# Do Post-Training Algorithms Actually Differ? A Controlled Study Across Model Scales Uncovers Scale-Dependent Ranking Inversions

arXiv: https://arxiv.org/abs/2603.19335 · HTML: https://mlsanity.com/paper/2603.19335/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

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

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [Insights into Alignment: Evaluating DPO and its Variants Across Multiple Tasks](https://mlsanity.com/paper/2404.14723/) (2024)
- [It Takes Two: Your GRPO Is Secretly DPO](https://mlsanity.com/paper/2510.00977/) (2025)

## Built on by (most cited first, 2 of 2)

- [Multimodal Reward Hacking in Reinforcement Learning](https://mlsanity.com/paper/2607.09492/) (2026)
- [Scaling Near-Optimal SFT-RL Annotation Budget Allocation from Small to Large LLMs](https://mlsanity.com/paper/2609.01573/) (2026)

## Abstract (arXiv)

Post-training alignment has produced dozens of competing algorithms -- DPO, SimPO, KTO, GRPO, and others -- yet practitioners lack controlled comparisons to guide algorithm selection. We present OXRL, a unified framework implementing 51 post-training algorithms with identical infrastructure, enabling the first large-scale apples-to-apples evaluation. Our study spans 8 algorithms across 4 model scales (0.5B--7B), 3 evaluation domains, and a 20-variant DPO taxonomy (100 runs at 1.5B, 5 seeds each), totaling ~240 training runs on H100 GPUs. Three headline findings emerge. (1)~Algorithm rankings are unstable across scale: at 1.5B, online RL (SGRPO) tops all methods at 58.0%~±0.57 on GSM8K; by 7B, the worst small-scale method (SimPO) becomes the best (85.8%), a complete ranking inversion driven by model scale rather than LoRA regularization (confirmed via 2×2 factorial). (2)~Loss function modifications yield negligible gains: none of 20 DPO variants significantly outperform vanilla DPO after Bonferroni correction; the sole significant outlier, SimPO, is worse (-11.5~pp, p < 10-4). (3)~Algorithm leverage is task-specific: the 19.3~pp GSM8K spread collapses to 0.54~pp on MATH (36×) and 0.47~pp on general-domain benchmarks (41×), confirming that algorithm choice matters primarily within the training distribution. These findings yield a hierarchy of leverage for practitioners: model scale (~50~pp) gg training paradigm (~10~pp) gg online vs. offline (~9~pp) gg loss function (~1~pp). We release all code, configs, and evaluation data as a living community benchmark.