Autoregressive language models are the currently dominant paradigm for text generation, however they have some fundamental limitations that cannot be remedied by scale—for example inherently sequential and unidirectional generation. While alternate classes of models have been explored, we have limited mathematical understanding of their fundamental power and limitations. In this paper we focus on Generative Masked Language Models (GMLMs), a non-autoregressive paradigm in which we train a model to fit conditional probabilities of the data distribution via masking, which are subsequently used as inputs to a Markov Chain to draw samples from the model. These models empirically strike a promising speed-quality trade-off as each step can be typically parallelized by decoding the entire sequence in parallel. We develop a mathematical framework for analyzing and improving such models which sheds light on questions of sample complexity and inference speed and quality. Empirically, we adapt the T5 model for iteratively-refined parallel decoding, achieving 2-3x speedup in machine translation with minimal sacrifice in quality compared with autoregressive models. We run careful ablation experiments to give recommendations on key design choices, and make fine-grained observations on the common error modes in connection with our theory. Our mathematical analyses and empirical observations characterize both potentials and limitations of this approach, and can be applied to future works on improving understanding and performance of GMLMs. We released codes for our experiments.

In computer vision, 2D convolution is arguably the most important operation performed by a ConvNet. Unsurprisingly, it has been the focus of intense software and hardware optimization and enjoys highly efficient implementations. In this work, we ask an intriguing question: can we make a ConvNet work without 2D convolutions? Surprisingly, we find that the answer is yes—we show that a ConvNet consisting entirely of 1D convolutions can do just as well as 2D on ImageNet classification. Specifically, we find that one key ingredient to a high-performing 1D ConvNet is oriented 1D kernels: 1D kernels that are oriented not just horizontally or vertically, but also at other angles. Our experiments show that oriented 1D convolutions can not only replace 2D convolutions but also augment existing architectures with large kernels, leading to improved accuracy with minimal FLOPs increase. A key contribution of this work is a highly-optimized custom CUDA implementation of oriented 1D kernels, specialized to the depthwise convolution setting. Our benchmarks demonstrate that our custom CUDA implementation almost perfectly realizes the theoretical advantage of 1D convolution: it is faster than a native horizontal convolution for any arbitrary angle. Code is available at https://github.com/princeton-vl/Oriented1D.