# FAEDKV: Infinite-Window Fourier Transform for Unbiased KV Cache Compression

arXiv: https://arxiv.org/abs/2507.20030 · HTML: https://mlsanity.com/paper/2507.20030/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 17 of 17)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Model Tells You What to Discard: Adaptive KV Cache Compression for LLMs](https://mlsanity.com/paper/2310.01801/) (2023)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Long Context Compression with Activation Beacon](https://mlsanity.com/paper/2401.03462/) (2024)
- [NeedleBench: Evaluating LLM Retrieval and Reasoning Across Varying Information Densities](https://mlsanity.com/paper/2407.11963/) (2024)
- [Fourier Transformer: Fast Long Range Modeling by Removing Sequence Redundancy with FFT Operator](https://mlsanity.com/paper/2305.15099/) (2023)
- [LoCoCo: Dropping In Convolutions for Long Context Compression](https://mlsanity.com/paper/2406.05317/) (2024)
- [InfiniteHiP: Extending Language Model Context Up to 3 Million Tokens on a Single GPU](https://mlsanity.com/paper/2502.08910/) (2025)
- [FreqKV: Key-Value Compression in Frequency Domain for Context Window Extension](https://mlsanity.com/paper/2505.00570/) (2025)

## Built on by (most cited first, 11 of 11)

- [SCRIBE: Structured Mid-Level Supervision for Tool-Using Language Models](https://mlsanity.com/paper/2601.03555/) (2026)
- [When Truthful Representations Flip Under Deceptive Instructions?](https://mlsanity.com/paper/2507.22149/) (2025)
- [Quantized but Deceptive? A Multi-Dimensional Truthfulness Evaluation of Quantized LLMs](https://mlsanity.com/paper/2508.19432/) (2025)
- [Demystifying Hybrid Thinking: Can LLMs Truly Switch Between Think and No-Think?](https://mlsanity.com/paper/2510.12680/) (2025)
- [Path-Lock Expert: Separating Reasoning Mode in Hybrid Thinking via Architecture-Level Separation](https://mlsanity.com/paper/2604.27201/) (2026)
- [Pruning Weights but Not Truth: Safeguarding Truthfulness While Pruning LLMs](https://mlsanity.com/paper/2509.00096/) (2025)
- [Blurry Window Attention](https://mlsanity.com/paper/2606.09862/) (2026)
- [VisuoAlign: Safety Alignment of LVLMs with Multimodal Tree Search](https://mlsanity.com/paper/2510.15948/) (2025)
- [FreqDepthKV: Frequency-Guided Depth Sharing for Robust KV Cache Compression in Long-Context LLM Inference](https://mlsanity.com/paper/2607.06519/) (2026)
- [Codec-Gauge: Learning Compression-Friendly Gauges for Transformer KV Caches](https://mlsanity.com/paper/2607.20538/) (2026)
- [What Matters for Aggressive Decoding-Time KV Eviction? Temporal Aggregation and Ranking Preservation](https://mlsanity.com/paper/2609.03515/) (2026)

## Abstract (arXiv)

The efficacy of Large Language Models (LLMs) in long-context tasks is often hampered by the substantial memory footprint and computational demands of the Key-Value (KV) cache. Current compression strategies, including token eviction and learned projections, frequently lead to biased representations -- either by overemphasizing recent/high-attention tokens or by repeatedly degrading information from earlier context -- and may require costly model retraining. We present FAEDKV (Frequency-Adaptive Infinite-Window for KV cache), a novel, training-free KV cache compression framework that ensures unbiased information retention. FAEDKV operates by transforming the KV cache into the frequency domain using a proposed Infinite-Window Fourier Transform (IWDFT). This approach allows for the equalized contribution of all tokens to the compressed representation, effectively preserving both early and recent contextual information. A preliminary frequency ablation study identifies critical spectral components for layer-wise, targeted compression. Experiments on LongBench benchmark demonstrate FAEDKV's superiority over existing methods by up to 22%. In addition, our method shows superior, position-agnostic retrieval accuracy on the Needle-In-A-Haystack task compared to compression based approaches.