Awesome

Awesome-state-space-models

Collection of papers/repos on state-space models.

ICLR 2025 submissions

1. Autocorrelation Matters: Understanding the Role of Initialization Schemes for State Space Models (https://openreview.net/forum?id=sZJNkorXMk)

2. HOPE for a Robust Parameterization of Long-memory State Space Models (https://openreview.net/forum?id=RZwtbg3qYD) Arxiv

3. Tuning Frequency Bias of State Space Models (https://openreview.net/forum?id=wkHcXDv7cv) Arxiv

4. Demystifying the Token Dynamics of Deep Selective State Space Models (https://openreview.net/forum?id=qtTIP5Gjc5) Arxiv

5. Gated Delta Networks: Improving Mamba2 with Delta Rule (https://openreview.net/forum?id=r8H7xhYPwz)

6. Quantifying Memory Utilization with Effective State-Size (https://openreview.net/forum?id=DHVjLvSps6)

7. Forgetting Transformer: Softmax Attention with a Forget Gate (https://openreview.net/forum?id=q2Lnyegkr8)

8. S7: Selective and Simplified State Space Layers for Sequence Modeling (https://openreview.net/forum?id=4wtcXV0kbi) Arxiv

9. Unlocking State-Tracking in Linear RNNs Through Negative Eigenvalues (https://openreview.net/forum?id=UvTo3tVBk2)

10. Understanding Bottlenecks of State Space Models through the Lens of Recency and Over-smoothing (https://openreview.net/forum?id=pymXpl4qvi)

11. Parameter-Efficient Fine-Tuning of State Space Models (https://openreview.net/forum?id=27n0kvWgqT)

12. State-space models can learn in-context by gradient descent (https://openreview.net/forum?id=52XG8eexal)

13. On the interplay between learning and memory in deep state space models (https://openreview.net/forum?id=hgjpO0H0id)

14. A New Look at Low-Rank Recurrent Neural Networks (https://openreview.net/forum?id=fWXYD0ZCdd)

15. Were RNNs All We Needed? (https://openreview.net/forum?id=GrmFFxGnOR) Arxiv

16. Oscillatory State-Space Models (https://openreview.net/forum?id=GRMfXcAAFh) Arxiv

17. Mimetic Initialization Helps State Space Models Learn to Recall (https://openreview.net/forum?id=iVy7aRMb0K) Arxiv

18. Gradient-free training of recurrent neural networks (https://openreview.net/forum?id=vcJiPLeC48)

19. Sparse Mamba: Reinforcing Controllability In Structural State Space Models (https://openreview.net/forum?id=vOfDGYGVyj) Arxiv

20. Stuffed Mamba: State Collapse and State Capacity of RNN-Based Long-Context Modeling (https://openreview.net/forum?id=cu2CT2VAvs) Arxiv

21. FlashRNN: I/O-Aware Optimization of Traditional RNNs on modern hardware (https://openreview.net/forum?id=l0ZzTvPfTw)

22. LoLCATs: On Low-Rank Linearizing of Large Language Models (https://openreview.net/forum?id=8VtGeyJyx9)

23. LONGHORN: STATE SPACE MODELS ARE AMORTIZED ONLINE LEARNERS (https://openreview.net/forum?id=8jOqCcLzeO) Arxiv

24. MAMBA STATE-SPACE MODELS ARE LYAPUNOV-STABLE LEARNERS (https://openreview.net/forum?id=i9RTCC6whL)

CVPR 2024

1. (Spotlight) State Space Models for Event Cameras (https://arxiv.org/abs/2402.15584) GitHub

ICML 2024

1. StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization (https://arxiv.org/abs/2311.14495)

2. Gated Linear Attention Transformers with Hardware-Efficient Training (https://arxiv.org/abs/2312.06635)

3. Transformers are SSMs: Generalized Models and Efficient Algorithms with Structured State Space Duality (https://arxiv.org/abs/2405.21060)

4. From generalization analysis to optimization designs for state space models (https://arxiv.org/abs/2405.02670)

5. The Illusion of State in State-Space Models (https://arxiv.org/abs/2404.08819)

6. State-Free Inference of State-Space Models: The Transfer Function Approach (https://arxiv.org/pdf/2405.06147) GitHub

7. PAC-Bayesian Error Bound, via Renyi Divergence, for a Class of Linear Time-Invariant State-Space Models (https://openreview.net/pdf?id=a1Olc2QhPv)

