Controllability Analysis of State Space-based Language Model
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909917447716864 |
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| author | Mabrok, Mohamed Zafari, Yalda |
| author_facet | Mabrok, Mohamed Zafari, Yalda |
| contents | State-space models (SSMs), particularly Mamba, have become powerful architectures for sequence modeling, yet their internal dynamics remain poorly understood compared to attention-based models. We introduce and validate the Influence Score, a controllability-based metric derived from the discretized state-space parameters of Mamba and computed through a backward recurrence analogous to system observability. The score quantifies how strongly a token at position k affects all later states and outputs. We evaluate this measure across three Mamba variants: mamba-130m, mamba-2.8b, and mamba-2.8b-slimpj, using six experiments that test its sensitivity to temperature, prompt complexity, token type, layer depth, token position, and input perturbations. The results show three main insights: (1) the Influence Score increases with model size and training data, reflecting model capacity; (2) Mamba exhibits consistent architectural patterns, including recency bias and concentrated influence in mid-to-late layers; and (3) emergent behaviors appear only at scale, with mamba-2.8b-slimpj uniquely prioritizing content words and reducing internal influence in the presence of noise. These findings establish the Influence Score as a practical diagnostic tool for interpreting and comparing SSM-based language models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17970 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Controllability Analysis of State Space-based Language Model Mabrok, Mohamed Zafari, Yalda Machine Learning State-space models (SSMs), particularly Mamba, have become powerful architectures for sequence modeling, yet their internal dynamics remain poorly understood compared to attention-based models. We introduce and validate the Influence Score, a controllability-based metric derived from the discretized state-space parameters of Mamba and computed through a backward recurrence analogous to system observability. The score quantifies how strongly a token at position k affects all later states and outputs. We evaluate this measure across three Mamba variants: mamba-130m, mamba-2.8b, and mamba-2.8b-slimpj, using six experiments that test its sensitivity to temperature, prompt complexity, token type, layer depth, token position, and input perturbations. The results show three main insights: (1) the Influence Score increases with model size and training data, reflecting model capacity; (2) Mamba exhibits consistent architectural patterns, including recency bias and concentrated influence in mid-to-late layers; and (3) emergent behaviors appear only at scale, with mamba-2.8b-slimpj uniquely prioritizing content words and reducing internal influence in the presence of noise. These findings establish the Influence Score as a practical diagnostic tool for interpreting and comparing SSM-based language models. |
| title | Controllability Analysis of State Space-based Language Model |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.17970 |