# Given an input $x \in R^{1\times d}$ and a network with $s$ hidden layers, is the time complexity of the forward pass $O(d^{2}s)$? [duplicate]

I have a neural network that takes as an input a vector of $$x \in R^{1\times d}$$ with $$s$$ hidden layers and each layer has $$d$$ neurons (including the output layer).

If I understand correctly the computational complexity of the forward pass of a single input vector would be $$O(d^{2}(s-1))$$, where $$d^{2}$$ is the computational complexity for the multiplication of the output of each layer and the weight matrix, and this happens $$(s-1)$$ times, given that the neural network has $$s$$ layers. We can ignore the activation function because the cost is $$O(d)$$.

So, if I am correct so far, and the computational complexity of the forward pass is $$O(d^{2}(s-1))$$, is the following correct?

$$O(d^{2}(s-1)) = O(d^{2}s + d^{2}) = O(d^{2}s)$$

Would the computational complexity of the forward pass for this NN be $$O(d^{2}s)$$?

• Welcome to SE:AI! This question has been closed as a duplicate. Please review the linked Q&A. (If not a duplicate, you can explain and submit for re-opening.) – DukeZhou Dec 2 '19 at 21:03