EQ-VMamba adds rotation-equivariant cross-scan and group Mamba blocks to enforce end-to-end rotation equivariance, yielding better rotation robustness, competitive accuracy, and roughly 50% fewer parameters than non-equivariant baselines across classification, segmentation, and super-resolution.
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Efficiently Modeling Long Sequences with Structured State Spaces
Canonical reference. 77% of citing Pith papers cite this work as background.
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Background
77% of classified citations
abstract
A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of $10000$ or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the state matrix \( A \), this system could handle long-range dependencies mathematically and empirically. However, this method has prohibitive computation and memory requirements, rendering it infeasible as a general sequence modeling solution. We propose the Structured State Space sequence model (S4) based on a new parameterization for the SSM, and show that it can be computed much more efficiently than prior approaches while preserving their theoretical strengths. Our technique involves conditioning \( A \) with a low-rank correction, allowing it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. S4 achieves strong empirical results across a diverse range of established benchmarks, including (i) 91\% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet, (ii) substantially closing the gap to Transformers on image and language modeling tasks, while performing generation $60\times$ faster (iii) SoTA on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors.
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- abstract A central goal of sequence modeling is designing a single principled model that can address sequence data across a range of modalities and tasks, particularly on long-range dependencies. Although conventional models including RNNs, CNNs, and Transformers have specialized variants for capturing long dependencies, they still struggle to scale to very long sequences of $10000$ or more steps. A promising recent approach proposed modeling sequences by simulating the fundamental state space model (SSM) \( x'(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) \), and showed that for appropriate choices of the
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representative citing papers
Test-time training with KV binding reduces to learned linear attention.
Promptbreeder evolves both task prompts and the mutation prompts that improve them using LLMs, outperforming Chain-of-Thought and Plan-and-Solve on arithmetic and commonsense reasoning benchmarks.
Exact analytical expression for the time-dependent maximum Lyapunov exponent during transients in a network supporting dynamics-based computation.
Social-Mamba introduces a Cycle Mamba block and social triplet factorization to achieve state-of-the-art trajectory forecasting accuracy with linear-time social interaction modeling on five benchmarks.
A real Schur decomposition projection maps the state matrix of discrete-time state-space layers onto its nearest stable counterpart, delivering accuracy comparable to prior stable identification methods with fewer weights.
QLAM extends state-space models with quantum superposition in the hidden state for linear-time long-sequence modeling and reports consistent gains over RNN and transformer baselines on sequential image tasks.
PSR-NQS makes recurrent neural quantum states scalable for variational Monte Carlo by using parallel scan recurrence, reaching accurate results on 52x52 two-dimensional lattices.
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.
PairAlign learns compact audio token sequences via self-alignment of paired content views using an autoregressive decoder, achieving strong cross-view consistency and edit-distance preservation while reducing token count by 55% on TIMIT.
NOVA represents world states as INR weights for decoder-free rendering, compactness, and unsupervised disentanglement of background, foreground, and motion in video world models.
In linear recurrent models, infinite-width signal propagation remains accurate only for depths t much smaller than sqrt(width n), with a critical regime at t ~ c sqrt(n) where finite-width effects emerge and dominate for larger t.
Predictive representation learning structurally favors encoding slower or less noisy environment modes over causal system modes, as shown by an impossibility theorem for linear-Gaussian dynamics and large-scale neural experiments.
FLUID is a continuous-time transformer using Liquid Attention Networks to model attention as stable ODE solutions that interpolate between discrete SDPA and CT-RNNs, with an explicit sink gate and liquid hyper-connections for better information flow.
Token order in frozen visual representations is exploitable via SSM-based LTI probes, revealing pre-training-dependent heterogeneity that fixed pooling misses.
Mamba-MPC stabilizes and tracks references on SISO and MIMO systems in simulation and hardware while outperforming LSTM-MPC with faster computation.
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Short input phrases can irreversibly overwrite hidden states in Mamba models, impairing information retrieval on a new benchmark while leaving pure Transformer models unaffected.
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L2RU parametrizes SSMs to enforce a prescribed L2-gain bound for guaranteed input-output stability and robustness in all parameter regimes.
MbaGCN combines message aggregation, selective state space transitions, and node state prediction to create a more scalable deep graph convolutional network.
citing papers explorer
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Rotation Equivariant Mamba for Vision Tasks
EQ-VMamba adds rotation-equivariant cross-scan and group Mamba blocks to enforce end-to-end rotation equivariance, yielding better rotation robustness, competitive accuracy, and roughly 50% fewer parameters than non-equivariant baselines across classification, segmentation, and super-resolution.
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Test-Time Training with KV Binding Is Secretly Linear Attention
Test-time training with KV binding reduces to learned linear attention.
