I just got out of the shower, so I'll add my recent showerthought: In a human brain, each neuron is a CPU in and of itself; this means that every neuron in the human brain can run in parallel. In modern computers, the "perceptrons" are virtual, and there are only between 1 and 4 CPUs to allow activation of a specific "perceptron" at a given time.
So if you have a biological brain with 100 billion neurons sitting next to a virtual brain with 100 billion perceptrons, the virtual brain will run 100 billion times slower even with equivalent intelligence.
I think many of the AI algorithms can run on GPUs, where core counts can get into the thousands (still very far from millions). But these are largely independent — the interconnects between GPUs are not on the scale of neurons.
My guess: we develop specialized hardware that, over time, will increasingly resemble organic brain structure.
And if what you care about is running a wide variety of mainstream stats or machine learning algorithms, the "specialized hardware" you mention is the modern GPU, or something very much like it - I don't see any low-hanging fruit that might make some other HW architecture more feasible. Fixed-point compute might get there someday, but it's way too fiddly at present - it's not really clear how to "tweak" mainstream learning algorithms so as to dispense with the large dynamic range that floating point compute provides.