ICTSS Playground

Poke at a test matrix, watch the spectral complexity react.

Published result · Interactive intuition The linked paper reports the evaluated result. This playground illustrates the spectral metrics; it is not a reproduction of the study or a proof of the relationship.

The ICTSS 2024 Best Paper evaluated spectral matrix-complexity metrics as predictors of combinatorial t-way coverage.

The intuition is that a random-looking matrix covers more combinations than a structured one, and its singular value spectrum is visibly flatter.

Click cells to toggle bits. Try making a highly structured matrix vs. a random one and watch how the singular value distribution changes.

Rows 6 Cols 5

Click any cell to toggle · Stripe = maximally structured

SVD Entropy

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Spectral Radius σ₁

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Rank

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What you’re seeing: The singular values of the matrix are the square roots of the eigenvalues of $A^T A$. A flat spectrum (high SVD entropy) means the spectral mass is spread across more dimensions; a peaked spectrum (low entropy, high $\sigma_1$) means it is concentrated. The published study tested how metrics like these predict combinatorial t-way coverage without enumerating every combination. This toy does not calculate coverage, so the relationship itself is not demonstrated here.