State-space models (SSMs) have emerged as promising alternatives to Transformers for sequence modeling. However, training competitive SSMs from scratch remains computationally intensive, and the ecosystem around them is far less mature than that of Transformers. Moreover, the architectural differences between SSMs and Transformers make it challenging to efficiently transfer knowledge from pretrained Transformers. In this work, we propose Cross-architecture distillation via Attention Bridge (CAB), a distillation framework that transfers attention-related representations from Transformer teachers to state-space student models. Unlike conventional knowledge distillation that supervises only final predictions, CAB enables token-level intermediate supervision through a lightweight bridge and flexible layer-wise alignment. By aligning Transformer attention-related representations with Mamba's token-dependent state projections, CAB facilitates efficient cross-architecture knowledge transfer without inference-time overhead. Experiments on image classification and language modeling demonstrate that CAB improves Transformer-to-SSM distillation, particularly under limited-supervision settings. Overall, CAB provides an efficient pathway for transferring Transformer representations to SSM-based models, helping bridge the gap between mature Transformer ecosystems and emerging SSM ecosystems.
Selective state space models (SSMs) have recently emerged as a compelling alternative to transformers, combining competitive performance with substantially improved inference efficiency. At each SSM layer, a sequence of hidden states are propagated by a recurrence, mixing information of different tokens. Despite using a different mechanism, this mixing plays a role analogous to attention in transformers. In fact, recent works have shown that the two architectures may be closer than they first appear, as this recurrence admits a formulation akin to linear attention. In transformers, attention is known to drive the tokens to cluster, i.e., to reach consensus, collapsing in the limit to a single direction. Thus, we ask: does the recurrence at the core of SSMs drive the tokens to consensus, as attention does in transformers? To answer this question, we take a dynamical systems perspective on SSMs, modeling the evolution of tokens across layers as an ordinary differential equation. By exploiting input-to-state stability arguments, we establish local exponential stability of the consensus equilibria and characterize their domain of attraction for time-varying weight matrices, a setting not addressed by previous results. We thereby show that the resemblance between SSMs and transformers does run deeper: the recurrence at the core of SSMs aggregates tokens just as attention does. Numerical experiments on a pretrained Mamba-2 model point to the output gate as the component that regulates the extent of this consensus, preventing the tokens from reaching it in full.
João Pedro Silvestre, Álvaro Rodríguez Abella, Paulo Tabuada
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.
Rithin Nagaraj, Rupa Laalasa Oruganti, Prerna Subhashchandra Kunder +1
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.
Ramprasath Ganesaraja, Sahil Dilip Panse, Swathika N