# Towards Efficient Post-Training via Fourier-Driven Adapter Architectures

arXiv: https://arxiv.org/abs/2512.22378 · HTML: https://mlsanity.com/paper/2512.22378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 56 references that are in the map.
- First posted on arXiv 26 Dec 2025.

## Builds on (most cited first, 30 of 39)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Compacter: Efficient Low-Rank Hypercomplex Adapter Layers](https://mlsanity.com/paper/2106.04647/) (2021)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [Multi-Task Deep Neural Networks for Natural Language Understanding](https://mlsanity.com/paper/1901.11504/) (2019)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [Exploring Versatile Generative Language Model Via Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2004.03829/) (2020)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)
- [Revisiting Out-of-distribution Robustness in NLP: Benchmark, Analysis, and LLMs Evaluations](https://mlsanity.com/paper/2306.04618/) (2023)
- [Pretrained Language Models for Text Generation: A Survey](https://mlsanity.com/paper/2105.10311/) (2021)
- [Evaluating the State-of-the-Art of End-to-End Natural Language Generation: The E2E NLG Challenge](https://mlsanity.com/paper/1901.07931/) (2019)
- [CF-VLM:CounterFactual Vision-Language Fine-tuning](https://mlsanity.com/paper/2506.17267/) (2025)
- [GAM-Agent: Game-Theoretic and Uncertainty-Aware Collaboration for Complex Visual Reasoning](https://mlsanity.com/paper/2505.23399/) (2025)
- [Language Through a Prism: A Spectral Approach for Multiscale Language Representations](https://mlsanity.com/paper/2011.04823/) (2020)
- [Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization](https://mlsanity.com/paper/2412.17739/) (2024)
- [MAT-Agent: Adaptive Multi-Agent Training Optimization](https://mlsanity.com/paper/2510.17845/) (2025)
- [DrDiff: Dynamic Routing Diffusion with Hierarchical Attention for Breaking the Efficiency-Quality Trade-off](https://mlsanity.com/paper/2509.02785/) (2025)
- [MM-CoT:A Benchmark for Probing Visual Chain-of-Thought Reasoning in Multimodal Models](https://mlsanity.com/paper/2512.08228/) (2025)
- [DepthSSC: Monocular 3D Semantic Scene Completion via Depth-Spatial Alignment and Voxel Adaptation](https://mlsanity.com/paper/2311.17084/) (2023)

## Abstract (arXiv)

We propose a novel framework, termed Fourier-Activated Adapter (FAA), for parameter-efficient fine-tuning of large pre-trained language models. By incorporating random Fourier features into lightweight adapter modules, FAA decomposes intermediate representations into complementary low- and high-frequency components, enabling frequency-aware modulation of semantic information. This design allows the model to selectively emphasize informative frequency bands during adaptation while preserving the representational capacity of the frozen backbone. Extensive experiments on GLUE, E2E NLG, and instruction-tuning benchmarks demonstrate that FAA consistently achieves competitive or superior performance compared to existing parameter-efficient fine-tuning methods, while maintaining low computational and memory overhead. Ablation studies further verify the effectiveness of frequency-aware activation and adaptive weighting mechanisms, highlighting FAA as a robust and efficient approach for post-training large language models.