8. Hierarchical State Space Models for Continuous Sequence-to-Sequence Modeling (https://arxiv.org/abs/2402.10211) GitHub

9. Repeat After Me: Transformers are Better than State Space Models at Copying (https://arxiv.org/pdf/2402.01032) GitHub

10. SLAB: Efficient Transformers with Simplified Linear Attention and Progressive Re-parameterized Batch Normalization (https://www.arxiv.org/abs/2405.11582)

11. Short-Long Convolutions Help Hardware-Efficient Linear Attention to Focus on Long Sequences (https://arxiv.org/abs/2406.08128)

12. When Linear Attention Meets Autoregressive Decoding: Towards More Effective and Efficient Linearized Large Language Models (https://arxiv.org/abs/2406.07368)

13. Simple linear attention language models balance the recall-throughput tradeoff (https://arxiv.org/abs/2402.18668) GitHub

14. Universality of Linear Recurrences Followed by Non-linear Projections: Finite-Width Guarantees and Benefits of Complex Eigenvalues (https://arxiv.org/abs/2307.11888)

Input-dependent gating.

1. Mamba (https://arxiv.org/abs/2312.00752) Official GitHub

   $$g_k = \sigma(Linear(x_k)),$$ $$h_{k+1} = (1-g_k) h_{k} + g_k x_k.$$

   The activation is SiLU / Swish. The continuous form is $$\frac{dh_t}{dt} = g_t (x_t - h_t).$$

   Various (unofficial) implementations:

   1. Mamba-minimal-in-JAX
   2. Mamba-minimal-in-PyTorch
   3. Mamba.py
   4. Mamba-jax
   5. Mamba-mini
   6. LongMamba
   7. Mamba the hard way Annotated Mamba
   8. Mamba the easy way

2. [ICML2024] Gated Linear Attention (GLA) (https://arxiv.org/abs/2312.06635) Official GitHub

   The following repo aims at providing a collection of efficient Triton-based implementations for state-of-the-art linear attention models. Flash-linear-attention

On the replacement of transformer/attention by SSMs

1. [Video] Long Movie Clip Classification with State-Space Video Models (https://arxiv.org/abs/2204.01692) GitHub

2. [Language model] Pretraining Without Attention (https://arxiv.org/abs/2212.10544) GitHub

   Feature: Bidirectional Language Modeling with State-space Model

3. [Reinforcement Learning] Structured State Space Models for In-Context Reinforcement Learning (https://arxiv.org/abs/2303.03982) GitHub

4. [Diffusion Model] Diffusion Models Without Attention (https://arxiv.org/abs/2311.18257) (NeurIPS 2023 Workshop on Diffusion Models)

5. [Graph] Recurrent Distance-Encoding Neural Networks for Graph Representation Learning (https://arxiv.org/abs/2312.01538) GitHub

6. [Mixture of Experts] MoE-Mamba: Efficient Selective State Space Models with Mixture of Experts (https://arxiv.org/abs/2401.04081) GitHub

7. [Bio] U-Mamba, a versatile network designed specifically for biomedical image segmentation. (https://arxiv.org/abs/2401.04722) GitHub

8. [Vision] VMamba: Visual State Space Model. (https://arxiv.org/abs/2401.10166) GitHub

9. [Tabular data] MambaTab: A Simple Yet Effective Approach for Handling Tabular Data (https://arxiv.org/abs/2401.08867)

10. [RWKV-TS] RWKV-TS: Beyond Traditional Recurrent Neural Network for Time Series Tasks (https://arxiv.org/abs/2401.09093) GitHub

11. [Vision] Vision Mamba (Vim) is 2.8× faster than DeiT and saves 86.8% GPU memory when performing batch inference to extract features on images with a resolution of 1248×1248. (https://arxiv.org/abs/2401.09417) GitHub

12. [Vision] SegMamba: Long-range Sequential Modeling Mamba For 3D Medical Image Segmentation. (https://arxiv.org/abs/2401.13560) GitHub

13. [Token-free language models] MambaByte: Token-free Selective State Space Model.（https://arxiv.org/abs/2401.13660）[GitHub](https://github.com/kyegomez/MambaByte)

    Token-free language models learn directly from raw bytes and remove the bias of subword tokenization.

