Density Field State Space Models: 1-Bit Distillation, Efficient Inference, and Knowledge Organization in Mamba-2

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.

Modern language models are built primarily from Transformers, recurrent models, and their hybrid architectures. Transformers rely on token-level attention memories, while recurrent models such as state space models (SSMs) and linear attention maintain compact recurrent states. These architectures are typically instantiated separately or interleaved at the layer level, leaving open whether a shared memory representation can support both recurrent compression and attention-style retrieval. We study this question through the state space duality (SSD) view of Mamba-2, where the SSM state can be interpreted as a compressed associative key--value (KV) cache. We observe that Mamba-2 decodes token-conditioned values from this state but does not decode token-conditioned keys. Based on this observation, we propose DART (Decoded Attention over Recurrent sTates), which retains the chunk state contributions produced by the Mamba-2 chunked scan as chunk state memories, decodes token-conditioned keys and values from these memories, and performs state-memory attention (SMA) over the resulting KV pairs. The retrieved output is then combined with the native Mamba-2 output through a gated residual connection. DART supports practical training by reusing the Mamba-2 chunked scan and implementing SMA as a FlashAttention-style computation. Our analysis and experiments show that DART substantially reduces the length-dependent inference cache compared with a matched attention baseline (e.g., $75\%$ savings when the chunk size is $S=256$ and the state size is $N=128$). Compared with Mamba-2, DART substantially improves associative recall and retrieval while preserving general language-modeling quality.

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.