Author

Uliana Parkina

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Preprint Sep 2026

A lower bound for $\langle 3,2,m \rangle$ matrix multiplication

We prove that, over any field, the bilinear complexity of multiplying a $3\times 2$ matrix by a $2\times m$ matrix is strictly greater than $24m/5$. In particular, every exact bilinear algorithm for multiplying a $3\times 2$ matrix by a $2\times 5$ matrix requires at least $25$ multiplications. Together with the Hopcro...

Askar Tsyganov, Uliana Parkina, S. Samsonov et al. · 0 citations

#machine learning Preprint Sep 2026

Fast Differentiable SVD on GPU via Polar Decomposition

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 iteration. We show that this approach enables up to a $2\times$ speedup compared to standard implementations. Furthermore, we derive a numerical...

Uliana Parkina, Askar Tsyganov, Sergei Kudriashov et al. · 0 citations