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.
super hub Canonical reference
Efficiently Modeling Long Sequences with Structured State Spaces
Canonical reference. 77% of citing Pith papers cite this work as background.
128
Pith papers citing it
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.
hub tools
citation-role summary
background 20
method 5
baseline 1
citation-polarity summary
claims ledger
- 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
authors
co-cited works
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.
MASS reformulates SSM-based feature scanning in flow-based VFI to follow dynamic motion trajectories via learnable path integration and velocity-aware sampling, claiming SOTA on challenging large-displacement cases.
AURA-Mem uses an action-gated recurrent memory trained on closed-loop action error to deliver constant 4,224-byte state and 5-9x fewer writes than baselines while matching base policy success on LIBERO-Long.
Presents a structured generalized linear token mixing framework that extends recurrence equations to multiple past states, enabling new patterns with provable complexity-expressivity trade-offs for causal generation.
UWM-JEPA uses a density-matrix latent and unitary predictor in JEPA to preserve joint-state spectrum during blind rollouts, achieving 0.77 accuracy on a five-step hidden-velocity task versus 0.53 for an LSTM baseline.
MVCHead uses a hierarchical state space model with bi-directional scans and an SE(3) critic to enforce 3D consistency in Gaussian avatars trained only on 2D images.
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 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.
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.
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.
citing papers explorer
-
Test-Time Training with KV Binding Is Secretly Linear Attention
Test-time training with KV binding reduces to learned linear attention.
-
Trading Complexity for Expressivity Through Structured Generalized Linear Token Mixing
Presents a structured generalized linear token mixing framework that extends recurrence equations to multiple past states, enabling new patterns with provable complexity-expressivity trade-offs for causal generation.
-
UWM-JEPA: Predictive World Models That Imagine in Belief Space
UWM-JEPA uses a density-matrix latent and unitary predictor in JEPA to preserve joint-state spectrum during blind rollouts, achieving 0.77 accuracy on a five-step hidden-velocity task versus 0.53 for an LSTM baseline.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
Topological Neural Dynamics: A Neuron-wise Framework for Sequence Modeling
TND models sequences via independent neuron evolution on a directed graph and outperforms RNN, LSTM, CfC, and Transformer baselines on Pong behavior cloning with over 3x more consecutive catches.
-
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.
-
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.
-
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.
-
Beyond Similarity: Temporal Operator Attention for Time Series Analysis
TOA augments attention with learnable sequence-space operators and stochastic regularization to enable signed temporal mixing, yielding gains on forecasting and related benchmarks when added to PatchTST and iTransformer.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
Upper Generalization Bounds for Neural Oscillators
Upper generalization bounds for neural oscillators scale polynomially with MLP size and time length, avoiding the curse of parametric complexity, with numerical validation on a Bouc-Wen nonlinear system.
-
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.
-
Physics-Guided Tiny-Mamba Transformer for Reliability-Aware Early Fault Warning
PG-TMT couples a physics-aligned tri-branch encoder with EVT-calibrated decision rules to achieve higher PR-AUC and shorter detection times at controlled false-alarm rates across multiple bearing datasets.
-
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.
-
Higher-order Linear Attention
Higher-order Linear Attention realizes second-order and higher interactions in linear-time causal attention via constant-size state and associative scans.
-
Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks
Gating in RNNs couples state time-scales with parameter gradients to produce lag- and direction-dependent effective learning rates, shown via exact Jacobians and first-order expansion.
-
CodeBrain: Bridging Decoupled Tokenizer and Multi-Scale Architecture for EEG Foundation Model
CodeBrain introduces a decoupled TFDual-Tokenizer and multi-scale EEGSSM architecture for an EEG foundation model pretrained on a large corpus, claiming strong generalization across eight downstream tasks and ten datasets.
-
Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs
Introduces quantitative error feedback from digital filter techniques to exactly compensate quantization noise in graph filtering, with closed-form optimal coefficients for deterministic, random-graph, and asynchronous scenarios.
-
Why Linear Recurrent Memory Works in Partially Observable Reinforcement Learning
Linear recurrent filters exactly reproduce HMM belief logits under deterministic transitions and achieve near-zero decoding error under nearly deterministic ones, extending to action-controlled cases.
-
Graph Mamba Survival Analysis Based on Topology-Aware ordering
TopoMamSurv introduces topology-aware ordering and bidirectional Mamba with GCN for efficient WSI graph survival analysis, claiming performance gains on five TCGA datasets.
-
Kaczmarz Linear Attention
Kaczmarz Linear Attention replaces the empirical coefficient in Gated DeltaNet with a key-norm-normalized step size derived from the online regression objective, yielding lower perplexity and better needle-in-haystack performance.
-
mHC-SSM: Manifold-Constrained Hyper-Connections for State Space Language Models with Stream-Specialized Adapters
Manifold-constrained multi-stream mixing plus per-stream adapters improves SSM language model validation loss from 6.3507 to 6.1353 and perplexity from 572.91 to 461.88 on WikiText-2.
-
StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models
StreamPhy introduces an end-to-end streaming framework using state-space models and an expressive FT-FiLM decoder to infer continuous physical dynamics from irregular sparse data, claiming 48% better accuracy and 20-100X faster inference than diffusion baselines.
-
Cubit: Token Mixer with Kernel Ridge Regression
Cubit replaces Transformer's attention with a closed-form Kernel Ridge Regression token mixer and reports larger gains as training sequence length increases.
-
Neural Co-state Policies: Structuring Hidden States in Recurrent Reinforcement Learning
Recurrent RL policies can have their hidden states aligned with PMP co-states through a derived loss, yielding robust performance on partially observable control tasks.
-
FG$^2$-GDN: Enhancing Long-Context Gated Delta Networks with Doubly Fine-Grained Control
FG²-GDN replaces the scalar beta in the delta update with a channel-wise vector and decouples key/value scaling to improve recall over prior GDN and KDA models.
-
Sessa: Selective State Space Attention
Sessa integrates attention within recurrent paths to achieve power-law memory tails and flexible non-decaying selective retrieval, outperforming baselines on long-context tasks.
-
CARE-ECG: Causal Agent-based Reasoning for Explainable and Counterfactual ECG Interpretation
CARE-ECG unifies ECG representation learning, causal graph-based diagnosis, and counterfactual assessment in an agentic LLM pipeline to improve accuracy and explanation faithfulness.
-
Upper Approximation Bounds for Neural Oscillators
Upper bounds are derived showing that neural oscillator approximation errors for causal operators and stable second-order dynamical systems scale polynomially with the reciprocals of the widths of the two MLPs.
-
STM3: Mixture of Multiscale Mamba for Long-Term Spatio-Temporal Time-Series Prediction
STM3 is a new multiscale Mamba mixture-of-experts model with graph causal networks and contrastive routing that reports state-of-the-art results on 10 long-term spatio-temporal forecasting benchmarks.
-
The Serial Scaling Hypothesis
The serial scaling hypothesis formalizes inherently serial problems in complexity theory and demonstrates that diffusion models cannot solve them.
-
An Efficient Self-Supervised Framework for Long-Sequence EEG Modeling
EEGM2 is a Mamba-2 integrated self-supervised model for EEG that claims linear complexity and state-of-the-art performance on long-sequence modeling and classification tasks.