Anushka Idamekorala | Searcharxiv

arXiv2026

55 Additions Suffice for 3x3 Matrix Multiplication at Rank 23

We give a 55-addition realization of rank-23 multiplication of two arbitrary $3\times3$ matrices. Together with its 23 bilinear products, the circuit uses 78 scalar operations. This improves the previous state of the art of 56 additions, due to Sun. The construction starts from Perminov's public 58-addition realization cr58_cn122 of a ternary tensor; the contribution is a shorter and, for this fixed orientation of that tensor, provably optimal linear circuit: 13 additions on the left input, 14 on the right input, and 28 at the output. The last circuit is obtained by transposing a 14-addition factor circuit. Because the coefficient alphabet is $\{-1,0,1\}$ and the order of every bilinear product is retained, the algorithm applies over every associative ring, commutative or not. We provide the full straight-line program and tensor factors together with four exact computational checks, including independent Python and Node.js implementations of all 729 Brent identities over $\mathbb Z$.

cs.CC↗

arXiv2025

Deep Learning Foundation and Pattern Models: Challenges in Hydrological Time Series

There has been active investigation into deep learning approaches for time series analysis, including foundation models. However, most studies do not address significant scientific applications. This paper aims to identify key features in time series by examining hydrology data. Our work advances computer science by emphasizing critical application features and contributes to hydrology and other scientific fields by identifying modeling approaches that effectively capture these features. Scientific time series data are inherently complex, involving observations from multiple locations, each with various time-dependent data streams and exogenous factors that may be static or time-varying and either application-dependent or purely mathematical. This research analyzes hydrology time series from the CAMELS and Caravan global datasets, which encompass rainfall and runoff data across catchments, featuring up to six observed streams and 209 static parameters across approximately 8,000 locations. Our investigation assesses the impact of exogenous data through eight different model configurations for key hydrology tasks. Results demonstrate that integrating exogenous information enhances data representation, reducing mean squared error by up to 40% in the largest dataset. Additionally, we present a detailed performance comparison of over 20 state-of-the-art pattern and foundation models. The analysis is fully open-source, facilitated by Jupyter Notebook on Google Colab for LSTM-based modeling, data preprocessing, and model comparisons. Preliminary findings using alternative deep learning architectures reveal that models incorporating comprehensive observed and exogenous data outperform more limited approaches, including foundation models. Notably, natural annual periodic exogenous time series contribute the most significant improvements, though static and other periodic factors are also valuable.

cs.LG↗