# Contextual Representation Flow Across Depth in State-Space and Transformer Architectures

arXiv: https://arxiv.org/abs/2510.06640 · HTML: https://mlsanity.com/paper/2510.06640/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [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)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Emerging Cross-lingual Structure in Pretrained Language Models](https://mlsanity.com/paper/1911.01464/) (2019)
- [Probing Pretrained Language Models for Lexical Semantics](https://mlsanity.com/paper/2010.05731/) (2020)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [A Comprehensive Survey on Long Context Language Modeling](https://mlsanity.com/paper/2503.17407/) (2025)
- [Not All Layers of LLMs Are Necessary During Inference](https://mlsanity.com/paper/2403.02181/) (2024)
- [The Hidden Attention of Mamba Models](https://mlsanity.com/paper/2403.01590/) (2024)
- [Is Cosine-Similarity of Embeddings Really About Similarity?](https://mlsanity.com/paper/2403.05440/) (2024)
- [Insights into LLM Long-Context Failures: When Transformers Know but Don't Tell](https://mlsanity.com/paper/2406.14673/) (2024)
- [Is It Really Long Context if All You Need Is Retrieval? Towards Genuinely Difficult Long Context NLP](https://mlsanity.com/paper/2407.00402/) (2024)
- [Understanding and Mitigating Bottlenecks of State Space Models through the Lens of Recency and Over-smoothing](https://mlsanity.com/paper/2501.00658/) (2024)
- [Does Transformer Interpretability Transfer to RNNs?](https://mlsanity.com/paper/2404.05971/) (2024)

## Built on by (most cited first, 3 of 3)

- [Block-Recurrent Dynamics in Vision Transformers](https://mlsanity.com/paper/2512.19941/) (2025)
- [Benchmarking the Computational and Representational Efficiency of State Space Models against Transformers on Long-Context Dyadic Sessions](https://mlsanity.com/paper/2601.01237/) (2026)
- [The Attention Within: Consensus Dynamics in Selective State Space Models](https://mlsanity.com/paper/2609.17997/) (2026)

## Abstract (arXiv)

State Space Models (SSMs) have emerged as efficient, linear-time alternatives to Transformer-Based Models (TBMs) for long-context processing. However, their different mechanisms raise an important question: how does contextual representation flow across depth differ between these model families and their hybrids? We examine this question across twenty-one pretrained models, combining token-wise spectral diversity, layer-wise variation on seven datasets, and answer-location probing on two retrieval tasks. This joint analysis reveals that TBMs retain most of their token diversity at the output, whereas SSMs reach richer intermediate diversity but retain less of it on average, with late-layer compression. Comparisons with reinitialized weights reveal that these profiles depend on pretrained weights, while hybrids combine strong answer-location accessibility with architecture-dependent geometry, showing that high accessibility need not require the steadiest representation flow. Finally, we conduct theoretical case studies connecting these contrasts to mechanism-level differences: query-time token mixing in TBMs, repeated recurrent updates in SSMs, and preserved attention updates in hybrids.