On synthetic data with 64 dimensions, the algorithm found exactly two macrovariables, as intended. For one pair, it correctly identified the cause: the estimate of noise dependence on the presumed cause was 0.32 in one direction and 3.15 in the reverse.

On real climate data, the algorithm identified two patterns corresponding to the warm pool and cold tongue of El Niño. It could not find a causal link between them, which is consistent with the weekly scale of the data: over such a short period, one phenomenon does not have time to cause the other.

Previously, finding macrovariables was a matter of scientific intuition. Now the neural network itself finds variables that preserve all the mutual information between two datasets. This paves the way for automatic extraction of meaningful patterns in climatology, neuroscience, and other fields where data are high-dimensional and causal links lack a natural numerical scale. The translator no longer needs to know the language; it learns to compress meaning on its own.