# PERK: Long-Context Reasoning as Test-Time Learning

arXiv: https://arxiv.org/abs/2507.06415 · HTML: https://mlsanity.com/paper/2507.06415/

## Key facts

- Cited by 4 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 50 of its 83 references that are in the map.
- First posted on arXiv 8 Jul 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, 30 of 50)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Long-context LLMs Struggle with Long In-context Learning](https://mlsanity.com/paper/2404.02060/) (2024)
- [LongLoRA: Efficient Fine-tuning of Long-Context Large Language Models](https://mlsanity.com/paper/2309.12307/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [mGTE: Generalized Long-Context Text Representation and Reranking Models for Multilingual Text Retrieval](https://mlsanity.com/paper/2407.19669/) (2024)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Simple linear attention language models balance the recall-throughput tradeoff](https://mlsanity.com/paper/2402.18668/) (2024)
- [Data Engineering for Scaling Language Models to 128K Context](https://mlsanity.com/paper/2402.10171/) (2024)
- [Qwen2.5-1M Technical Report](https://mlsanity.com/paper/2501.15383/) (2025)
- [Same Task, More Tokens: the Impact of Input Length on the Reasoning Performance of Large Language Models](https://mlsanity.com/paper/2402.14848/) (2024)

## Built on by (most cited first, 4 of 4)

- [Accumulating Context Changes the Beliefs of Language Models](https://mlsanity.com/paper/2511.01805/) (2025)
- [DySCO: Dynamic Attention-Scaling Decoding for Long-Context Language Models](https://mlsanity.com/paper/2602.22175/) (2026)
- [Beyond Perplexity: A Behavioral Evaluation Framework for Deployment-Memory Claims in LLM Test-Time Training](https://mlsanity.com/paper/2607.00368/) (2026)
- [Self-Guided Test-Time Training for Long-Context LLMs](https://mlsanity.com/paper/2607.09415/) (2026)

## Abstract (arXiv)

Long-context reasoning requires accurately identifying relevant information in extensive, noisy input contexts. In this work, we propose PERK (Parameter Efficient Reasoning over Knowledge), a scalable approach for learning to encode long contexts using gradient updates at test time. Specifically, PERK employs two nested optimization loops in a meta-training phase. The inner loop rapidly encodes contexts into a low-rank adapter (LoRA) that serves as a parameter-efficient memory module for the base model. Concurrently, the outer loop learns to use the updated adapter to accurately recall and reason over relevant information from the encoded long context. Our evaluations on several long-context reasoning tasks show that PERK significantly outperforms the standard long-context finetuning, achieving average absolute performance gains of up to 20% for Qwen-2.5 (0.5B & 7B) on synthetic and real-world long-context reasoning. PERK also maintains its advantages across model scales and families. Compared to specialized long-context LLMs, PERK matches or surpasses their performance. Finally, our analyses show PERK is more robust to reasoning complexity, length extrapolation, and the positions of relevant information in contexts. https://perk-long-context.web.app