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Equation 1 · Part 4 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Symbol V^*

M=UΣV∗M = U \Sigma V^{*}
V∗V^{*}

What this part means

V∗V^* is one factor in the product that computes the quantity on the left.

Its job in the formula

V∗V^* is one factor in the product that computes the quantity on the left.

The passage around this formula

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 M=UΣV∗M = U \Sigma V^{*}. 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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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