Lost in State Space: Probing Frozen Mamba Representations

Recurrent linear attention models (RLAs) such as Mamba offer efficient linear-time sequence modeling as an alternative to Transformers, yet their fixed-capacity recurrent states limit long-sequence modeling. Drawing inspiration from hierarchical human memory, we propose Hierarchical Memory Mamba (HMM) to address this limitation. Building upon a pre-trained Mamba backbone, HMM integrates a lightweight working memory that extracts slow paragraph-level semantics (PLS) from the fast sensory memory embedded in the backbone's hidden states. The PLS is subsequently compressed into persistent long-term memory for task-relevant retrieval. The hierarchical processing of semantic information overcomes the representation bottleneck of RLAs and endows HMM cross-task generalization through parametric learning, which is not observed in other long-context enhanced Mamba variants. Evaluations on Passkey Retrieval and LongBench-E tasks demonstrate that HMM improves retrieval success by 34.3--37.1% and reasoning accuracy by 1.6--14.2% over strong Mamba-based models, while adding only 2% extra parameters and with minimal training overhead.

State Space Models (SSMs) such as Mamba-2 offer linear-time inference but their memory footprint limits edge deployment. Prior ternary SSM work (Slender-Mamba) trains from scratch on 150B tokens; we show a pretrained checkpoint suffices, reducing the marginal token budget by 1,000x. Using grouped quantization-aware training (QAT) with knowledge distillation from a frozen FP16 teacher, we compress Mamba-2 1.3B to 3.61x (2,687 to 744 MB) and achieve 48.1% zero-shot accuracy (7-task average) in just 102M tokens (4 GPU-hours, single H100) -- approaching Bi-Mamba's 48.4% (within +/-0.9pp CI). This QAT-from-pretrained setting reveals zero-ratio collapse, a novel instability caused by learnable quantization scales that does not arise in from-scratch training. We further show that post-hoc correction strategies effective for Transformers fail for SSMs due to error accumulation through the recurrence. These results demonstrate that ternary SSMs do not require expensive from-scratch training: QAT from pretrained checkpoints with KD is a data-efficient alternative.

The quadratic scaling of Transformer self-attention has driven the adoption of sub-quadratic Selective State Space Models (SSMs) like Mamba, which compress past context into a fixed-size recurrent hidden state. This strict informational bottleneck raises a foundational question for mechanistic interpretability: do SSMs and Transformers learn fundamentally distinct latent representations? In this work, we employ Sparse Autoencoders (SAEs) to conduct a large-scale, feature-level correspondence analysis between Mamba-130m and Pythia-70m over a 10-million token corpus. Contrary to hypotheses predicting widespread architectural divergence, we find no evidence of systematic representational divergence between architectures: across the observed Jaccard distribution, 99.98% of Mamba features cluster toward the upper alignment boundary, providing preliminary feature-level support for the Universality Hypothesis. We further identify and qualitatively characterize this microscopic fraction (0.02%) of diverging features, finding patterns consistent with the hypothesis that the recurrent bottleneck selectively limits the parsing of rigid syntax rather than broad semantic ontology. We demonstrate that while Pythia's unconstrained attention permits the monosemantic decomposition of distinct formatting edge-cases, Mamba is forced to compress unrelated syntactical anomalies into polysemantic "junk drawer" neurons to preserve state capacity. Collectively, these results suggest that architectural routing mechanisms may have negligible impact on core semantic understanding, with representational divergence confined to extreme structural margins.