Bio: My research (see Research tab) focuses on integrating symbolic and neural network computation for modeling reasoning and, especially, grammar in the human mind/brain. The work is formal and computational, with emerging applications to neuroscience and applied natural language processing. My research has primarily addressed issues of representation and processing rather than learning. Principal contributions (see Publications tab) are to linguistic theory, the theory of vectorial neural network computation, and the philosophical foundations of cognitive science.
During Fall semesters I am on leave from Johns Hopkins, working at Microsoft Research in Redmond, Washington (for a non-technical synopsis of some of my recent work there, see this link: Mind/Brain Networks). Prior to joining the faculty of the Cognitive Science Department at Johns Hopkins, I was a professor in the Computer Science Department and Institute of Cognitive Science at the University of Colorado Boulder. I had been a postdoc at the Center for Cognitive Science at the University of California at San Diego, where I was a founding member of the Parallel Distributed Processing Research Group and worked with Dave Rumelhart, James McClelland and Geoff Hinton. (I also contributed to the User-Centered System Design group led by Don Norman.) My degrees are an A.B. in Physics from Harvard and, from Indiana University, Bloomington, a M.S. in Physics and a Ph.D. in Mathematical Physics. (CV)
Goal
Unification of the sciences of mind & brain through integration of
- compositional, structured, symbolic computation
- at the core of many successful classical theories of the mind
- in particular, the theory of language
- a branch of discrete mathematics
- dynamic, distributed, vectorial connectionist computation
- at the core of the theory of neural networks, crucial for
- computational models of the brain
- emergentist models of the mind
- contemporary machine learning and Artificial Intelligence
- a branch of continuous mathematics
Current
The theory, and application to language, of Gradient Symbolic Computation, a new cognitive architecture in which a single computational system can simultaneously be described formally at two levels:
- a higher ‘abstract mental’ level, where
- data
- consist of symbols that have partial degrees of presence — gradient activity levels
- which blend together to form Gradient Symbol Structures (such as gradient trees)
- processing
- is algebraic operations on vectors and tensors
- a lower ‘abstract neural’ level, where
- data
- consist of distributed activation vectors over many model neurons
- which superimpose to implement Gradient Symbol Structures…
- processing
- is probabilistic spreading of activation (governed by stochastic differential equations)
- through networks with numerically weighted interconnections
- AS.050.326/626 Foundations of Cognitive Science.
- AS.050.372/672 Foundations of Neural Network Theory
- AS.050.829. Research Seminar on Formal Theory in Cognitive Science
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January 2011 , MIT Press
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Role: co-author
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Géraldine Legendre, co-author
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January 2011 , MIT Press
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Role: co-author
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Géraldine Legendre, co-author
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November 1993 , Lawrence Erlbaum Publishers
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Role: co-editor
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January 1992 , Marietti/Cambridge University Press
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Role: author
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