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Weakly-supervised temporal action localization (WTAL) intends to detect action instances with only weak supervision, e.g., video-level labels. The current~\textit{de facto} pipeline locates action instances by thresholding and grouping continuous high-score regions on temporal class activation sequences. In this route, the capacity of the model to recognize the relationships between adjacent snippets is of vital importance which determines the quality of the action boundaries. However, it is error-prone since the variations between adjacent snippets are typically subtle, and unfortunately this is overlooked in the literature. To tackle the issue, we propose a novel WTAL approach named Convex Combination Consistency between Neighbors (C$^3$BN). C$^3$BN consists of two key ingredients: a micro data augmentation strategy that increases the diversity in-between adjacent snippets by convex combination of adjacent snippets, and a macro-micro consistency regularization that enforces the model to be invariant to the transformations~\textit{w.r.t.} video semantics, snippet predictions, and snippet representations. Consequently, fine-grained patterns in-between adjacent snippets are enforced to be explored, thereby resulting in a more robust action boundary localization. Experimental results demonstrate the effectiveness of C$^3$BN on top of various baselines for WTAL with video-level and point-level supervisions. Code is at https://github.com/Qinying-Liu/C3BN.