Search Results for author: Artur Pak

Found 3 papers, 2 papers with code

Gradient Descent Fails to Learn High-frequency Functions and Modular Arithmetic

no code implementations19 Oct 2023 Rustem Takhanov, Maxat Tezekbayev, Artur Pak, Arman Bolatov, Zhenisbek Assylbekov

In the novel framework, the hardness of a class is usually quantified by the variance of the gradient with respect to a random choice of a target function.

Intractability of Learning the Discrete Logarithm with Gradient-Based Methods

1 code implementation2 Oct 2023 Rustem Takhanov, Maxat Tezekbayev, Artur Pak, Arman Bolatov, Zhibek Kadyrsizova, Zhenisbek Assylbekov

The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols.

Long-Tail Theory under Gaussian Mixtures

1 code implementation20 Jul 2023 Arman Bolatov, Maxat Tezekbayev, Igor Melnykov, Artur Pak, Vassilina Nikoulina, Zhenisbek Assylbekov

We suggest a simple Gaussian mixture model for data generation that complies with Feldman's long tail theory (2020).

Memorization

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