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Equation 3 · Part 6 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

subscript

Ij=∑iVi GijI_j = \sum_i V_i\, G_{ij}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

The multiplication step follows directly from two textbook circuit laws. Apply a voltage ViV_i simultaneously to each row i, representing the i-th component of an input vector. By Ohm’s law, the cell at row i and column j draws a current ViV_i times its conductance GiG_ij. By Kirchhoff’s current law, every current flowing into a given column sums automatically on that column’s wire, so the total current collected at the bottom of column j is Ij=∑iVi GijI_j = \sum_i V_i\, G_{ij}. which is precisely the j-th component of the matrix-vector product between the input vector and the conductance matrix stored across the array — computed in one step, in parallel across every cell, using nothing but the physics of the…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.