# Blending Complementary Memory Systems in Hybrid Quadratic-Linear Transformers

arXiv: https://arxiv.org/abs/2506.00744 · HTML: https://mlsanity.com/paper/2506.00744/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 77 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 30 of 58)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [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)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [Simple linear attention language models balance the recall-throughput tradeoff](https://mlsanity.com/paper/2402.18668/) (2024)
- [Leave No Context Behind: Efficient Infinite Context Transformers with Infini-attention](https://mlsanity.com/paper/2404.07143/) (2024)
- [The Parallelism Tradeoff: Limitations of Log-Precision Transformers](https://mlsanity.com/paper/2207.00729/) (2022)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)

## Built on by (most cited first, 12 of 12)

- [Distilling to Hybrid Attention Models via KL-Guided Layer Selection](https://mlsanity.com/paper/2512.20569/) (2025)
- [Fast-weight Product Key Memory](https://mlsanity.com/paper/2601.00671/) (2026)
- [Artificial Hippocampus Networks for Efficient Long-Context Modeling](https://mlsanity.com/paper/2510.07318/) (2025)
- [Fast weight programming and linear transformers: from machine learning to neurobiology](https://mlsanity.com/paper/2508.08435/) (2025)
- [The End of Transformers? On Challenging Attention and the Rise of Sub-Quadratic Architectures](https://mlsanity.com/paper/2510.05364/) (2025)
- [Memory for Large Language Models](https://mlsanity.com/paper/2607.25380/) (2026)
- [Effective Distillation to Hybrid xLSTM Architectures](https://mlsanity.com/paper/2603.15590/) (2026)
- [Untangling Component Imbalance in Hybrid Linear Attention Conversion Methods](https://mlsanity.com/paper/2510.05901/) (2025)
- [Hybrid Associative Memories](https://mlsanity.com/paper/2603.22325/) (2026)
- [Multi-Mixer Models: Flexible Sequence Modeling with Shared Representations](https://mlsanity.com/paper/2605.28769/) (2026)
- [Taylor-Calibrate: Principled Initialization for Hybrid Linear Attention Distillation](https://mlsanity.com/paper/2606.16429/) (2026)
- [Rethinking Expressivity and Efficiency in Test-Time Training](https://mlsanity.com/paper/2608.21308/) (2026)

## Abstract (arXiv)

We develop hybrid memory architectures for general-purpose sequence processing neural networks, that combine key-value memory using softmax attention (KV-memory) with fast weight memory through dynamic synaptic modulation (FW-memory) -- the core principles of quadratic and linear transformers, respectively. These two memory systems have complementary but individually limited properties: KV-memory offers precise retrieval but is constrained by quadratic complexity in sequence length, while FW-memory supports arbitrarily long sequences and enables more expressive computation but sacrifices precise recall. We propose and compare three methods to blend these two systems into a single memory system, differing in how and when input information is delivered to each system, to leverage the strengths of both. We conduct experiments on general language modeling and retrieval tasks by training 340M- and 1.3B-parameter models from scratch, as well as on synthetic algorithmic tasks designed to precisely illustrate the benefits of certain hybrid methods over others. We also evaluate our hybrid memory systems on reinforcement learning in partially observable environments. Overall, we demonstrate how a well-designed hybrid can overcome the limitations of its individual components, offering new insights into the design principle of neural memory systems.