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
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
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 space. We propose Geometric Fixed-Point Reasoning (GFPR), in which the iterated state is the prediction itself: a field of categorical belief...
T. Daulbaev, И. Д. Глазков, Maxim V. Rakhuba et al.· 0 citations
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 recently drawn interest in deep learning architectures for its balanced expressivity-efficiency trade-off, yet efficient computational strategies...
Aliev S. E. Aliev, Maxim V. Rakhuba· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
