1,186 research outputs found
Generic regularity of conservative solutions to Camassa-Holm type equations
This paper mainly proves the generic properties of the Camassa-Holm equation and the two-component Camassa-Holm equation by Thom's transversality Lemma. We reveal their differences in generic regularity and singular behavior
Technical Note: Defining and Quantifying AND-OR Interactions for Faithful and Concise Explanation of DNNs
In this technical note, we aim to explain a deep neural network (DNN) by
quantifying the encoded interactions between input variables, which reflects
the DNN's inference logic. Specifically, we first rethink the definition of
interactions, and then formally define faithfulness and conciseness for
interaction-based explanation. To this end, we propose two kinds of
interactions, i.e., the AND interaction and the OR interaction. For
faithfulness, we prove the uniqueness of the AND (OR) interaction in
quantifying the effect of the AND (OR) relationship between input variables.
Besides, based on AND-OR interactions, we design techniques to boost the
conciseness of the explanation, while not hurting the faithfulness. In this
way, the inference logic of a DNN can be faithfully and concisely explained by
a set of symbolic concepts.Comment: arXiv admin note: text overlap with arXiv:2111.0620
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