# The Attention Within: Consensus Dynamics in Selective State Space Models

arXiv: https://arxiv.org/abs/2609.17997 · HTML: https://mlsanity.com/paper/2609.17997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Core SSM architectures for language, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Placed in

- State-space sequence models (S4, Mamba) / [Core SSM architectures for language](https://mlsanity.com/ssm/core-ssm-architectures-for-language/)

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [The Illusion of State in State-Space Models](https://mlsanity.com/paper/2404.08819/) (2024)
- [An Empirical Study of Mamba-based Language Models](https://mlsanity.com/paper/2406.07887/) (2024)
- [A mathematical perspective on Transformers](https://mlsanity.com/paper/2312.10794/) (2023)
- [Signal Propagation in Transformers: Theoretical Perspectives and the Role of Rank Collapse](https://mlsanity.com/paper/2206.03126/) (2022)
- [The emergence of clusters in self-attention dynamics](https://mlsanity.com/paper/2305.05465/) (2023)
- [The Hidden Attention of Mamba Models](https://mlsanity.com/paper/2403.01590/) (2024)
- [Understanding and Mitigating Bottlenecks of State Space Models through the Lens of Recency and Over-smoothing](https://mlsanity.com/paper/2501.00658/) (2024)
- [The Asymptotic Behavior of Attention in Transformers](https://mlsanity.com/paper/2412.02682/) (2024)
- [Clustering in pure-attention hardmax transformers and its role in sentiment analysis](https://mlsanity.com/paper/2407.01602/) (2024)
- [Lambda-Skip Connections: the architectural component that prevents Rank Collapse](https://mlsanity.com/paper/2410.10609/) (2024)
- [Contextual Representation Flow Across Depth in State-Space and Transformer Architectures](https://mlsanity.com/paper/2510.06640/) (2025)

## Abstract (arXiv)

Selective state space models (SSMs) have recently emerged as a compelling alternative to transformers, combining competitive performance with substantially improved inference efficiency. At each SSM layer, a sequence of hidden states are propagated by a recurrence, mixing information of different tokens. Despite using a different mechanism, this mixing plays a role analogous to attention in transformers. In fact, recent works have shown that the two architectures may be closer than they first appear, as this recurrence admits a formulation akin to linear attention. In transformers, attention is known to drive the tokens to cluster, i.e., to reach consensus, collapsing in the limit to a single direction. Thus, we ask: does the recurrence at the core of SSMs drive the tokens to consensus, as attention does in transformers? To answer this question, we take a dynamical systems perspective on SSMs, modeling the evolution of tokens across layers as an ordinary differential equation. By exploiting input-to-state stability arguments, we establish local exponential stability of the consensus equilibria and characterize their domain of attraction for time-varying weight matrices, a setting not addressed by previous results. We thereby show that the resemblance between SSMs and transformers does run deeper: the recurrence at the core of SSMs aggregates tokens just as attention does. Numerical experiments on a pretrained Mamba-2 model point to the output gate as the component that regulates the extent of this consensus, preventing the tokens from reaching it in full.