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.

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thaumasiotes 5 hours ago | parent [-]

> Similarly for the second component.

Hmm.

{a + b, c + d} = {a, c + d} + {b, c + d} = {a, c} + {a, d} + {b, c} + {b, d}.

{a + b + c, x + y + z} = {a, x + y + z} + {b, x + y + z} + {c, x + y + z} = (a sum of nine direct brackets).

This doesn't look like it will scale well.

	▲	measurablefunc 5 hours ago \| parent [-]
		Then don't use the Lie bracket. All bilinear forms scale the same way.