Conditional crystal generation requires Large Language Models (LLMs) to produce Crystal Strings with discrete and continuous variables while satisfying composition, symmetry, and property constraints. Desired regions are often sparse in supervised data, while retraining for each objective preference is costly. We present a verifier-grounded framework combining label-free Test-Time Reinforcement Learning (TTRL) and Model Merging (MM). TTRL performs one batch-level, partially transductive adaptation per property using composition, symmetry, and learned band-gap rewards, without target reference structures. Property-specific experts are interpolated to navigate bounded symmetry–band-gap trade-offs without retraining intermediate policies. On MP-20, TTRL improves symmetry control, band-gap accuracy, and compositional fidelity over High-Precision SFT and Standard RL, and is competitive with diffusion and preference-aligned baselines. In a held-out high-band-gap region, TTRL generalizes to test prompts unseen during adaptation, reducing the mean squared error between surrogate-predicted and target band gaps by 52% relative to standard reinforcement learning under best-of-ten sampling. An independent band-gap predictor shows consistent gains, while density functional theory calculations further assess selected candidates. Similar gains with Qwen3.5-9B provide cross-backbone evidence. Model Merging recovers competitive two-objective trade-offs from two endpoint experts without additional RL, enabling efficient adaptation and preference control for structured scientific generation.

Large language models (LLMs) have demonstrated proficiency across various natural language processing (NLP) tasks but often require additional training, such as continual pre-training and supervised fine-tuning. However, the costs associated with this, primarily due to their large parameter count, remain high. This paper proposes leveraging sparsity in pre-trained LLMs to expedite this training process. By observing sparsity in activated neurons during forward iterations, we identify the potential for computational speed-ups by excluding inactive neurons. We address associated challenges by extending existing neuron importance evaluation metrics and introducing a ladder omission rate scheduler. Our experiments on Llama-2 demonstrate that Sparsity-Accelerated Training (SAT) achieves comparable or superior performance to standard training while significantly accelerating the process. Specifically, SAT achieves a 45% throughput improvement in continual pre-training and saves 38% training time in supervised fine-tuning. It offers a simple, hardware-agnostic, and easily deployable framework for additional LLM training.