# Taylor-Calibrate: Principled Initialization for Hybrid Linear Attention Distillation

arXiv: https://arxiv.org/abs/2606.16429 · HTML: https://mlsanity.com/paper/2606.16429/

## Key facts

- Cited by 1 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 48 of its 53 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Placed in

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

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [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)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Linear Transformers Are Secretly Fast Weight Programmers](https://mlsanity.com/paper/2102.11174/) (2021)
- [Jamba: A Hybrid Transformer-Mamba Language Model](https://mlsanity.com/paper/2403.19887/) (2024)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling](https://mlsanity.com/paper/2406.07522/) (2024)
- [MiniMax-01: Scaling Foundation Models with Lightning Attention](https://mlsanity.com/paper/2501.08313/) (2025)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)
- [Hymba: A Hybrid-head Architecture for Small Language Models](https://mlsanity.com/paper/2411.13676/) (2024)
- [Finetuning Pretrained Transformers into RNNs](https://mlsanity.com/paper/2103.13076/) (2021)
- [RNNs are not Transformers (Yet): The Key Bottleneck on In-context Retrieval](https://mlsanity.com/paper/2402.18510/) (2024)
- [Just read twice: closing the recall gap for recurrent language models](https://mlsanity.com/paper/2407.05483/) (2024)

## Built on by (most cited first, 1 of 1)

- [On-Policy Attention Linearization](https://mlsanity.com/paper/2609.31947/) (2026)

## Abstract (arXiv)

Hybrid linear attention models offer an appealing path to faster long-context inference: they reduce the quadratic cost and KV-cache burden of full softmax attention while retaining much of the quality of Transformer models. A practical way to obtain such models is to convert a pretrained Transformer instead of pretraining a new architecture from scratch, but this conversion is still brittle. Simply copying the teacher attention projections into a Gated DeltaNet (GDN) student does not specify the new recurrent decay, write, and output-gating dynamics. As a result, the converted model often starts in a poor dynamical regime and must spend many distillation tokens repairing initialization rather than learning the remaining teacher behavior. We propose Taylor-Calibrate, a lightweight initialization method for hybrid GDN students. The method uses Taylor-guided teacher attention statistics to set the value projection, memory timescale, write gates, and output gate, then applies a short per-layer alignment step to match each converted layer to the teacher output. Across four teacher settings and three retained-layer policies, Taylor-Calibrate gives substantially stronger zero-shot students, with up to an 88x improvement in a representative ablation, and reaches matched recovery targets with 4.9x--9.2x fewer training tokens than naive conversion.