7 papers
Structure of kissing arrangements in and a place for the st sphere
Rustem Takhanov, Zhenisbek Assylbekov, Stanislav Yun
Most currently known kissing arrangements of size in share a common structure. They consist of vectors supported on , an…
Classification of independent sets in signed Johnson graphs and applications to kissing arrangements
Rustem Takhanov, Stanislav Yun
Johnson graph are a family of graphs that play an important role in the theory of constant-weight codes, extremal combinatorics, and combinatorial geometry. We study signed analogu…
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…
Deep Linear Discriminant Analysis Revisited
Maxat Tezekbayev, Rustem Takhanov, Arman Bolatov +1
We show that for unconstrained Deep Linear Discriminant Analysis (LDA) classifiers, maximum-likelihood training admits pathological solutions in which class means drift together, c…
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…