I've studied Numenta's CLA's, previously HTM's, as well as established ML approaches fairly in-depth over the past couple of years. Hawkins definitely takes a new approach to neural networks and focuses more on modeling the brain's biology rather than building on known artificial neural network concepts. HTM's did incorporate bayesian nets, but have been abandoned, probably with the departure of Dileep George, who now runs http://vicarious.com/.

However, Hawkins work is similar to Deep Neural Nets in that both are unsupervised neural nets (unlike perceptrons and back-prop) and both aim to represent data as sparse representations. Also, here's a similar question I answered on Quora: http://www.quora.com/Machine-Learning/Does-Numenta-build-on-...

In addition, Numenta does use CLA's to solve real problems for customers: https://www.groksolutions.com/solutions.html

Finally, Hawkins' book, On Intelligence, has at least inspired researchers like Stanford's Andrew Ng at a philosophical level which he talks about IIRC in his online ML course. https://class.coursera.org/ml/class

Here's an independent review of the older version of the algorithm: http://bias.csr.unibo.it/maltoni/HTM_TR_v1.0.pdf

"Systematic experiments on three line-drawing datasets have been carried out to better understand HTM peculiarities and to extensively compare it against other well-know pattern recognition approaches. Our results prove the effectiveness of the new algorithms introduced and that HTM, even if still in its infancy, compares favorably with other existing technologies."