# SmolTulu: Higher Learning Rate to Batch Size Ratios Can Lead to Better Reasoning in SLMs

arXiv: https://arxiv.org/abs/2412.08347 · HTML: https://mlsanity.com/paper/2412.08347/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 22 of its 26 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 22 of 22)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Don't Decay the Learning Rate, Increase the Batch Size](https://mlsanity.com/paper/1711.00489/) (2017)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [Measuring the Effects of Data Parallelism on Neural Network Training](https://mlsanity.com/paper/1811.03600/) (2018)
- [VinePPO: Refining Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2410.01679/) (2024)
- [Revisiting Small Batch Training for Deep Neural Networks](https://mlsanity.com/paper/1804.07612/) (2018)
- [OpenRLHF: An Easy-to-use, Scalable and High-performance RLHF Framework](https://mlsanity.com/paper/2405.11143/) (2024)
- [Training Chain-of-Thought via Latent-Variable Inference](https://mlsanity.com/paper/2312.02179/) (2023)

## Built on by (most cited first, 3 of 3)

- [Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2504.12501/) (2025)
- [TransforMerger: Transformer-based Voice-Gesture Fusion for Robust Human-Robot Communication](https://mlsanity.com/paper/2504.01708/) (2025)
- [EasyMath: A 0-shot Math Benchmark for SLMs](https://mlsanity.com/paper/2505.14852/) (2025)

## Abstract (arXiv)

We present SmolTulu-1.7b-Instruct, referenced in this report as SmolTulu-DPO-1130, an instruction-tuned language model that adapts AllenAI's Tulu 3 post-training pipeline to enhance Huggingface's SmolLM2-1.7B base model. Through comprehensive empirical analysis using a 135M parameter model, we demonstrate that the relationship between learning rate and batch size significantly impacts model performance in a task-dependent manner. Our findings reveal a clear split: reasoning tasks like ARC and GSM8K benefit from higher learning rate to batch size ratios, while pattern recognition tasks such as HellaSwag and IFEval show optimal performance with lower ratios. These insights informed the development of SmolTulu, which achieves state-of-the-art performance among sub-2B parameter models on instruction following, scoring 67.7% on IFEval (Delta11%), and mathematical reasoning with 51.6% on GSM8K (Delta3.4%), with an alternate version achieving scoring 57.1% on ARC (Delta5.4%). We release our model, training recipes, and ablation studies to facilitate further research in efficient model alignment, demonstrating that careful adaptation of optimization dynamics can help bridge the capability gap between small and large language models.