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Electronic Colloquium on Computational Complexity

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TR22-159 | 18th November 2022
Songhua He, Periklis Papakonstantinou

Deep Neural Networks: The Missing Complexity Parameter

Deep neural networks are the dominant machine learning model. We show that this model is missing a crucial complexity parameter. Today, the standard neural network (NN) model is a circuit whose gates (neurons) are ReLU units. The complexity of a NN is quantified by the depth (number of layers) and ... more >>>


TR22-158 | 18th November 2022
Ivan Hu, Andrew Morgan, Dieter van Melkebeek

Query Complexity of Inversion Minimization on Trees

Revisions: 1

We consider the following computational problem: Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the well-known problem of counting inversions in arrays originated in mathematical psychology. It ... more >>>


TR22-157 | 16th November 2022
Pranjal Dutta, Fulvio Gesmundo, Christian Ikenmeyer, Gorav Jindal, Vladimir Lysikov

Border complexity via elementary symmetric polynomials

Revisions: 1

In (ToCT’20) Kumar surprisingly proved that every polynomial can be approximated as a sum of a constant and a product of linear polynomials. In this work, we prove the converse of Kumar's result which ramifies in a surprising new formulation of Waring rank and border Waring rank. From this conclusion, ... more >>>



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