# Mamba Modulation: On the Length Generalization of Mamba

arXiv: https://arxiv.org/abs/2509.19633 · HTML: https://mlsanity.com/paper/2509.19633/

## Key facts

- Cited by 16 papers in the map (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 112 of its 148 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## 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, 30 of 112)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)

## Built on by (most cited first, 16 of 16)

- [InfMem: Learning System-2 Memory Control for Long-Context Agent](https://mlsanity.com/paper/2602.02704/) (2026)
- [Raven: High-Recall Sequence Modeling with Sparse Memory Routing](https://mlsanity.com/paper/2607.25357/) (2026)
- [On the Spatiotemporal Dynamics of Generalization in Neural Networks](https://mlsanity.com/paper/2602.01651/) (2026)
- [CLIMP: Contrastive Language-Image Mamba Pretraining](https://mlsanity.com/paper/2601.06891/) (2026)
- [Mamba-driven multi-perspective structural understanding for molecular ground-state conformation prediction](https://mlsanity.com/paper/2511.09564/) (2025)
- [Probing Length Generalization in Mamba via Image Reconstruction](https://mlsanity.com/paper/2603.12499/) (2026)
- [How Many Different Outputs Can a Transformer Generate?](https://mlsanity.com/paper/2605.22223/) (2026)
- [Refit the Probe: Single-Direction Ablation Is Not a Necessity Test](https://mlsanity.com/paper/2606.00926/) (2026)
- [Mutual Modality Trust with Lightweight Reconstruction Regularization for Fine-grained Tire Pattern Recognition](https://mlsanity.com/paper/2607.23979/) (2026)
- [SpectralShift: Effective Context Window Extension of Gated DeltaNet via Spectral Reparameterization](https://mlsanity.com/paper/2609.14320/) (2026)
- [On the Importance of Gating: Memorization vs. In-Context Learning in State Space Models](https://mlsanity.com/paper/2609.16540/) (2026)
- [ARM: Attention with Routed-Memory for Learnable Sparse Control](https://mlsanity.com/paper/2609.24417/) (2026)
- [Fractional State Space Transition for Long Sequence Modeling](https://mlsanity.com/paper/2609.36314/) (2026)
- [Length Generalization Needs Proper Regularization](https://mlsanity.com/paper/2610.04518/) (2026)
- [Understanding Mamba-3 Through Oscillatory Dynamics](https://mlsanity.com/paper/2610.13341/) (2026)
- [History Replays Itself: Unleashing Long-Context Capability in Linear Attention](https://mlsanity.com/paper/2610.15715/) (2026)

## Abstract (arXiv)

The quadratic complexity of the attention mechanism in Transformer models has motivated the development of alternative architectures with sub-quadratic scaling, such as state-space models. Among these, Mamba has emerged as a leading architecture, achieving state-of-the-art results across a range of language modeling tasks. However, Mamba's performance significantly deteriorates when applied to contexts longer than those seen during pre-training, revealing a sharp sensitivity to context length extension. Through detailed analysis, we attribute this limitation to the out-of-distribution behaviour of its state-space dynamics, particularly within the parameterization of the state transition matrix A. Unlike recent works which attribute this sensitivity to the vanished accumulation of discretization time steps, exp(-sumt=1NDeltat), we establish a connection between state convergence behavior as the input length approaches infinity and the spectrum of the transition matrix A, offering a well-founded explanation of its role in length extension. Next, to overcome this challenge, we propose an approach that applies spectrum scaling to pre-trained Mamba models to enable robust long-context generalization by selectively modulating the spectrum of A matrices in each layer. We show that this can significantly improve performance in settings where simply modulating Deltat fails, validating our insights and providing avenues for better length generalization of state-space models with structured transition matrices.