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Learning representations of stochastic processes is an emerging problem in machine learning with applications from meta-learning to physical object models to time series. Typical methods rely on exact reconstruction of observations, but this approach breaks down as observations become high-dimensional or noise distributions become complex. To address this, we propose a unifying framework for learning contrastive representations of stochastic processes (CRESP) that does away with exact reconstruction. We dissect potential use cases for stochastic process representations, and propose methods that accommodate each. Empirically, we show that our methods are effective for learning representations of periodic functions, 3D objects and dynamical processes. Our methods tolerate noisy high-dimensional observations better than traditional approaches, and the learned representations transfer to a range of downstream tasks.
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Existing language model compression methods mostly use a simple L2 loss to distill knowledge in the intermediate representations of a large BERT model to a smaller one. Although widely used, this objective by design assumes that all the dimensions of hidden representations are independent, failing to capture important structural knowledge in the intermediate layers of the teacher network. To achieve better distillation efficacy, we propose Contrastive Distillation on Intermediate Representations (CoDIR), a principled knowledge distillation framework where the student is trained to distill knowledge through intermediate layers of the teacher via a contrastive objective. By learning to distinguish positive sample from a large set of negative samples, CoDIR facilitates the students exploitation of rich information in teachers hidden layers. CoDIR can be readily applied to compress large-scale language models in both pre-training and finetuning stages, and achieves superb performance on the GLUE benchmark, outperforming state-of-the-art compression methods.
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