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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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
co-cited works
representative citing papers
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.
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.
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.
REACT reinforcement learning agent learns a state-dependent policy from experimental measurements that suppresses coherent wake structures to reduce drag with net energy savings, outperforming baselines by 2-4x and generalizing across Reynolds numbers 86400-518400 without retraining.
MbaGCN combines message aggregation, selective state space transitions, and node state prediction to create a more scalable deep graph convolutional network.
SANA-Streaming delivers 1280x704 streaming video editing at 24 FPS end-to-end on an RTX 5090 using hybrid DiT blocks, cycle-reverse training, and mixed-precision quantization.
Deformba introduces context-adaptive state fusion to vision SSMs for better spatial augmentation and cross-stream interactions, showing strong results on 2D classification/detection/segmentation and 3D BEV perception benchmarks.
LayerTracer analysis identifies deep LLM layers as stable task-critical regions, leading to a shallow-train deep-freeze strategy that outperforms full fine-tuning on C-Eval and CMMLU.
A compact Mamba-2 model performs end-to-end byte-level network traffic classification without tokenization or pre-training and remains competitive with substantially larger pre-trained systems.
citing papers explorer
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WriteSAE: Sparse Autoencoders for Recurrent State
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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When Does Content-Based Routing Work? Representation Requirements for Selective Attention in Hybrid Sequence Models
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.
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Learning to (Learn at Test Time): RNNs with Expressive Hidden States
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.
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Asymmetric Virtual Memory Paging for Hybrid Mamba-Transformer Inference
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.
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DSSP: Diffusion State Space Policy with Full-History Encoding
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.
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Enjoy Your Layer Normalization with the Computational Efficiency of RMSNorm
A framework to identify and convert foldable layer normalizations to RMSNorm for exact equivalence and faster inference in deep neural networks.
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Selection, Not Fusion: Radar-Modulated State Space Models for Radar-Camera Depth Estimation
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: Efficient Vision State Space Models with Token-Conditioned Poles
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: Implicit Time-Awareness in Selective State Space Models
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.
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FRACTAL: SSM with Fractional Recurrent Architecture for Computational Temporal Analysis of Long Sequences
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.
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Star Elastic: Many-in-One Reasoning LLMs with Efficient Budget Control
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.
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Rethink MAE with Linear Time-Invariant Dynamics
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 for Hybrid and Recurrent LLM Serving
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.
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The UNDO Flip-Flop: A Controlled Probe for Reversible Semantic State Management in State Space Model
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.
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S0 Tuning: Zero-Overhead Adaptation of Hybrid Recurrent-Attention Models
S0 tuning optimizes initial recurrent states in hybrid models to outperform LoRA with zero inference cost on HumanEval and partial cross-domain transfer.
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The Randomness Floor: Measuring Intrinsic Non-Randomness in Language Model Token Distributions
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: Exact Solution from Continuous-Time Dynamics
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: More Accurate NVFP4 Quantization with Adaptive Block Scaling
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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Real-time reinforcement learning for turbulent state-dependent control in a bluff-body wake
REACT reinforcement learning agent learns a state-dependent policy from experimental measurements that suppresses coherent wake structures to reduce drag with net energy savings, outperforming baselines by 2-4x and generalizing across Reynolds numbers 86400-518400 without retraining.
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Mamba-Based Graph Convolutional Networks: Tackling Over-smoothing with Selective State Space
MbaGCN combines message aggregation, selective state space transitions, and node state prediction to create a more scalable deep graph convolutional network.
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SANA-Streaming: Real-time Streaming Video Editing with Hybrid Diffusion Transformer
SANA-Streaming delivers 1280x704 streaming video editing at 24 FPS end-to-end on an RTX 5090 using hybrid DiT blocks, cycle-reverse training, and mixed-precision quantization.
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Deformba: Vision State Space Model with Adaptive State Fusion
Deformba introduces context-adaptive state fusion to vision SSMs for better spatial augmentation and cross-stream interactions, showing strong results on 2D classification/detection/segmentation and 3D BEV perception benchmarks.
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Freeze Deep, Train Shallow: Interpretable Layer Allocation for Continued Pre-Training
LayerTracer analysis identifies deep LLM layers as stable task-critical regions, leading to a shallow-train deep-freeze strategy that outperforms full fine-tuning on C-Eval and CMMLU.
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MambaNetBurst: Direct Byte-level Network Traffic Classification without Tokenization or Pretraining
A compact Mamba-2 model performs end-to-end byte-level network traffic classification without tokenization or pre-training and remains competitive with substantially larger pre-trained systems.
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RT-Transformer: The Transformer Block as a Spherical State Estimator
Transformer components arise as the natural solution to precision-weighted directional state estimation on the hypersphere.
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PIMSM: Physics-Informed Multi-Scale Mamba for Stable Neural Representations under Distribution Shift
PIMSM is a Mamba-based architecture that maps knee frequencies from spectra to multi-scale discretization parameters to reduce representation drift under distribution shifts in fMRI and weather forecasting.
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Echo: KV-Cache-Free Associative Recall with Spectral Koopman Operators
Spectral Koopman operators let SSMs achieve 100% accuracy on long-gap multi-query associative recall with fixed memory, where pure Mamba fails.
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The Impossibility Triangle of Long-Context Modeling
No model can achieve efficiency, compactness, and recall capacity scaling with sequence length at once, as any two imply a strict bound of O(poly(d)/log V) on recallable facts.
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Long-Context Aware Upcycling: A New Frontier for Hybrid LLM Scaling
HyLo upcycles Transformer LLMs into hybrids with MLA and Mamba2/Gated DeltaNet blocks via staged training and distillation, extending context to 2M tokens and outperforming prior upcycled hybrids on long-context benchmarks.
