Neural operations as convolutions, self-attention, and vector aggregation are the go-to choices for recognizing short-range actions. However, they have three limitations in modeling long-range activities. This paper presents PIC, Permutation Invariant Convolution, a novel neural layer to model the temporal structure of long-range activities. It has three desirable properties. i. Unlike standard convolution, PIC is invariant to the temporal permutations of features within its receptive field, qualifying it to model the weak temporal structures. ii. Different from vector aggregation, PIC respects local connectivity, enabling it to learn long-range temporal abstractions using cascaded layers. iii. In contrast to self-attention, PIC uses shared weights, making it more capable of detecting the most discriminant visual evidence across long and noisy videos. We study the three properties of PIC and demonstrate its effectiveness in recognizing the long-range activities of Charades, Breakfast, and MultiThumos.
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