Symbol M
M is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
An MZI mesh built this way implements a unitary matrix: a transformation that preserves the total optical power passing through it. Most matrices a neural-network layer actually needs are not unitary. The standard fix is a singular value decomposition, writing the desired matrix M as . where U and V* are unitary matrices, each realized by its own MZI mesh, and Σ is a diagonal matrix of non-negative singular values, realized by a bank of tunable optical attenuators placed between the two meshes. Light entering the chip passes through the first mesh, has each of its modes independently attenuated by the corresponding singular value, then passes through the second mesh — end…
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Symbol U
U is one factor in the product that computes the quantity on the left.
Read this term in its guide →Symbol Sigma
Sigma is one factor in the product that computes the quantity on the left.
Read this term in its guide →Symbol V^*
is one factor in the product that computes the quantity on the left.
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Published contexts (1)
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Equation 1 · Future Hardware
How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
An MZI mesh built this way implements a unitary matrix: a transformation that preserves the total optical power passing through it. Most matrices a neural-network layer actually needs are not unitary. The standard fix is a singular value decomposition, writing the desired matrix M as . where U and V* are unitary matrices, each realized by its own MZI mesh, and Σ is a diagonal matrix of non-negative singular values, realized by a bank of tunable optical attenuators placed between the two meshes. Light entering the chip passes through the first mesh, has each of its modes independently attenuated by the corresponding singular value, then passes through the second mesh — end…
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