Why Constrained Updates Still Forget: A Functional-Path Analysis of Continual SFT

Continual supervised fine-tuning (SFT) is the de facto recipe for adapting large language models (LLMs) to a stream of downstream tasks, but it suffers from catastrophic forgetting of earlier capabilities. Recent work shows that on-policy signals -- training on the model's own outputs -- reduce forgetting more reliably than off-policy supervision. Existing on-policy methods route this signal through a new training objective (e.g., self-distillation losses with a teacher copy), inheriting an extra forward pass, schedule sensitivity, and stylistic drift from the teacher.We instead route the on-policy signal through the training data source. Our method, On-Policy Replay (OPR), rolls out the most recent checkpoint on a small budget of historical prompts, filters the generations by a task reward, and replays the surviving (prompt, model response) pairs as ordinary SFT examples. There is no teacher, no auxiliary loss, and no on-the-fly distillation. Across three 7--8B instruction-tuned backbones (Qwen2.5-7B-Instruct, Qwen3-8B, Llama3.1-8B-Instruct) on the TRACE continual-learning benchmark, OPR consistently reduces forgetting; on the sharpest stress test (Qwen2.5-7B-Instruct, Sequential SFT BWT -13.93), OPR lifts BWT to -0.65 at a 10% replay budget and to -2.29 at a 1% budget -- a 46% reduction in |BWT| over a tuned Vanilla Replay baseline, with 42--46% reductions observed across all three backbones. We give a KL-shrinkage interpretation that places OPR and prior on-policy distillation methods on a single axis, and we present a counterintuitive finding that explains why Vanilla Replay is already a strong baseline: low-score replay is uniformly worse than Vanilla Replay, demonstrating that the active ingredient in OPR is the on-policy distribution, not the response quality alone.Our code is available at https://github.com/Yancey2024/OnPolicyReplay.

Continual learning (CL) seeks to adapt pretrained models while preserving prior capabilities. Yet the tasks supplied for preservation cover only part of what a model knows, while forgetting can extend beyond them. Recent work shows that language models can supplement this limited evidence by generating useful replay without access to their original training data. This raises a question about self-preservation: can a model help choose preservation targets that protect its own capabilities more broadly? To study this question, we organize task descriptions and their examples into Task Banks, whose entries can be selected and combined to guide replay generation by a frozen model. Continual instruction tuning with Qwen models of varying sizes yields three findings. First, the new task and learning rate shape which prior capabilities degrade, while tracking previously correct answers reveals losses that average accuracy can conceal. Second, generated replay reduces forgetting on tasks outside the bank. Combining partial banks strengthens this protection, improving mean retention of previously correct answers over either bank alone across the tested sizes. Third, the model can also help choose replay targets: selection informed by the new task improves mean held-out retention over random selection at 4B, with similar new-task gains, although smaller models show no corresponding advantage. Under a fixed example budget, however, replacing new-task examples with replay improves preservation at the cost of smaller new-task gains. Together, these findings show that models can support broader self-preservation by generating replay data and, in some settings, choosing which tasks to replay.

Fine-tuning large language models (LLMs) frequently induces catastrophic forgetting of prior capabilities. Recent work has shown that reinforcement learning (RL) retains prior capabilities more effectively than supervised fine-tuning (SFT), attributing this to policy-gradient updates remaining closer to the base policy \cite{shenfeld2025rl}. We extend this behavioral account to the mechanistic level and ask whether RL's advantage is mirrored by stronger preservation of internal computational circuits. We introduce differential circuit vulnerability, a head-level measure of how much a circuit degrades under fine-tuning, and use it to compare RL and SFT on Qwen2.5-3B-Instruct adapted to scientific question-answering. We find a clear mechanistic trade-off: SFT adapts more rapidly to the target task but produces substantially greater circuit disruption and forgetting of prior capabilities, whereas RL preserves a larger fraction of the base circuit at the cost of slower task adaptation. These findings suggest that circuit preservation may help explain why RL is more robust to catastrophic forgetting. We released our code here: https://github.com/rl-sft-circuit-research/differential-circuit-vulnerability.