Probabilistic Learning and Generation in Deep Sequence Models

TL;DR

This paper explores how deep sequence models can incorporate probabilistic reasoning and uncertainty quantification, improving their interpretability and robustness through novel Bayesian inference methods and self-supervised learning techniques.

Contribution

It introduces new Bayesian inference methods tailored for Transformers and Gaussian processes, and investigates self-supervised learning for sequential latent variables in generative models.

Findings

Developed a Transformer-specific Bayesian inference method based on attention-Gaussian process similarity.

Constructed an interdomain inducing point using HiPPOs for online learning and memory retention.

Enhanced sequential generative models with self-supervision for latent states.

Abstract

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with unobserved variables with rules of probability. Notably, Bayesian methods leverage Bayes' rule to express our belief of unobserved variables in a principled way. Since exact Bayesian inference is computationally infeasible at scale, approximate inference is required in practice. Two major bottlenecks of Bayesian methods, especially when applied in deep neural networks, are prior specification and approximation quality. In Chapter 3 & 4, we investigate how the architectures of DSMs themselves can be informative for the design of priors or approximations in probabilistic models. We first develop an approximate Bayesian inference method tailored to the Transformer based on the similarity between attention and sparse Gaussian process. Next, we exploit the long-range memory preservation capability of HiPPOs (High-order Polynomial Projection Operators) to construct an interdomain inducing point for Gaussian process, which successfully memorizes the history in online learning. In addition to the progress of DSMs in predictive tasks, sequential generative models consisting of a sequence of latent variables are popularized in the domain of deep generative models. Inspired by the explicit self-supervised signals for these latent variables in diffusion models, in Chapter 5, we explore the possibility of improving other generative models with self-supervision for their sequential latent states, and investigate desired probabilistic structures over them. Overall, this thesis leverages inductive biases in DSMs to design probabilistic inference or structure, which bridges the gap between DSMs and probabilistic models, leading to mutually reinforced improvement.