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Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution
Promptbreeder evolves both task prompts and the mutation prompts that improve them using LLMs, outperforming Chain-of-Thought and Plan-and-Solve on arithmetic and commonsense reasoning benchmarks.
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Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Exact analytical expression for the time-dependent maximum Lyapunov exponent during transients in a network supporting dynamics-based computation.
-
Social-Mamba: Socially-Aware Trajectory Forecasting with State-Space Models
Social-Mamba introduces a Cycle Mamba block and social triplet factorization to achieve state-of-the-art trajectory forecasting accuracy with linear-time social interaction modeling on five benchmarks.
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A Novel Schur-Decomposition-Based Weight Projection Method for Stable State-Space Neural-Network Architectures
A real Schur decomposition projection maps the state matrix of discrete-time state-space layers onto its nearest stable counterpart, delivering accuracy comparable to prior stable identification methods with fewer weights.
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QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modeling
QLAM extends state-space models with quantum superposition in the hidden state for linear-time long-sequence modeling and reports consistent gains over RNN and transformer baselines on sequential image tasks.
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Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlo
PSR-NQS makes recurrent neural quantum states scalable for variational Monte Carlo by using parallel scan recurrence, reaching accurate results on 52x52 two-dimensional lattices.
-
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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PairAlign: A Framework for Sequence Tokenization via Self-Alignment with Applications to Audio Tokenization
PairAlign learns compact audio token sequences via self-alignment of paired content views using an autoregressive decoder, achieving strong cross-view consistency and edit-distance preservation while reducing token count by 55% on TIMIT.
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Render, Don't Decode: Weight-Space World Models with Latent Structural Disentanglement
NOVA represents world states as INR weights for decoder-free rendering, compactness, and unsupervised disentanglement of background, foreground, and motion in video world models.
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How Long Does Infinite Width Last? Signal Propagation in Long-Range Linear Recurrences
In linear recurrent models, infinite-width signal propagation remains accurate only for depths t much smaller than sqrt(width n), with a critical regime at t ~ c sqrt(n) where finite-width effects emerge and dominate for larger t.
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The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence
Predictive representation learning structurally favors encoding slower or less noisy environment modes over causal system modes, as shown by an impossibility theorem for linear-Gaussian dynamics and large-scale neural experiments.
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FLUID: Continuous-Time Hyperconnected Sparse Transformer for Sink-Free Learning
FLUID is a continuous-time transformer using Liquid Attention Networks to model attention as stable ODE solutions that interpolate between discrete SDPA and CT-RNNs, with an explicit sink gate and liquid hyper-connections for better information flow.
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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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Mamba Sequence Modeling meets Model Predictive Control
Mamba-MPC stabilizes and tracks references on SISO and MIMO systems in simulation and hardware while outperforming LSTM-MPC with faster computation.
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RSGMamba: Reliability-Aware Self-Gated State Space Model for Multimodal Semantic Segmentation
RSGMamba introduces a reliability-aware self-gated Mamba block for dynamic cross-modal feature selection in semantic segmentation, delivering state-of-the-art mIoU on RGB-D and RGB-T benchmarks with 48.6M parameters.
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Is Flow Matching Just Trajectory Replay for Sequential Data?
Flow matching on time series targets a closed-form nonparametric velocity field that is a similarity-weighted mixture of observed transition velocities, making neural models approximations to an ideal memory-augmented dynamical system sampler.
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Hidden State Poisoning Attacks against Mamba-based Language Models
Short input phrases can irreversibly overwrite hidden states in Mamba models, impairing information retrieval on a new benchmark while leaving pure Transformer models unaffected.
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Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics
Mamba-based neural operators predict stiff chemical kinetics evolution with high fidelity from initial states on Syngas and GRI-Mech 3.0 mechanisms.
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L2RU: a Structured State Space Model with prescribed L2-bound
L2RU parametrizes SSMs to enforce a prescribed L2-gain bound for guaranteed input-output stability and robustness in all parameter regimes.
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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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Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models
Griffin hybrid model matches Llama-2 performance while trained on over 6 times fewer tokens and offers lower inference latency with higher throughput.
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Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model
Vim is a bidirectional Mamba vision backbone that outperforms DeiT in accuracy on standard tasks while being substantially faster and more memory-efficient for high-resolution images.
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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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GeoMamba: A Geometry-driven MambaVision Framework and Dataset for Fine-grained Optical-SAR Object Retrieval
GeoMamba with Geometric Feature Injection and Geometric Consistency Constraint modules achieves 63.3% mAP and 77.0% Rank-1 on the new FGOS-as dataset for unaligned optical-SAR fine-grained retrieval.
