Lemma 5 ([Coordinate expansion]). Assume Equation and fix an even dimension as in Lemma 4 ([Rank-layer limit]). For fixed type laws and activation laws, t_ I,J (W_q), =1+ ∑_ a:I→ A\,, b:J→ B (∏_ i∈I π_ a(i) ) (∏_ j∈J ν_ b(j) …

Lemma 5 ([Coordinate expansion]). Assume Equation and fix an even dimension as in Lemma 4 ([Rank-layer limit]). For fixed type laws and activation laws, t_ I,J (W_q), =1+ ∑_ a:I→ A\,, b:J→ B (∏_ i∈I π_ a(i) ) (∏_ j∈J ν_ b(j) )C_A(a,b)+o(1). The corresponding formula for W_q^ has type maps b:I→ B , a:J→ A and the corner factors A_ a(j)b(i) .