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NAKUL-Med: Spectral-Graph State Space Models with Dynamics Kernels for Medical Signals
NAKUL achieves 91.7% accuracy on motor imagery EEG with 28% fewer parameters than EEG-Conformer by using dynamic kernel generation, spectral context modeling, and graph-guided spatial attention.
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HubRouter: A Pluggable Sub-Quadratic Routing Primitive for Hybrid Sequence Models
HubRouter is a sub-quadratic routing primitive using learned hubs that replaces attention layers in hybrid models while delivering competitive perplexity and large throughput gains.
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HypEHR: Hyperbolic Modeling of Electronic Health Records for Efficient Question Answering
HypEHR is a hyperbolic embedding model for EHR data that uses Lorentzian geometry and hierarchy-aware pretraining to answer clinical questions nearly as well as large language models but with much smaller size.
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M$^{2}$GRPO: Mamba-based Multi-Agent Group Relative Policy Optimization for Biomimetic Underwater Robots Pursuit
M²GRPO uses a Mamba-based policy and normalized group-relative advantages under CTDE to achieve higher pursuit success and capture efficiency than MAPPO and recurrent baselines in simulations and pool tests.
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Sonata: A Hybrid World Model for Inertial Kinematics under Clinical Data Scarcity
Sonata is a small hybrid world model pre-trained to predict future IMU states that outperforms autoregressive baselines on clinical discrimination, fall-risk prediction, and cross-cohort transfer while fitting on-device wearables.
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MambaBack: Bridging Local Features and Global Contexts in Whole Slide Image Analysis
MambaBack is a hybrid Mamba-CNN model with Hilbert sampling and chunked inference that reports better performance than seven prior methods on five whole-slide image datasets.
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Feed-Forward 3D Scene Modeling: A Problem-Driven Perspective
The paper proposes a problem-driven taxonomy for feed-forward 3D scene modeling that groups methods by five core challenges: feature enhancement, geometry awareness, model efficiency, augmentation strategies, and temporal-aware modeling.
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Parcae: Scaling Laws For Stable Looped Language Models
Parcae stabilizes looped LLMs via spectral norm constraints on injection parameters, enabling power-law scaling for training FLOPs and saturating exponential scaling at test time that improves quality over fixed-depth baselines under fixed parameter budgets.
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Scal3R: Scalable Test-Time Training for Large-Scale 3D Reconstruction
Scal3R achieves better accuracy and consistency in large-scale 3D scene reconstruction by maintaining a compressed global context through test-time adaptation of lightweight neural networks on long video sequences.
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Optimal Decay Spectra for Linear Recurrences
PoST reparameterizes decay spectra in linear recurrences with geometric log-spacing and position-adaptive scaling to achieve O(exp(-cN/log t)) decay, improving zero-shot language modeling and long-context retrieval across Mamba-2, RWKV-7 and similar models.
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In-Place Test-Time Training
In-Place TTT adapts LLM MLP projection matrices at test time with a next-token-aligned objective and chunk-wise updates, enabling better long-context performance as a drop-in enhancement.
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Phase-Associative Memory: Sequence Modeling in Complex Hilbert Space
PAM, a complex-valued associative memory model, exhibits steeper power-law scaling in loss and perplexity than a matched real-valued baseline when trained on WikiText-103 from 5M to 100M parameters.
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Stochastic KV Routing: Enabling Adaptive Depth-Wise Cache Sharing
Stochastic training with random cross-layer KV attention enables depth-wise cache sharing in transformers, cutting memory footprint while preserving or improving performance.
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Attention to Mamba: A Recipe for Cross-Architecture Distillation
A two-stage distillation recipe converts a Pythia-1B Transformer into a Mamba model that preserves performance with perplexity 14.11 versus the teacher's 13.86.
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Computer Architecture's AlphaZero Moment: Automated Discovery in an Encircled World
Automated architectural discovery engines can outperform human design teams by exploring massive design spaces and compressing development cycles from months to weeks.
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M$^2$RNN: Non-Linear RNNs with Matrix-Valued States for Scalable Language Modeling
M²RNN achieves perfect state tracking at unseen lengths and outperforms Gated DeltaNet hybrids by 0.4-0.5 perplexity on 7B models with 3x smaller recurrent states.
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LPC-SM: Local Predictive Coding and Sparse Memory for Long-Context Language Modeling
LPC-SM is a hybrid architecture separating local attention, persistent memory, predictive correction, and control with ONT for memory writes, showing loss reductions on 158M-parameter models up to 4096-token contexts.
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Echoes Over Time: Unlocking Length Generalization in Video-to-Audio Generation Models
MMHNet enables video-to-audio models trained on short clips to generalize and generate audio for videos over 5 minutes long.
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Rethinking Efficiency in Neural Combinatorial Optimization: Batched Preference Optimization with Mamba
ECO uses supervised warm-up plus iterative batched DPO on a Mamba backbone to reach top neural performance on TSP and CVRP while lowering memory growth and raising throughput.
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When to Think Fast and Slow? AMOR: Adaptive Entropy Gate for Hybrid Models
AMOR uses output entropy to gate attention in recurrent hybrids, matching full attention performance at roughly 22% attention invocations across 180M-1.5B models.
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Gated KalmaNet: A Fading Memory Layer Through Test-Time Ridge Regression
Gated KalmaNet uses exact Kalman gain computation with adaptive gating and Chebyshev iteration to improve SSM performance on long-context tasks over prior approximations like DeltaNet.