35 citations · 189 across the 40 of their papers we have counts for
45 papers
Bispectral Neural Networks
Sophia Sanborn, Christian Shewmake, Bruno Olshausen +1
We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the spac…
Biologically Plausible Sequence Learning with Spiking Neural Networks
Zuozhu Liu, Thiparat Chotibut, Christopher Hillar +1
Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (…
Equivariant Gröbner bases
Christopher J. Hillar, Robert Krone, Anton Leykin
Algorithmic computation in polynomial rings is a classical topic in mathematics. However, little attention has been given to the case of rings with an infinite number of variables…
On the uniqueness and stability of dictionaries for sparse representation of noisy signals
Charles J. Garfinkle, Christopher J. Hillar
Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features…
Robust exponential memory in Hopfield networks
Christopher Hillar, Ngoc M. Tran
The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically-coupled McCulloch-Pitts neurons interact to perform eme…
Lower Bounds in Real Schubert Calculus
Nickolas Hein, Christopher J. Hillar, Frank Sottile
We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Sc…