20 citations · 43 across the 29 of their papers we have counts for
13 papers · 1 filter
Conditional KRR: Injecting Unpenalized Features into Kernel Methods with Applications to Kernel Thresholding
Rustem Takhanov, Zhenisbek Assylbekov
Conditionally positive definite (CPD) kernels are defined with respect to a function class . It is well known that such a kernel is associated with its native spac…
On the Intrinsic Dimensions of Data in Kernel Learning
Rustem Takhanov
The manifold hypothesis suggests that the generalization performance of machine learning methods improves significantly when the intrinsic dimension of the input distribution's sup…
The informativeness of the gradient revisited
Rustem Takhanov
In the past decade gradient-based deep learning has revolutionized several applications. However, this rapid advancement has highlighted the need for a deeper theoretical understan…
Multi-layer random features and the approximation power of neural networks
Rustem Takhanov
A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Net…
Intractability of Learning the Discrete Logarithm with Gradient-Based Methods
Rustem Takhanov, Maxat Tezekbayev, Artur Pak +3
The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations…
Gradient Descent Fails to Learn High-frequency Functions and Modular Arithmetic
Rustem Takhanov, Maxat Tezekbayev, Artur Pak +2
Classes of target functions containing a large number of approximately orthogonal elements are known to be hard to learn by the Statistical Query algorithms. Recently this classica…