Summary: We consider normalized Boolean circuits that use binary operations of disjunction and conjunction, and unary negation, with the restriction that negation can be only applied to input variables. We derive a lower bound trade-off between the size of normalized Boolean circuits computing Boolean semi-disjoint bilinear forms and their conjunction-depth (i.e., the maximum number of and-gates on a directed path to an output gate). In particular, we show that any normalized Boolean circuit of at most \(\epsilon \log n\) conjunction-depth computing the \(n\)-dimensional Boolean vector convolution has \(\Omega( n^{2 - 4 \epsilon})\) and-gates. For Boolean matrix product, we derive even a stronger lower-bound trade-off. Instead of conjunction-depth we use the negation-dependent conjunction-depth, where one counts only and-gates whose each direct predecessor has a (not necessarily direct) predecessor representing a negated input variable. We show that if a normalized Boolean circuit of at most \(\epsilon \log n\) negation-dependent conjunction-depth computes the \(n \times n\) Boolean matrix product then the circuit has \(\Omega( n^{3 - 2 \epsilon})\) and-gates. We complete our lower-bound trade-offs for the Boolean convolution and matrix product with upper-bound trade-offs of similar form yielded by the known fast algebraic algorithms.