Practical deployment of large language models (LLMs) requires families of post-trained variants—instruction-tuned, reasoning-tuned, and chat-style models—each at multiple sizes to meet diverse latency and memory budgets. Producing each (variant, size) pair independently is prohibitive, so model families typically span only a handful of coarse-grained sizes per post-trained variant. Boomerang distillation (Kangaslahti et al., 2026) reduces this cost along the size axis for base models. Through model size interpolation, it constructs models of intermediate sizes from a single teacher-student pair without additional training. However, it still treats each post-trained variant as a separate object of optimization. We introduce ADAPT—Amortized Distillation Across Post-Trained LLMs—a framework for amortizing distillation across both axes of a model family: size and post-training variant, producing L × K models for L interpolated sizes across K post-trained variants with a single distillation run. ADAPT combines two components. First, a two-phase distillation procedure constructs post-trained students through pre-training alignment and supervised fine-tuning distillation, enabling smooth size–performance interpolation on generation and reasoning tasks. Second, weight-delta initialization approximates this construction across post-trained variants by transferring the distillation-induced weight change from the base model to students initialized from different post-trained variants. The resulting continuum of interpolated models also enables adaptive model-size selection at inference time, improving the compute–accuracy trade-off for long-form reasoning tasks.

Parameter efficient finetuning methods like low-rank adaptation (LoRA) aim to reduce the computational costs of finetuning pretrained Language Models (LMs). Enabled by these low-rank settings, we propose an even more efficient optimization strategy: Fast Forward, a simple and effective approach to accelerate large segments of SGD training. In a Fast Forward stage, we repeat the most recent optimizer step until the loss stops improving on a tiny validation set. By alternating between regular optimization steps and Fast Forward stages, Fast Forward provides up to an 87% reduction in FLOPs over standard SGD with Adam. We validate Fast Forward by finetuning various models on different tasks and demonstrate that it speeds up training without compromising model performance. Additionally, we analyze when and how to apply Fast Forward.