# Design Principles for Sequence Models via Coefficient Dynamics

arXiv: https://arxiv.org/abs/2510.09389 · HTML: https://mlsanity.com/paper/2510.09389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 67 references that are in the map.
- First posted on arXiv 10 Oct 2025.

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [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)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models](https://mlsanity.com/paper/2402.19427/) (2024)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Transformer Dissection: A Unified Understanding of Transformer's Attention via the Lens of Kernel](https://mlsanity.com/paper/1908.11775/) (2019)

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

- [SHiPPO: Recurrent Memory with Transported Polynomial Projections](https://mlsanity.com/paper/2607.03055/) (2026)

## Abstract (arXiv)

Deep sequence models, ranging from Transformers and State Space Models (SSMs) to more recent approaches such as gated linear RNNs, fundamentally compute outputs as linear combinations of past value vectors. To draw insights and systematically compare such architectures, we develop a unified framework that makes this output operation explicit, by casting the linear combination coefficients as the outputs of autonomous linear dynamical systems driven by impulse inputs. This viewpoint, in spirit substantially different from approaches focusing on connecting linear RNNs with linear attention, reveals a common mathematical theme across diverse architectures and crucially captures softmax attention, on top of RNNs, SSMs, and related models. In contrast to new model proposals that are commonly evaluated on benchmarks, we derive design principles linking architectural choices to model properties. Thereby identifying tradeoffs between expressivity and efficient implementation, geometric constraints on input selectivity, and stability conditions for numerically stable training and information retention. By connecting several insights and observations from recent literature, the framework both explains empirical successes of recent designs and provides guiding principles for systematically designing new sequence model architectures.