832 citations · 1.3k across the 79 of their papers we have counts for
11 papers · 1 filter
Algebraic optimization of sequential decision problems
Mareike Dressler, Marina Garrote-López, Guido Montúfar +2
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of d…
Geometry and convergence of natural policy gradient methods
Johannes Müller, Guido Montúfar
We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a varie…
Characterizing the Spectrum of the NTK via a Power Series Expansion
Michael Murray, Hui Jin, Benjamin Bowman +1
Under mild conditions on the network initialization we derive a power series expansion for the Neural Tangent Kernel (NTK) of arbitrarily deep feedforward networks in the infinite…
FoSR: First-order spectral rewiring for addressing oversquashing in GNNs
Kedar Karhadkar, Pradeep Kr. Banerjee, Guido Montúfar
Graph neural networks (GNNs) are able to leverage the structure of graph data by passing messages along the edges of the graph. While this allows GNNs to learn features depending o…
Enumeration of max-pooling responses with generalized permutohedra
Laura Escobar, Patricio Gallardo, Javier González-Anaya +3
We investigate the combinatorics of max-pooling layers, which are functions that downsample input arrays by taking the maximum over shifted windows of input coordinates, and which…
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…
On the effectiveness of persistent homology
Renata Turkeš, Guido Montúfar, Nina Otter
Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind i…
Spectral Bias Outside the Training Set for Deep Networks in the Kernel Regime
Benjamin Bowman, Guido Montufar
We provide quantitative bounds measuring the difference in function space between the trajectory of a finite-width network trained on finitely many samples from the idealized…
Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space
Johannes Müller, Guido Montúfar
Reward optimization in fully observable Markov decision processes is equivalent to a linear program over the polytope of state-action frequencies. Taking a similar perspective in t…
Continuity and Additivity Properties of Information Decompositions
Johannes Rauh, Pradeep Kr. Banerjee, Eckehard Olbrich +2
Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been pr…
Implicit Bias of MSE Gradient Optimization in Underparameterized Neural Networks
Benjamin Bowman, Guido Montufar
We study the dynamics of a neural network in function space when optimizing the mean squared error via gradient flow. We show that in the underparameterized regime the network lear…