# Thinking Forward: Memory-Efficient Federated Finetuning of Language Models

arXiv: https://arxiv.org/abs/2405.15551 · HTML: https://mlsanity.com/paper/2405.15551/

## Key facts

- Cited by 7 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 18 of its 58 references that are in the map.
- First posted on arXiv 24 May 2024.

## 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, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [FedScale: Benchmarking Model and System Performance of Federated Learning at Scale](https://mlsanity.com/paper/2105.11367/) (2021)
- [OpenFedLLM: Training Large Language Models on Decentralized Private Data via Federated Learning](https://mlsanity.com/paper/2402.06954/) (2024)
- [Gradients without Backpropagation](https://mlsanity.com/paper/2202.08587/) (2022)
- [FATE-LLM: A Industrial Grade Federated Learning Framework for Large Language Models](https://mlsanity.com/paper/2310.10049/) (2023)
- [Motley: Benchmarking Heterogeneity and Personalization in Federated Learning](https://mlsanity.com/paper/2206.09262/) (2022)
- [FwdLLM: Efficient FedLLM using Forward Gradient](https://mlsanity.com/paper/2308.13894/) (2023)
- [BAFFLE: A Baseline of Backpropagation-Free Federated Learning](https://mlsanity.com/paper/2301.12195/) (2023)
- [FedFwd: Federated Learning without Backpropagation](https://mlsanity.com/paper/2309.01150/) (2023)

## Built on by (most cited first, 7 of 7)

- [Distributed LLMs and Multimodal Large Language Models: A Survey on Advances, Challenges, and Future Directions](https://mlsanity.com/paper/2503.16585/) (2025)
- [Unity is Power: Semi-Asynchronous Collaborative Training of Large-Scale Models with Structured Pruning in Resource-Limited Clients](https://mlsanity.com/paper/2410.08457/) (2024)
- [Memory Savings at What Cost? A Study of Alternatives to Backpropagation](https://mlsanity.com/paper/2506.21833/) (2025)
- [Efficient Zeroth-Order Federated Finetuning of Language Models on Resource-Constrained Devices](https://mlsanity.com/paper/2502.10239/) (2025)
- [Federated Learning with Ad-hoc Adapter Insertions: The Case of Soft-Embeddings for Training Classifier-as-Retriever](https://mlsanity.com/paper/2509.16508/) (2025)
- [CooperLLM: Cloud-Edge-End Cooperative Federated Fine-tuning for LLMs via ZOO-based Gradient Correction](https://mlsanity.com/paper/2601.12917/) (2026)
- [ZorBA: Zeroth-order Federated Fine-tuning of LLMs with Heterogeneous Block Activation](https://mlsanity.com/paper/2603.04436/) (2026)

## Abstract (arXiv)

Finetuning large language models (LLMs) in federated learning (FL) settings has become increasingly important as it allows resource-constrained devices to finetune a model using private data. However, finetuning LLMs using backpropagation requires excessive memory (especially from intermediate activations) for resource-constrained devices. While Forward-mode Auto-Differentiation (AD) can significantly reduce memory footprint from activations, we observe that directly applying it to LLM finetuning results in slow convergence and poor accuracy. In this paper, we introduce Spry, an FL algorithm that splits trainable weights of an LLM among participating clients, such that each client computes gradients using forward-mode AD that are closer estimations of the true gradients. Spry achieves a low memory footprint, high accuracy, and fast convergence. We formally prove that the global gradients in Spry are unbiased estimators of true global gradients for homogeneous data distributions across clients, while heterogeneity increases bias of the estimates. We also derive Spry's convergence rate, showing that the gradients decrease inversely proportional to the number of FL rounds, indicating the convergence up to the limits of heterogeneity. Empirically, Spry reduces the memory footprint during training by 1.4-7.1x in contrast to backpropagation, while reaching comparable accuracy, across a wide range of language tasks, models, and FL settings. Spry reduces the convergence time by 1.2-20.3x and achieves 5.2-13.5% higher accuracy against zero-order methods. When finetuning Llama2-7B with LoRA, compared to the peak memory consumption of 33.9GB of backpropagation, Spry only consumes 6.2GB of peak memory. For OPT13B, the reduction is from 76.5GB to 10.8GB. Spry makes feasible previously impossible FL deployments on commodity edge devices. Our source code is available at https://github.com/Astuary/Spry.