14 citations · 16 across the 19 of their papers we have counts for
5 papers · 1 filter
Reasoning on the Simplex: Geometric Fixed-Point Models
Talgat Daulbaev, Ilya Glazkov, Maxim Rakhuba +1
Looped reasoners spend test-time compute by iterating a weight-tied map, but a small residual does not mean the state is a fixed point when that map lives in unconstrained latent s…
Fast Differentiable SVD on GPU via Polar Decomposition
Uliana Parkina, Askar Tsyganov, Sergei Kudriashov +2
We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iter…
Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices
Ali Aliev, Maxim Rakhuba
In this paper, we are concerned with matrices formed by block-diagonal factors interleaved with fixed permutations -- a flexible family of structured matrices. This class has recen…
A lower bound for matrix multiplication
Askar Tsyganov, Uliana Parkina, Sergey Samsonov +1
We prove that, over any field, the bilinear complexity of multiplying a matrix by a matrix is strictly greater than . In particular, every exact bili…
Muon on the Stiefel Manifold Admits an Exact Closed-Form Update
Mikhail Solonko, Molozhavenko Alexander, Maxim Rakhuba
We study Muon, a recently proposed matrix-aware optimization method, in the context of the Stiefel manifold. This manifold consists of matrices with orthonormal columns and is ubiq…