Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elements in the batch, i.e. {a + b + c, d} = {a, d} + {b, d} + {c, d}. Similarly for the second component.
Eventually ML folks will discover fiber bundles.
Could this be used for batch filtering?
Lie brackets are bi-linear so whatever you do per example automatically carries over to sums, the bracket for the batch is just the pairwise brackets for elements in the batch, i.e. {a + b + c, d} = {a, d} + {b, d} + {c, d}. Similarly for the second component.