Title: wMAN: WEAKLY-SUPERVISED MOMENT ALIGNMENT NETWORK FOR TEXT-BASED VIDEO SEGMENT RETRIEVAL. Abstract: Given a video and a sentence, the goal of weakly-supervised video moment retrieval is to locate the video segment which is described by the sentence without having access to temporal annotations during training.  Instead, a model must learn how to identify the correct segment (i.e. moment) when only being provided with video-sentence pairs.  Thus, an inherent challenge is automatically inferring the latent correspondence between visual and language representations. To facilitate this alignment, we propose our Weakly-supervised Moment Alignment Network (wMAN) which exploits a multi-level co-attention mechanism to learn richer multimodal representations. The aforementioned mechanism is comprised of a Frame-By-Word interaction module as well as a novel Word-Conditioned Visual Graph (WCVG). Our approach also incorporates a novel application of positional encodings, commonly used in Transformers, to learn visual-semantic representations that contain contextual information of their relative positions in the temporal sequence through iterative message-passing. Comprehensive experiments on the DiDeMo and Charades-STA datasets demonstrate the effectiveness of our learned representations: our combined wMAN model not only outperforms the state-of-the-art weakly-supervised method by a significant margin but also does better than strongly-supervised state-of-the-art methods on some metrics.