  Datasets scraped from the internet have been critical to the successes of
large-scale machine learning. Yet, this very success puts the utility of future
internet-derived datasets at potential risk, as model outputs begin to replace
human annotations as a source of supervision.
  In this work, we first formalize a system where interactions with one model
are recorded as history and scraped as training data in the future. We then
analyze its stability over time by tracking changes to a test-time bias
statistic (e.g. gender bias of model predictions). We find that the degree of
bias amplification is closely linked to whether the model's outputs behave like
samples from the training distribution, a behavior which we characterize and
define as consistent calibration. Experiments in three conditional prediction
scenarios - image classification, visual role-labeling, and language generation
- demonstrate that models that exhibit a sampling-like behavior are more
calibrated and thus more stable. Based on this insight, we propose an
intervention to help calibrate and stabilize unstable feedback systems.
  Code is available at https://github.com/rtaori/data_feedback.
