WriteSAE introduces sparse autoencoders with rank-1 matrix atoms for recurrent state updates, allowing replacement tests that outperform deletion on 92.4% of positions and a formula predicting logit changes with R²=0.98.
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Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality
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abstract
While Transformers have been the main architecture behind deep learning's success in language modeling, state-space models (SSMs) such as Mamba have recently been shown to match or outperform Transformers at small to medium scale. We show that these families of models are actually quite closely related, and develop a rich framework of theoretical connections between SSMs and variants of attention, connected through various decompositions of a well-studied class of structured semiseparable matrices. Our state space duality (SSD) framework allows us to design a new architecture (Mamba-2) whose core layer is an a refinement of Mamba's selective SSM that is 2-8X faster, while continuing to be competitive with Transformers on language modeling.
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- abstract While Transformers have been the main architecture behind deep learning's success in language modeling, state-space models (SSMs) such as Mamba have recently been shown to match or outperform Transformers at small to medium scale. We show that these families of models are actually quite closely related, and develop a rich framework of theoretical connections between SSMs and variants of attention, connected through various decompositions of a well-studied class of structured semiseparable matrices. Our state space duality (SSD) framework allows us to design a new architecture (Mamba-2) whose c
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Content-based routing succeeds only when models provide bidirectional context and perform pairwise comparisons, with bidirectional Mamba plus rank-1 projection reaching 99.7% precision at linear inference cost.
TTT layers treat the hidden state as a trainable model updated at test time, allowing linear-complexity sequence models to scale perplexity reduction with context length unlike Mamba.
FlashMorph formulates hybrid layer selection as budget-constrained optimization, trains per-layer gates on synthetic retrieval data with linearization regularization, then discretizes and distills to produce efficient hybrid architectures.
LongSpike integrates fractional-order state-space modeling into spiking neural networks, enabling better long-sequence performance than prior SNNs on LRA, WikiText-103, and Speech Commands benchmarks while retaining sparse computation.
SISA adds an SSM importance term inside the attention score and runs the full operation as one SDPA call on augmented Q/K vectors, reporting better LAMBADA and perfect NIAH at small scale.
CaMBRAIN introduces a causal Mamba-based SSM with a multi-stage self-supervised training pipeline that achieves SOTA results on three EEG datasets while enabling linear-time long-range inference.
A sleep mechanism with N offline recurrent passes consolidates context into fast weights, improving performance on reasoning tasks where standard transformers fail.
AVMP separates KV and SSM cache pools behind unified virtual addressing with failure-triggered migration, cutting OOM events 7.6% and raising throughput 1.83-13.3x on synthetic loads and 2.36x on ShareGPT traces.
DSSP is a history-conditioned diffusion state space policy that uses SSMs to encode full observation streams with an auxiliary dynamics objective and hierarchical fusion, achieving SOTA results with reduced model size in robot manipulation.
A framework to identify and convert foldable layer normalizations to RMSNorm for exact equivalence and faster inference in deep neural networks.
Radar-Modulated Selection perturbs only the step size Δ and readout C parameters inside Mamba's selective scan with radar data while keeping other components image-only, yielding state-of-the-art depth estimation on nuScenes with up to 34% MAE reduction.
TCP-SSM conditions stable poles on visual tokens to explicitly control memory decay and oscillation in SSMs, cutting computation up to 44% while matching or exceeding accuracy on classification, segmentation, and detection.
TIDES reconciles selective SSM expressivity with continuous-time physical discretization by moving input dependence onto the state matrix, enabling native irregular time series handling and achieving SOTA on UEA and Physiome-ODE benchmarks.
FRACTAL integrates fractional recurrent architecture into SSMs using a tunable singularity index to capture multi-scale temporal features, reporting 87.11% average on Long Range Arena and outperforming S5.
Star Elastic trains N nested submodels in a single post-training job on a parent reasoning LLM, supporting elastic budget control that matches or exceeds independent baselines while cutting training compute by up to 360x.
PairAlign learns compact variable-length token sequences for audio via self-alignment on paired content-preserving views, achieving 55% fewer archive tokens than VQ while preserving edit-distance retrieval at 12.71 tokens/s.
Token order in frozen visual representations is exploitable via SSM-based LTI probes, revealing pre-training-dependent heterogeneity that fixed pooling misses.
Sparse prefix caching via dynamic programming for optimal checkpoint placement under overlap distributions improves the Pareto frontier for recurrent and hybrid LLM serving on shared-prefix data.
Mamba-2 models fail to learn reversible state retrieval in the UNDO Flip-Flop task, defaulting to a toggle heuristic and achieving only 41% accuracy under adversarial conditions.
S0 tuning optimizes initial recurrent states in hybrid models to outperform LoRA with zero inference cost on HumanEval and partial cross-domain transfer.
Language models have an intrinsic randomness floor: transformers show ~0.30 entropic deviation from uniform on neutral prompts, accounting for 88-93% of observed non-randomness, while state-space models exhibit twice the deviation and strong temperature sensitivity.
Exact Flow Linear Attention derives a closed-form exact update for delta-rule linear attention from continuous-time dynamics, removing Euler discretization error while preserving linear complexity and structure.
Four Over Six adaptively scales blocks in NVFP4 quantization to smaller FP4 values, making representable value distributions more uniform and reducing quantization error especially for near-maximal values.
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