In this paper, we consider a linear decision tree such that a linear threshold function at each internal node has a bounded weight: the sum of the absolute values of its integer weights is at most w. We prove that if a Boolean function f is computable by such a linear decision tree of size (i.e., the number of leaves) s and rank r, then f is also computable by a depth-2 threshold circuit containing at most s(2w+1)r threshold gates with weight at most (2w+1)r+1 in the bottom level. Combining a known lower bound on the size of depth-2 threshold circuits, we obtain a 2Ω(n/ logw) lower bound on the size of linear decision trees computing the Inner-Product function modulo 2, which improves on the previous bound 2√n if w = 2o(√n).
CITATION STYLE
Uchizawa, K., & Takimoto, E. (2015). Lower bounds for linear decision trees with bounded weights. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8939, pp. 412–422). Springer Verlag. https://doi.org/10.1007/978-3-662-46078-8_34
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