40 citations · 51 across the 8 of their papers we have counts for
8 papers
The Real Tropical Geometry of Neural Networks
Marie-Charlotte Brandenburg, Georg Loho, Guido Montúfar
We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReL…
Supermodular Rank: Set Function Decomposition and Optimization
Rishi Sonthalia, Anna Seigal, Guido Montufar
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summa…
Oversquashing in GNNs through the lens of information contraction and graph expansion
Pradeep Kr. Banerjee, Kedar Karhadkar, Yu Guang Wang +2
The quality of signal propagation in message-passing graph neural networks (GNNs) strongly influences their expressivity as has been observed in recent works. In particular, for pr…
Universal Approximation of Markov Kernels by Shallow Stochastic Feedforward Networks
Guido Montufar
We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer i…
Deep Narrow Boltzmann Machines are Universal Approximators
Guido Montufar
We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many…
Sequential Recurrence-Based Multidimensional Universal Source Coding of Lempel-Ziv Type
Tyll Krueger, Guido Montufar, Ruedi Seiler +1
We define an algorithm that parses multidimensional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resultin…