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Ranks
The ranks of the weight tensor are:
- rank-3 tensor \(W\)
all weights in the neural network - rank-2 matrix \(W^{[i]}\)
all weights of all neurons in the \(i\)-th layer - rank-1 row vector1 \(w^{[i]}_{j}\)
all weights of the \(j\)-th neuron in the \(i\)-th layer - rank-0 scalar \(w^{[i](k)}_{j}\)
the \(k\)-th weight of the \(j\)-th neuron in the \(i\)-th layer.
Footnotes:
1
\(w^{[i]}_{j}\) is a row vector.