7 papers
The Exact Overlaps Conjecture for Self-Similar Measures on the Real Line
Samuel Kittle, Constantin Kogler
A generalization of the exact overlaps conjecture predicts a formula for the dimension of self-similar measures in terms of the random walk entropy and the Lyapunov exponent. We pr…
Optimal Initialization in Depth: Lyapunov Initialization and Limit Theorems for Deep Leaky ReLU Networks
Constantin Kogler, Tassilo Schwarz, Samuel Kittle
Effective initialization in deep networks requires an understanding of random neural networks. In this work, a rigorous probabilistic analysis of deep bias-free random Leaky ReLU n…
Permutation-Invariant Spectral Learning via Dyson Diffusion
Tassilo Schwarz, Cai Dieball, Constantin Kogler +4
Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to such represent…
Polynomial Tail Decay for Stationary Measures
Samuel Kittle, Constantin Kogler
We show on complete metric spaces a polynomial tail decay for stationary measures of contracting on average generating measures.
Dimension of contracting on average self-similar measures
Samuel Kittle, Constantin Kogler
We generalise Hochman's theorem on the dimension of self-similar measures to contracting on average measures and show that a weaker condition than exponential separation on all sca…
Entropy Theory for Random Walks on Lie Groups
Samuel Kittle, Constantin Kogler
We develop entropy and variance results for the product of independent identically distributed random variables on Lie groups. Our results apply to the study of stationary measures…
On absolute continuity of inhomogeneous and contracting on average self-similar measures
Samuel Kittle, Constantin Kogler
We give a condition for absolute continuity of self-similar measures in arbitrary dimensions. This allows us to construct the first explicit absolutely continuous examples of inhom…