# Rethinking Local Learning: A Cheaper and Faster Recipe for LLM Post-Training

arXiv: https://arxiv.org/abs/2605.04913 · HTML: https://mlsanity.com/paper/2605.04913/

## Key facts

- Cited by 4 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 30 of its 33 references that are in the map.
- First posted on arXiv 6 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [Training Neural Networks with Local Error Signals](https://mlsanity.com/paper/1901.06656/) (2019)
- [Decoupled Greedy Learning of CNNs](https://mlsanity.com/paper/1901.08164/) (2019)
- [Momentum Auxiliary Network for Supervised Local Learning](https://mlsanity.com/paper/2407.05623/) (2024)
- [Advancing Supervised Local Learning Beyond Classification with Long-term Feature Bank](https://mlsanity.com/paper/2406.00446/) (2024)
- [MLAAN: Scaling Supervised Local Learning with Multilaminar Leap Augmented Auxiliary Network](https://mlsanity.com/paper/2406.16633/) (2024)
- [HPFF: Hierarchical Locally Supervised Learning with Patch Feature Fusion](https://mlsanity.com/paper/2407.05638/) (2024)
- [Beyond Words and Pixels: A Benchmark for Implicit World Knowledge Reasoning in Generative Models](https://mlsanity.com/paper/2511.18271/) (2025)
- [MAN++: Scaling Momentum Auxiliary Network for Supervised Local Learning in Vision Tasks](https://mlsanity.com/paper/2507.16279/) (2025)

## Built on by (most cited first, 4 of 4)

- [Replacement Learning: Training Neural Networks with Fewer Parameters](https://mlsanity.com/paper/2605.19533/) (2026)
- [ZeroLock: Concurrent Memory-Efficient LLM Training via Modular Update Decoupling](https://mlsanity.com/paper/2608.07974/) (2026)
- [SOLO: Pretraining Billion-Parameter Language Models with Shared-Output Local Learning](https://mlsanity.com/paper/2609.35440/) (2026)
- [Greedy Local Learning for Language Model Pretraining: Gaps and Objective Design](https://mlsanity.com/paper/2610.04867/) (2026)

## Abstract (arXiv)

LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward dependencies and direct task-gradient access to pretrained representations. We argue that this full-depth backward coupling can be unnecessarily expensive and intrusive, particularly when post-training supervision is much narrower than pre-training. To this end, we propose LoPT: Local-Learning Post-Training, a simple post-training strategy that makes gradient reach an explicit design choice. LoPT places a single gradient boundary at the transformer midpoint: the second-half block learns from the task objective, while the first-half block is updated by a lightweight feature-reconstruction objective to preserve useful representations and maintain interface compatibility. LoPT shortens the task-induced backward path while limiting direct interference from narrow task gradients on early-layer representations. Extensive experiments demonstrate that LoPT achieves competitive performance with lower memory cost, higher training efficiency and better retention of pretrained capabilities. Our code is available at: https://github.com/HumyuShi/LoPT