Formal Detection of Negative Transfer

Develop a formal procedure for detecting negative transfer in the two-stage offset transfer learning framework when the group-specific offset \(G_{\ell}\) is highly complex or the pooled first-stage mean function \(\bar f\) is complicated.

Background

The framework can theoretically experience negative transfer when pooling groups produces a difficult overall mean function or when estimating the group-specific offset is more complex than directly estimating the target function. The paper notes that this situation may arise when groups differ substantially.

Although the experiments focus primarily on settings with cross-group similarity and positive transfer, the authors explicitly leave formal detection of negative transfer unresolved. A solution would help determine when the two-stage procedure should be used and when pooling information is harmful.

References

Such a case may arise when the groups are substantially different; in practice, however, groups in many real-world datasets exhibit strong cross-group similarity (e.g., our real-data experiments), and formal detection of negative transfer is left as future work.

— Transfer Learning in Nonparametric Regression with Deep ReLU Networks  (2608.20255 - Ren et al., 20 Aug 2026) in Section 6, Conclusion