4 papers
Augmented Lagrangian Predictive Coding
Jeffrey Seely, Julian Gould
Predictive coding (PC) is a local-learning alternative to backpropagation (BP), training deep networks via local energy-minimization dynamics rather than a global backward pass. We…
Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves
Kartik Tandon, Julian Gould, Tanishq Bhatia +3
Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operat…
Clearing Sections of Lattice Liability Networks
Robert Ghrist, Julian Gould, Miguel Lopez +1
Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present…
Lattice-Valued Bottleneck Duality
Robert Ghrist, Julian Gould, Miguel Lopez
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut…