Controllability Analysis of State Space-based Language Model
This provides a diagnostic tool for interpreting SSM-based language models, addressing a gap in understanding compared to attention-based models, but it is incremental as it builds on existing SSM architectures.
The paper tackled the problem of understanding the internal dynamics of state-space models (SSMs) like Mamba in language modeling by introducing the Influence Score, a controllability-based metric, and found that it increases with model size, reveals consistent architectural patterns such as recency bias, and shows emergent behaviors at scale, with mamba-2.8b-slimpj prioritizing content words and reducing influence under noise.
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.