[sarosh]

The author, David Mumford, is known for his distinguished work in algebraic geometry, and was awarded the Fields Medal in 1974. [2]

Pattern theory was formulated by Ulf Grenander to describe knowledge of the world as patterns. [3]

Prof. Mumford explains that "[s]everal essential ideas brought me to realize how Grenander's Pattern Theory was the right way to understand almost all cognitive skills and especially vision. One was the emphasis on pattern synthesis as well as pattern analysis." [0]. Second, "was that natural signals given by functions f vary not only by random additive perturbations but often by composition with random rearrangements of their domain. The resulting probability distribution in the vector space of signals is nothing like Gaussian. Its support is usually a twisted snakey submanifold. This puts the lie to all simplistic Gaussian pattern recognition algorithms." [0]. And third, "graphical structures were everywhere in the representations of ideas in cognitive domains" [0].

His most recent work seems to be "Pattern Theory, the Stochastic Analysis of Real World Signals" [1]

[0] https://www.dam.brown.edu/people/mumford/vision/pattern.html

[1] https://www.amazon.com/dp/1568815794/ref=sr_1_1?ie=UTF8&qid=...

[2] https://en.wikipedia.org/wiki/David_Mumford

[3] https://en.wikipedia.org/wiki/Pattern_theory

[mindcrime]

Something I stumbled across in the last day or two brought Ulf Grenander[1] and his idea of "Pattern Theory" to my attention, and I've been going down a bit of a rabbit-hole the last couple of days digging into this. Discovering David Mumford's work was especially interesting given that he is, as you say, a Field Medalist. Not to mention his also being a MacArthur Fellow and a recipient of a National Medal of Science. Not to go all "appeal to authority", but if he thinks this is valuable territory, then it's probably worth a little bit of my time exploring it.

[1]: https://en.wikipedia.org/wiki/Ulf_Grenander

[steppi]

Would you consider doing a write-up somewhere after getting further into your investigation of pattern theory? I'd certainly be interested in a distillation of any insights you find and I imagine others would too.