# HEFT: A Coarse-to-Fine Hierarchy for Enhancing the Efficiency and Accuracy of Language Model Reasoning

arXiv: https://arxiv.org/abs/2509.09801 · HTML: https://mlsanity.com/paper/2509.09801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 19 of its 20 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## 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, 19 of 19)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [On the Effectiveness of Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2211.15583/) (2022)
- [LoRA vs Full Fine-tuning: An Illusion of Equivalence](https://mlsanity.com/paper/2410.21228/) (2024)
- [A Survey on Parameter-Efficient Fine-Tuning for Foundation Models in Federated Learning](https://mlsanity.com/paper/2504.21099/) (2025)
- [Does Combining Parameter-efficient Modules Improve Few-shot Transfer Accuracy?](https://mlsanity.com/paper/2402.15414/) (2024)
- [FedReFT: Federated Representation Fine-Tuning with All-But-Me Aggregation](https://mlsanity.com/paper/2508.20295/) (2025)

## Abstract (arXiv)

The adaptation of large language models (LLMs) to specialized reasoning tasks is fundamentally constrained by computational resources. Parameter-Efficient Fine-Tuning (PEFT) methods have emerged as a powerful solution, yet the landscape of these techniques is diverse, with distinct methods operating in either the model's weight space or its representation space. This paper investigates the hypothesis that a synergistic combination of these paradigms can unlock superior performance and efficiency. We introduce HEFT (Hierarchical Efficient Fine-Tuning), a novel hierarchical adaptation strategy that composes two distinct PEFT methods in a coarse-to-fine manner: first, a broad, foundational adaptation in the weight space using Low-Rank Adaptation (LoRA), followed by a precise, surgical refinement of internal activations using Representation Fine-Tuning (ReFT). We evaluate this approach by fine-tuning a Llama-2-7B model on the BoolQ benchmark, a challenging dataset for inferential reasoning. Our results reveal a profound synergistic effect. A model fine-tuned for only three epochs with our HEFT strategy achieves an accuracy of 85.17%, exceeding the performance of models trained for 20 epochs with either LoRA-only (85.05%) or ReFT-only (83.36%) methodologies. This work demonstrates that the thoughtful composition of PEFT methods is a potent algorithmic innovation, offering a more efficient and effective path toward advancing the reasoning capabilities of language models. By achieving superior results with a fraction of the computational budget, our findings present a principled approach to overcoming the obstacles inherent in adapting large-scale models for complex cognitive tasks.