# FOLD: Position-Free Far Memory with Local Order for Long-Context Speculative Decoding

arXiv: https://arxiv.org/abs/2610.20392 · HTML: https://mlsanity.com/paper/2610.20392/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 32)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [LongBench v2: Towards Deeper Understanding and Reasoning on Realistic Long-context Multitasks](https://mlsanity.com/paper/2412.15204/) (2024)
- [∞Bench: Extending Long Context Evaluation Beyond 100K Tokens](https://mlsanity.com/paper/2402.13718/) (2024)
- [RepoBench: Benchmarking Repository-Level Code Auto-Completion Systems](https://mlsanity.com/paper/2306.03091/) (2023)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [InfLLM: Training-Free Long-Context Extrapolation for LLMs with an Efficient Context Memory](https://mlsanity.com/paper/2402.04617/) (2024)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [DFlash: Block Diffusion for Flash Speculative Decoding](https://mlsanity.com/paper/2602.06036/) (2026)
- [TriForce: Lossless Acceleration of Long Sequence Generation with Hierarchical Speculative Decoding](https://mlsanity.com/paper/2404.11912/) (2024)
- [MagicDec: Breaking the Latency-Throughput Tradeoff for Long Context Generation with Speculative Decoding](https://mlsanity.com/paper/2408.11049/) (2024)
- [Why Does the Effective Context Length of LLMs Fall Short?](https://mlsanity.com/paper/2410.18745/) (2024)
- [Long Code Arena: a Set of Benchmarks for Long-Context Code Models](https://mlsanity.com/paper/2406.11612/) (2024)
- [DSpark: Confidence-Scheduled Speculative Decoding with Semi-Autoregressive Generation](https://mlsanity.com/paper/2607.05147/) (2026)
- [Domino: Decoupling Causal Modeling from Autoregressive Drafting in Speculative Decoding](https://mlsanity.com/paper/2605.29707/) (2026)
- [LongSpec: Long-Context Lossless Speculative Decoding with Efficient Drafting and Verification](https://mlsanity.com/paper/2502.17421/) (2025)
- [SPEED-Bench: A Unified and Diverse Benchmark for Speculative Decoding](https://mlsanity.com/paper/2604.09557/) (2026)
- [Vegas: Self-Speculative Decoding with Verification-Guided Sparse Attention](https://mlsanity.com/paper/2602.07223/) (2026)
- [SpecExtend: A Drop-in Enhancement for Speculative Decoding of Long Sequences](https://mlsanity.com/paper/2505.20776/) (2025)

## Abstract (arXiv)

Speculative decoding accelerates LLM generation through lightweight drafting and parallel verification. It is particularly promising for long inputs, where KV-cache access costs can be amortized over multiple accepted tokens. Yet most drafters are trained on short sequences and degrade on long inputs, while long-context training is costly. Existing training-free approaches restrict the context window, rescale positions, or augment recent context with retrieved distant entries. Drafters, however, read target hidden states that already encode contextual and positional information, and their lightweight architecture makes full-history attention affordable. We propose FOLD, a training-free method that preserves exact local positions and treats all distant entries as far memory at a shared position. To counter attention dilution as the memory grows, we sharpen attention within it to emphasize relevant entries while separately controlling its total weight relative to the local window. Across six target-drafter pairs and diverse benchmarks of up to 256K tokens, FOLD predominantly delivers the highest speedup, with the best case more than doubling the speedup over autoregressive decoding, from 2.08× to 4.22×.