* Internal representation of floats is logarithmic
* Small processing elements are connected in a mesh network that is made explicit to the programmer
The outcome of the second is that there is more work for a programmer, as details of the hardware are no longer hidden. The tradeoff is that none of the overhead to hide those details is required in hardware anymore. This is not new in other application areas, I'm sure DSP folk (and probably GPU folk) can tell us all about it.
The first gives us very fast arithmetic. What I think he's describing is, instead of working with x and y, you would work with log(x) and log(y). If `x * y = z`, then `log(x) + log(y) = log(z)`. (Additionally, the logarithm of exponentiation is multiplication, so square roots are just bit shifts!) Addition can be done in an approximate manner as well, using a bit more work. This is all from slide 5.
Releasing the hardware from the requirement that it be extremely accurate (he sets up his logarithmic representation to allow for ~1% error) allows him to make all this much smaller. He's shown that it can work "well enough" in some cases, and is working on finding more applications for the tech.
This isn't a free lunch (and isn't proposed as such), and not applicable across all of general purpose computing. But I would think there are lots of areas it could improve; whether it's huge datasets and customers that can afford expensive, custom hardware, or low power application areas that would benefit from approximate methods only a full-blown desktop can handle now (pattern recognition or noise reduction on phones and cameras, for example).