PAL: Pluralistic Alignment Framework for Learning from Heterogeneous Preferences

Large foundation models pretrained on raw web-scale data are not readily deployable without additional step of extensive alignment to human preferences. Such alignment is typically done by collecting large amounts of pairwise comparisons from humans ("Do you prefer output A or B?") and learning a reward model or a policy with the Bradley-Terry-Luce (BTL) model as a proxy for a human's underlying implicit preferences. These methods generally suffer from assuming a universal preference shared by all humans, which lacks the flexibility of adapting to plurality of opinions and preferences. In this work, we propose PAL, a framework to model human preference complementary to existing pretraining strategies, which incorporates plurality from the ground up. We propose using the ideal point model as a lens to view alignment using preference comparisons. Together with our novel reformulation and using mixture modeling, our framework captures the plurality of population preferences while simultaneously learning a common preference latent space across different preferences, which can few-shot generalize to new, unseen users. Our approach enables us to use the penultimate-layer representation of large foundation models and simple MLP layers to learn reward functions that are on-par with the existing large state-of-the-art reward models, thereby enhancing efficiency of reward modeling significantly. We show that PAL achieves competitive reward model accuracy compared to strong baselines on 1) Language models with Summary dataset ; 2) Image Generative models with Pick-a-Pic dataset ; 3) A new semisynthetic heterogeneous dataset generated using Anthropic Personas. Finally, our experiments also highlight the shortcoming of current preference datasets that are created using rigid rubrics which wash away heterogeneity, and call for more nuanced data collection approaches.

Learning Capacity: A Measure of the Effective Dimensionality of a Model

We exploit a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to define a "learning capacity'' which is a measure of the effective dimensionality of a model. We show that the learning capacity is a tiny fraction of the number of parameters for many deep networks trained on typical datasets, depends upon the number of samples used for training, and is numerically consistent with notions of capacity obtained from the PAC-Bayesian framework. The test error as a function of the learning capacity does not exhibit double descent. We show that the learning capacity of a model saturates at very small and very large sample sizes; this provides guidelines, as to whether one should procure more data or whether one should search for new architectures, to improve performance. We show how the learning capacity can be used to understand the effective dimensionality, even for non-parametric models such as random forests and $k$-nearest neighbor classifiers.