Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications

תקציר מקורי באנגליתarXiv:2505.17964v2 Announce Type: replace Abstract: Cycle count statistics are fundamental tools in statistics and engineering, with applications in motif counting, channel coding, and statistical inference of network and matrix data. However, how to compute high-order cycle count statistics efficiently is still an open problem. In this paper, we aim to derive Computationally Efficient Equivalent Forms (CEEF) for cycle count statistics of any given order, where we express each cycle count statistic equivalently as a linear combination of finitely many terms. Using the CEEF, we provide a much more efficient way to compute the cycle count statistics. The CEEF problem has no known general solution and requires delicate combinatorial arguments together with extensive calculations. While this t