Tina: Tiny Reasoning Models via LoRA

How cost-effectively can strong reasoning abilities be achieved in language models? Driven by this question, we present Tina, a family of tiny reasoning models achieved with high cost-efficiency. Tina shows that substantial reasoning performance can be developed using only minimal resources, by applying low-rank adaptation (LoRA) during reinforcement learning (RL), to an already tiny 1.5B parameter base model. This minimalist approach produces models that are competitive with, and sometimes surpass, SOTA RL reasoning models built upon the same base model. Crucially, this is achieved at a tiny fraction of the computational cost employed by existing models. In fact, the best Tina model achieves a >20\% reasoning performance increase and 43.33\% zero-shot Pass@1 accuracy on AIME24, at only \$9 USD cost (i.e., an estimated 260x reduction). Our work reveals the surprising effectiveness of efficient RL reasoning via LoRA. We validate this across multiple open-source reasoning datasets and various ablation settings starting with a single, fixed set of hyperparameters. Furthermore, we explore the hypothesis that this effectiveness and efficiency stem from LoRA rapidly adapting the model to the structural format of reasoning rewarded by RL, while largely preserving the base model's underlying knowledge. In service of accessibility and open research, we fully open-source all code, training logs, model weights, and checkpoints.