Yilong Qin

Yuchen Li, Alexandre Kirchmeyer, Aashay Mehta et al.

Autoregressive language models are the currently dominant paradigm for text generation, but 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. Our codes are released at https://github.com/google-research/google-research/tree/master/padir

Yilong Qin, Andrej Risteski

Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the need to evaluate the constant of proportionality. While there's a clear algorithmic benefit, the statistical "cost'' can be steep: recent work by Koehler et al. 2022 showed that for distributions that have poor isoperimetric properties (a large Poincaré or log-Sobolev constant), score matching is substantially statistically less efficient than maximum likelihood. However, many natural realistic distributions, e.g. multimodal distributions as simple as a mixture of two Gaussians in one dimension -- have a poor Poincaré constant. In this paper, we show a close connection between the mixing time of a broad class of Markov processes with generator $\mathcal{L}$ and an appropriately chosen generalized score matching loss that tries to fit $\frac{\mathcal{O} p}{p}$. This allows us to adapt techniques to speed up Markov chains to construct better score-matching losses. In particular, ``preconditioning'' the diffusion can be translated to an appropriate ``preconditioning'' of the score loss. Lifting the chain by adding a temperature like in simulated tempering can be shown to result in a Gaussian-convolution annealed score matching loss, similar to Song and Ermon, 2019. Moreover, we show that if the distribution being learned is a finite mixture of Gaussians in $d$ dimensions with a shared covariance, the sample complexity of annealed score matching is polynomial in the ambient dimension, the diameter of the means, and the smallest and largest eigenvalues of the covariance -- obviating the Poincaré constant-based lower bounds of the basic score matching loss shown in Koehler et al. 2022.