My theory is that, instead, the brain is a super-duper complex neural network with some differences about how the update of the weights happen :) Let me explain:
Albeit true that our brain is much slower than a modern CPU in terms of ops/s, every neuron is connected to up to 10000 other neurons[0]. And we have something around 100 billion neurons in our brains. This means that the number of synapses is between 100 and 1000 trillions.
If we assume that every synapse can be considered like a "weight" in a neural network, we have a model that is much much bigger than anything developed to date. Moreover, the topology of said neural network is not a simple stack of layers, but much more complex like a super intricated residual network.
Finally, the brain is not using backpropagation to update the mentioned weights/synapses' strength, but instead is based on how often said synapses fire.
[0]: http://www.human-memory.net/brain_neurons.html