Given \(M, N\), matrices, let

\[m_{ij} = \lfloor \log_2 M_{ij} \rfloor \]

and similarly for \(n\). Then \(M_{ij} \approx 2^{m_{ij}}\). Define \(m \star n\) by

\[(m \star n)_{ij} = \max_k (m_{ik} + n_{kj}), \]

This gives us an approximation \((M \cdot N)_{ij}\approx 2^{(m \star n)_{ij}}\)

Has anyone here encountered this before? It's essentially floating point matrix multiplication without the mantissa bits, but I'm wondering if there are any papers or resources dealing with it.

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I say "essentially", but I just mean "similar to"

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