Pattern Theory: The Mathematics of Perception (2002)
arxiv.org
arxiv.org
Has anyone here worked through it? It seems like much of it is rooted in methods that have kind of fallen by the wayside due to the incredible success of modern techniques. I’d also be very interested to know David Mumford’s thoughts on modern deep learning and how he thinks it fits into his pattern theory framework. It looks like he goes into this to some extent in a 2019 blog post on whether AI can achieve consciousness [1] and another on the convergence between ML methods and the human brain [2].
[0] https://www.routledge.com/Pattern-Theory-The-Stochastic-Anal...
[1] https://www.dam.brown.edu/people/mumford/blog/2019/conscious...
[2] https://www.dam.brown.edu/people/mumford/blog/2020/Astonishi...
TBH, that's one reason I find this interesting to begin with. It's a pet interest (obsession?) of mine to look for ideas that have been "left behind" and forgotten about prematurely for whatever reason. I suspect that from time to time there's a technique / idea / whatever lying out there in the sands of history just waiting for somebody to pick it up, dust it off, and turn it into something amazing.
Researchers will find Neurocomputing an essential guide to the concepts employed in this field that have been taken from disciplines as varied as neuroscience, psychology, cognitive science, engineering, and physics. A number of these important historical papers contain ideas that have not yet been fully exploited, while the more recent articles define the current direction of neurocomputing and point to future research. Each article has an introduction that places it in historical and intellectual perspective.
Yes, I picked that up (both volumes) late last year. Same for Neural Smithing[1] which I just acquired a copy of about two days ago. I also read that Talking Nets: An Oral History of Neural Networks[2] book last year. Lots of threads to follow based on that. Actually, now that I think about it, I think that's where I found out about Neurocomputing.
[1]: https://mitpress.mit.edu/9780262527019/neural-smithing/
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=...
Like the breakthrough application was pattern recognition, and for low numbers of nodes (synapses?) you can see how it becomes more sophisticated as the net grows. Like it doesn't just explain human pattern recognition but weak nets model like chicken pattern recognition.
>Perhaps the ultimate dream is a fully unsupervised learning machine which is given only signals from the world and which finds their statistically significant patterns with no assistance: something like a baby in its first 6 months.
Keep in mind how a baby does with some supervision and assistance rather than none.
Until dreams come true I would think different levels of supervision and assistance would be key to somewhat functional operation.
Once perfection is achieved then the ideal judgement could be made about overall system maturity, and people should be able to plainly see if it is wise to go with less supervision or assistance, and to what degree.
- Pattern theory
- Abductive logic
- Machine learning
Do they converge?