Continual post-training faces a dual challenge of acquisition and retention: models must learn new capabilities while preserving prior knowledge.
While Self-Distillation Fine-Tuning (SDFT) mitigates this using self-supervision with in-context demonstrations, it relies on strong in-context learning and instruction-following abilities.
Consequently, SDFT fails on smaller models critical for low-latency, on-device use.
To enable continual learning at smaller scales, we first identify the root cause of failure.
We show that poor acquisition and forgetting correlate linearly with the post-trained model's distribution shift, revealing the necessity of in-distribution learning.
We thus introduce Synthetic Self-Distillation (SynthSelf), imitating SDFT's in-distribution rewrite by outsourcing the task to a minimally larger, same-family aligner.
Coupled with off-policy supervision and rejection sampling, this provides the high-quality supervision small models require without breaking their original distribution.
Evaluations spanning 4 acquisition datasets (including a mixture) and 14 retention benchmarks show SynthSelf consistently outperforms 6 methods (including off- and on-policy distillation) across 3 small model scales.
Extensive further analyses confirm SynthSelf paves the way toward effective small-model continual learning.