The disclosed invention includes systems and methods for training and employing equivariant models for generating representations (e.g., vector representations) of temporally-varying content, such as but not limited to video content. The trained models are equivariant to temporal transformations applied to the input content (e.g., video content). The trained models are additionally invariant to non-temporal transformations (e.g., spatial and/or color-space transformations) applied to the input content. Such representations are employed in various machine learning tasks, such as but not limited to video retrieval (e.g., video search engine applications), identification of actions depicted in video, and temporally ordering clips of the video.