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. Author manuscript; available in PMC: 2026 Aug 12.

Published in final edited form as: Int Conf Learn Represent. 2026;2026:84620–84648.

Table 1.

Impact of missingness on multimodality information for bitwise logic operators. Parentheses denote standard deviation across batches.

		AUROC			Information Decomposition
		$X_{1}$	$X_{2}$	$X_{1} + X_{2}$	Unique 1	Unique 2	Shared	Complementary
AND	Oracle	0.83 (0.01)	0.84 (0.01)	1.00 (0.00)	0.05 (0.00)	0.03 (0.00)	0.26 (0.00)	0.47 (0.00)
	Observed	0.66 (0.01)	0.93 (0.01)	1.00 (0.00)	0.44 (0.00)	0.00 (0.00)	0.15 (0.00)	0.36 (0.00)
	ICYM²I	0.83 (0.01)	0.85 (0.02)	1.00 (0.00)	0.03 (0.00)	0.03 (0.00)	0.27 (0.00)	0.45 (0.00)
OR	Oracle	0.84 (0.01)	0.83 (0.01)	1.00 (0.00)	0.04 (0.00)	0.05 (0.00)	0.27 (0.00)	0.46 (0.00)
	Observed	0.95 (0.01)	0.77 (0.01)	1.00 (0.00)	0.01 (0.00)	0.15 (0.00)	0.10 (0.00)	0.23 (0.00)
	ICYM²I	0.85 (0.02)	0.82 (0.01)	1.00 (0.00)	0.03 (0.00)	0.02 (0.00)	0.27 (0.00)	0.50 (0.00)
XOR	Oracle	0.51 (0.02)	0.49 (0.01)	1.00 (0.00)	0.00 (0.00)	0.00 (0.00)	0.00 (0.00)	0.99 (0.00)
	Observed	0.52 (0.02)	0.80 (0.02)	1.00 (0.00)	0.34 (0.00)	0.07 (0.00)	−0.07 (0.00)	0.62 (0.00)
	ICYM²I	0.53 (0.03)	0.49 (0.03)	1.00 (0.00)	0.00 (0.00)	0.00 (0.00)	0.01 (0.00)	0.96 (0.00)