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Phasor Memory Networks: Stable Backpropagation Through Time for Scalable Explicit Memory
PMNet uses unitary phasor dynamics and hierarchical anchors to make explicit memory stable for long sequences, matching a 3x larger Mamba model on long-context robustness with a 119M parameter network.
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Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction
GTF-DEER augments the DEER framework with Generalized Teacher Forcing to allow effective parallel training of nonlinear recurrent models on extremely long sequences, improving dynamical systems reconstruction for data with long time scales.
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A Single-Layer Model Can Do Language Modeling
A 130M-parameter 1-layer GPN achieves FineWeb-Edu perplexity 18.06, within 13% of a 12-layer Transformer++ (16.05) and 18% of a 10-layer GDN (15.34).
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Continuity Laws for Sequential Models
S4 models exhibit stable time-continuity unlike sensitive S6 models, with task continuity predicting performance and enabling temporal subsampling for better efficiency.
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EmambaIR: Efficient Visual State Space Model for Event-guided Image Reconstruction
EmambaIR is a visual state space model with cross-modal top-k sparse attention and gated SSM components that outperforms prior CNN and ViT methods on event-guided deblurring, deraining, and HDR reconstruction while reducing memory and compute costs.
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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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Training Transformers for KV Cache Compressibility
Training transformers with KV sparsification during continued pretraining produces representations that admit better post-hoc KV cache compression, improving quality under memory budgets for long-context tasks.
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ZAYA1-8B Technical Report
ZAYA1-8B is a reasoning MoE model with 700M active parameters that matches larger models on math and coding benchmarks and reaches 91.9% on AIME'25 via Markovian RSA test-time compute.
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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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State Stream Transformer (SST) V2: Parallel Training of Nonlinear Recurrence for Latent Space Reasoning
SST V2 introduces parallel-trainable nonlinear recurrence in latent space to let transformers reason continuously across positions, delivering +15 points on GPQA-Diamond and halving remaining GSM8K errors over matched baselines.
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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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FETS Benchmark: Foundation Models Outperform Dataset-specific Machine Learning in Energy Time Series Forecasting
Foundation models outperform dataset-specific machine learning in energy time series forecasting across 54 datasets in 9 categories.
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An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling
S4D state space models correspond exactly to wave propagation and nonlinear wave interactions in a one-dimensional ring oscillator network, with a closed-form operator describing the complete input-output map.
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Forget, Then Recall: Learnable Compression and Selective Unfolding via Gist Sparse Attention
Gist Sparse Attention uses learnable gist compression tokens as both summaries and routing signals, then selectively unfolds relevant raw chunks for fine-grained attention, outperforming compression and sparse-attention baselines on LongBench and RAG tasks at 8x-32x compression.
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Hero-Mamba: Mamba-based Dual Domain Learning for Underwater Image Enhancement
Hero-Mamba combines parallel spatial-spectral Mamba processing and a background-light-guided ColorFusion block to enhance underwater images, reporting PSNR 25.802 and SSIM 0.913 on the LSUI benchmark.
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Event-Adaptive State Transition and Gated Fusion for RGB-Event Object Tracking
MambaTrack improves RGB-Event object tracking via event-adaptive state transitions in a Dynamic State Space Model and a Gated Projection Fusion module, reporting state-of-the-art results on FE108 and FELT datasets.
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TCL: Enabling Fast and Efficient Cross-Hardware Tensor Program Optimization via Continual Learning
TCL delivers 16.8x faster tuning on CPU and 12.48x on GPU with modestly lower inference latency by combining RDU active sampling, a lightweight Mamba cost model, and cross-platform continual knowledge distillation.
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RetentiveKV: State-Space Memory for Uncertainty-Aware Multimodal KV Cache Eviction
RetentiveKV uses entropy to drive state-space model transitions that retain and reactivate low-attention visual tokens in a continuous memory instead of pruning them, delivering 5x KV cache compression and 1.5x faster decoding.
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Membership Inference Attacks Expose Participation Privacy in ECG Foundation Encoders
Membership inference attacks can detect whether specific ECG data participated in pretraining self-supervised foundation encoders, with leakage strongest in small cohorts and contrastive models.
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Tracking Listener Attention: Gaze-Guided Audio-Visual Speech Enhancement Framework
The GG-AVSE framework uses listener gaze direction combined with YOLO5Face and AVSEMamba to resolve target-speaker ambiguity in audio-visual speech enhancement, yielding gains in PESQ, STOI, and SI-SDR.
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CloudMamba: An Uncertainty-Guided Dual-Scale Mamba Network for Cloud Detection in Remote Sensing Imagery
CloudMamba combines uncertainty-guided refinement with a dual-scale Mamba network to outperform prior methods on cloud segmentation accuracy while maintaining linear computational cost.