4 papers
Is Dimensionality a Barrier for Retrieval Models?
Kiril Bangachev, Guy Bresler, Jonathan Kogan +1
Why does the low dimensionality of representations, typically , not prevent modern embedding-based retrieval models from scaling to billions, or even trillions, of d…
Complexity of One-Dimensional ReLU DNNs
Jonathan Kogan, Hayden Jananthan, Jeremy Kepner
We study the expressivity of one-dimensional (1D) ReLU deep neural networks through the lens of their linear regions. For randomly initialized, fully connected 1D ReLU networks (He…
Limiting behaviour of pattern counts in biased binary strings
Jon V. Kogan, Nicolò Paviato
For , sample a binary sequence from the infinite product measure of Bernoulli distributions. It is known that for , almost every binary sequence is Poisson…
Vertex-Minimal Triangulation of Complexes with Homology
Jon V. Kogan
For a given pair of numbers , we establish the minimal number of vertices in pure -dimensional simplicial complexes with non-trivial homology in dimension . Furthermor…