Multiple solutions with same minima in MLP with same weights
If one permutes the connections of the hidden layer ($d!$ ways to do that), and move and rename connections appropriately, then one effectively has the same MLP with the exact same minima, yet the configuration has changed (in a trivial sense). Thus there are (at least) $d!$ configurations only trivialy different with the exact same minima.
To see it in your notation, effectively the hidden layer output is the following sum:
$$O_{\text{hidden}} = \sum_{i=1}^d w_{\pi_i} \cdot x + b_{\pi_i}$$
Where $\pi_i$ is some order of the connections. For example $\pi_i = i$
But for $d$ items there are $d!$ permutations thus $d!$ order functions $\pi(i) = \pi_i$. Yet the difference is only in re-ordering the configuration and is trivial. The rest follow from that.
This is one reason why Neural Networks are non-convex models.
See also: Explanation of why Neural Networks are non convex