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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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.
Weaver builds conditional proposal trees from a factorized drafter’s top-K marginals and a rollback-free GDN tree-verify kernel, yielding 4.37× speedup over AR decoding.
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.
Tapered Language Models monotonically decrease MLP width across depth with a cosine schedule, yielding better perplexity and downstream performance than uniform-width baselines across multiple architectures and scales at no extra cost.
Verifiable search procedures cannot be learned as forward chain-of-thought by language models; they instead learn memorization, verification, or require precomputed catalogs.
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.
citing papers explorer
-
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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Trees from Marginals: Autoregressive drafting with factorized priors
Weaver builds conditional proposal trees from a factorized drafter’s top-K marginals and a rollback-free GDN tree-verify kernel, yielding 4.37× speedup over AR decoding.
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Morphing into Hybrid Attention Models
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.
-
Tapered Language Models
Tapered Language Models monotonically decrease MLP width across depth with a cosine schedule, yielding better perplexity and downstream performance than uniform-width baselines across multiple architectures and scales at no extra cost.
-
A Verifiable Search Is Not a Learnable Chain-of-Thought
Verifiable search procedures cannot be learned as forward chain-of-thought by language models; they instead learn memorization, verification, or require precomputed catalogs.
-
LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning
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.
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Forget Attention: Importance-Aware Attention Is All You Need
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.
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CaMBRAIN: Real-time, Continuous EEG Inference with Causal State Space Models
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.
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Do Language Models Need Sleep? Offline Recurrence for Improved Online Inference
A sleep mechanism with N offline recurrent passes consolidates context into fast weights, improving performance on reasoning tasks where standard transformers fail.
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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.
-
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.
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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.
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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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PairAlign: A Framework for Sequence Tokenization via Self-Alignment with Applications to Audio Tokenization
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.
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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.
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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.
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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.
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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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The Key to Going Linear: Analysis-Driven Transformer Linearization
Delta-rule linear attention faithfully approximates softmax attention through key-dependent rank-1 projections, enabling efficient post-hoc linearization of LLMs up to 32B parameters.
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NoDrift3R: Raymap-Guided Coupling for Drift-Robust Unposed Feed-Forward 3D Reconstruction
Anchoring Gaussian centers to predicted raymaps and jointly optimizing RGB, raymap, and camera losses with a dual-frequency curriculum suppresses pose drift and improves pose-free 3D reconstruction on long sequences.
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A Hippocampus for Linear Attention: An Exact Memory for What the Recurrent State Forgets
HOLA pairs a compressive delta-rule recurrent state with a residual-selected exact KV cache and decoupled RMSNorm-gamma read, yielding lower perplexity than both standard linear attention and full-attention baselines on Wikitext and LAMBADA plus stronger needle-in-haystack recall.
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Chronos: A Physics-Informed Full-History Framework for Non-Markovian Long-Horizon Manipulation
Chronos elevates full observation history to the policy's latent state via selective SSM tokens and a Schrödinger-inspired acceleration bridge, achieving large gains on memory-dependent robot tasks with fewer parameters.
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Bifocal Diffusion Language Models: Asymmetric Bidirectional Context for Parallel Generation
R2LM combines causal attention with a reverse Mamba SSM sidecar to supply right-side context in dLLMs, claiming 2.4x-12.9x throughput gains over bidirectional dLLMs and 1.9x-2.9x over AR baselines while matching or exceeding quality.
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MambaRaw: Selective State Space Modeling for Efficient 4K Raw Image Reconstruction
MambaRaw uses SSM-based context modeling with TileMambaBlock and EAR modules for efficient JPEG-guided 4K raw reconstruction, reporting 1.2-1.4 dB PSNR gains and 9% lower latency over baselines on Sony, Olympus, and Samsung datasets.
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Test-Time Training with Next-Token Prediction
TTT-NTP adapts pretrained LLMs at test time by training fast weights to match next-position hidden states from the forward pass, yielding consistent gains on long-context benchmarks across Llama, Mistral, and Qwen models.
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ITNet: A Learnable Integral Transform That Subsumes Convolution, Attention, and Recurrence
ITNet frames convolution, attention, and recurrence as special cases of one learnable integral transform with an MLP kernel and shows a single shared operator plus modality encoders matches specialized models on ImageNet-1K, GLUE, ModelNet40, VQA v2, and NLVR2.
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NarrativeWorldBench: A Frontier-Saturated Benchmark and a Latent World Model for Long-Horizon Co-Creative Audio Drama
NarrativeWorldBench evaluates 21 LLMs on nine narrative metrics across horizons to 200 episodes and introduces N-VSSM, a 256-dimensional variational state-space model that achieves plot-beat F1 >=0.84 with 4x lower compute and wins writer preference on consistency.
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Architecture-Aware Reinforcement Learning Makes Sliding-Window Attention Competitive in Math Reasoning
Reinforcement learning after SFT conversion narrows the performance gap between sliding-window attention and full self-attention on math reasoning benchmarks while preserving linear complexity.
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Blurry Window Attention
Blurry Window Attention stores a frequency window and reconstructs blurry KV history via Dirichlet kernel interpolation, achieving 8x better state efficiency than sliding window attention on the MQAR synthetic task.
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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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The Transformer as a Polar State Estimator
The paper casts the standard Transformer block with RoPE as a first-order approximation of a radial–tangential state estimator and introduces a Polar Transformer variant that retains the discarded geometric corrections.
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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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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.