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Current polyp detection methods from colonoscopy videos use exclusively normal (i.e., healthy) training images, which i) ignore the importance of temporal information in consecutive video frames, and ii) lack knowledge about the polyps. Consequently, they often have high detection errors, especially on challenging polyp cases (e.g., small, flat, or partially visible polyps). In this work, we formulate polyp detection as a weakly-supervised anomaly detection task that uses video-level labelled training data to detect frame-level polyps. In particular, we propose a novel convolutional transformer-based multiple instance learning method designed to identify abnormal frames (i.e., frames with polyps) from anomalous videos (i.e., videos containing at least one frame with polyp). In our method, local and global temporal dependencies are seamlessly captured while we simultaneously optimise video and snippet-level anomaly scores. A contrastive snippet mining method is also proposed to enable an effective modelling of the challenging polyp cases. The resulting method achieves a detection accuracy that is substantially better than current state-of-the-art approaches on a new large-scale colonoscopy video dataset introduced in this work.