Generating synthetic data to augment a small real dataset should, intuitively, help — more data means better estimates. This paper proves it does not, at least for statistical inference.
The reason is information-theoretic. Synthetic data is generated from a model fitted to the real data. The marginal Fisher information it contributes is bounded by what the real data already provided. You cannot create information by processing information. The synthetic samples may look like new data, but they carry no new evidence about the population — they carry evidence about the fitted model, which is itself a lossy compression of the real data.
The authors show that synthetic augmentation for boosting effective sample size lacks epistemic justification. The resulting confidence intervals are either the same width as those from the real data alone or, worse, narrower than they should be — not because the estimate is more precise but because the uncertainty has been artificially suppressed.
The salvageable use case is different: synthetic data can encode prior knowledge. If you know something about the data-generating process beyond what the sample contains, you can embed that knowledge in the synthetic generation procedure. But this is regularization, not augmentation — you are adding assumptions, not observations.
The distinction matters practically because the two use cases look identical in a pipeline. Both involve generating fake data and combining it with real data. But one is principled (encoding structural knowledge you actually possess) and the other is epistemically empty (pretending you have more evidence than you do). The boundary between them is whether the synthetic procedure adds information not already in the sample.