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math.DS2026
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…
stat.ML2026
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…