Architectural and Inferential Inductive Biases For Exchangeable Sequence Modeling

Autoregressive models have emerged as a powerful framework for modeling exchangeable sequences - i.i.d. observations when conditioned on some latent factor - enabling direct modeling of uncertainty from missing data (rather than a latent). Motivated by the critical role posterior inference plays as a subroutine in decision-making (e.g., active learning, bandits), we study the inferential and architectural inductive biases that are most effective for exchangeable sequence modeling. For the inference stage, we highlight a fundamental limitation of the prevalent single-step generation approach: inability to distinguish between epistemic and aleatoric uncertainty. Instead, a long line of works in Bayesian statistics advocates for multi-step autoregressive generation; we demonstrate this "correct approach" enables superior uncertainty quantification that translates into better performance on downstream decision-making tasks. This naturally leads to the next question: which architectures are best suited for multi-step inference? We identify a subtle yet important gap between recently proposed Transformer architectures for exchangeable sequences (Muller et al., 2022; Nguyen & Grover, 2022; Ye & Namkoong, 2024), and prove that they in fact cannot guarantee exchangeability despite introducing significant computational overhead. We illustrate our findings using controlled synthetic settings, demonstrating how custom architectures can significantly underperform standard causal masks, underscoring the need for new architectural innovations.

A Planning Framework for Adaptive Labeling

Ground truth labels/outcomes are critical for advancing scientific and engineering applications, e.g., evaluating the treatment effect of an intervention or performance of a predictive model. Since randomly sampling inputs for labeling can be prohibitively expensive, we introduce an adaptive labeling framework where measurement effort can be reallocated in batches. We formulate this problem as a Markov decision process where posterior beliefs evolve over time as batches of labels are collected (state transition), and batches (actions) are chosen to minimize uncertainty at the end of data collection. We design a computational framework that is agnostic to different uncertainty quantification approaches including those based on deep learning, and allows a diverse array of policy gradient approaches by relying on continuous policy parameterizations. On real and synthetic datasets, we demonstrate even a one-step lookahead policy can substantially outperform common adaptive labeling heuristics, highlighting the virtue of planning. On the methodological side, we note that standard REINFORCE-style policy gradient estimators can suffer high variance since they rely only on zeroth order information. We propose a direct backpropagation-based approach, Smoothed-Autodiff, based on a carefully smoothed version of the original non-differentiable MDP. Our method enjoys low variance at the price of introducing bias, and we theoretically and empirically show that this trade-off can be favorable.