127 citations · 162 across the 9 of their papers we have counts for
11 papers
Encoding syntactic objects and Merge operations in function spaces
Matilde Marcolli, Robert C. Berwick
We provide a mathematical argument showing that, given a representation of lexical items as functions (wavelets, for instance) in some function space, it is possible to construct a…
Parallel Algorithms for Exact Enumeration of Deep Neural Network Activation Regions
Sabrina Drammis, Bowen Zheng, Karthik Srinivasan +3
A feedforward neural network using rectified linear units constructs a mapping from inputs to outputs by partitioning its input space into a set of convex regions where points with…
Syntax-semantics interface: an algebraic model
Matilde Marcolli, Robert C. Berwick, Noam Chomsky
We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation…
Old and New Minimalism: a Hopf algebra comparison
Matilde Marcolli, Robert C. Berwick, Noam Chomsky
In this paper we compare some old formulations of Minimalism, in particular Stabler's computational minimalism, and Chomsky's new formulation of Merge and Minimalism, from the poin…
Mathematical Structure of Syntactic Merge
Matilde Marcolli, Noam Chomsky, Robert Berwick
The syntactic Merge operation of the Minimalist Program in linguistics can be described mathematically in terms of Hopf algebras, with a formalism similar to the one arising in the…
On the Computational Power of RNNs
Samuel A. Korsky, Robert C. Berwick
Recent neural network architectures such as the basic recurrent neural network (RNN) and Gated Recurrent Unit (GRU) have gained prominence as end-to-end learning architectures for…