14. [Vision] MambaMorph: a Mamba-based Backbone with Contrastive Feature Learning for Deformable MR-CT Registration. (https://arxiv.org/abs/2401.13934) GitHub

15. [Video] Vivim: a Video Vision Mamba for Medical Video Object Segmentation (https://arxiv.org/pdf/2401.14168.pdf) GitHub

16. [Document Summarization] LOCOST: State-Space Models for Long Document Abstractive Summarization (https://arxiv.org/abs/2401.17919) GitHub

17. [Graph] Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces (https://arxiv.org/abs/2402.00789) GitHub

18. [Mixture of Experts] BlackMamba: Mixture of Experts for State-Space Models (https://arxiv.org/abs/2402.01771) GitHub

19. [Vision] Swin-UMamba: Mamba-based UNet with ImageNet-based pretraining (https://arxiv.org/abs/2402.03302) GitHub

20. [Bio] VM-UNet: Vision Mamba UNet for Medical Image Segmentation (https://arxiv.org/abs/2402.02491) GitHub

21. [IN-CONTEXT LEARNING] IS MAMBA CAPABLE OF IN-CONTEXT LEARNING? (https://arxiv.org/abs/2402.03170)

22. [Bio] nnMamba: 3D Biomedical Image Segmentation, Classification and Landmark Detection with State Space Model (https://arxiv.org/abs/2402.03526) GitHub

23. [IN-CONTEXT LEARNING] Can Mamba Learn How to Learn? A Comparative Study on In-Context Learning Tasks (https://arxiv.org/abs/2402.04248)

24. [Diffusion Model] Scalable Diffusion Models with State Space Backbone (https://arxiv.org/abs/2402.05608) GitHub

25. [Vision] Mamba-ND: Selective State Space Modeling for Multi-Dimensional Data (https://arxiv.org/abs/2402.05892) GitHub

26. [Vision] FD-Vision Mamba for Endoscopic Exposure Correction (https://arxiv.org/pdf/2402.06378.pdf)

27. [Vision] Semi-Mamba-UNet: Pixel-Level Contrastive Cross-Supervised Visual Mamba-based UNet for Semi-Supervised Medical Image Segmentation (https://arxiv.org/abs/2402.07245) GitHub

28. [Segmentation] P-Mamba: Marrying Perona Malik Diffusion with Mamba for Efficient Pediatric Echocardiographic Left Ventricular Segmentation: (https://arxiv.org/abs/2402.08506)

29. [Graph] Graph Mamba: Towards Learning on Graphs with State Space Models (https://arxiv.org/abs/2402.08678) GitHub

30. [Theory] Spectral State Space Models (https://arxiv.org/abs/2312.06837v3) GitHub

31. [Point Cloud Analysis] PointMamba: A Simple State Space Model for Point Cloud Analysis (https://arxiv.org/abs/2402.10739) GitHub

32. [Vision] RES-VMAMBA: FINE-GRAINED FOOD CATEGORY VISUAL CLASSIFICATION USING SELECTIVE STATE SPACE MODELS WITH DEEP RESIDUAL LEARNING (https://arxiv.org/abs/2402.15761) GitHub

33. [Theory] Learning method for S4 with Diagonal State Space Layers using Balanced Truncation (https://arxiv.org/abs/2402.15993)

34. [Financial data] MambaStock: Selective state space model for stock prediction (https://arxiv.org/abs/2402.18959) GitHub

35. [Theory] Theoretical Foundations of Deep Selective State-Space Models (https://arxiv.org/abs/2402.19047)

    Theoretical analysis from the perspective of rough path theory (sig- nature transform).

36. [Scale-up] Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models (https://arxiv.org/abs/2402.19427)

37. [Point Cloud Analysis] Point Could Mamba: Point Cloud Learning via State Space Model (https://arxiv.org/abs/2403.00762) GitHub

38. [Language Model] DenseMamba: State Space Models with Dense Hidden Connection for Efficient Large Language Models (https://arxiv.org/abs/2403.00818) GitHub

39. [Vision] The Hidden Attention of Mamba Models (https://arxiv.org/abs/2403.01590) GitHub

40. [Target Detection] MiM-ISTD: Mamba-in-Mamba for Efficient Infrared Small Target Detection (https://arxiv.org/abs/2403.02148) GitHub

41. [Time Series] TimeMachine: A Time Series is Worth 4 Mambas for Long-term Forecasting (https://arxiv.org/abs/2403.09898) GitHub

42. [Time Series] Is Mamba Effective for Time Series Forecasting? (https://arxiv.org/abs/2403.11144) To-be-updated-GitHub

43. [Recommendation] Mamba4Rec: Towards Efficient Sequential Recommendation with Selective State Space Models (https://arxiv.org/abs/2403.03900) GitHub

44. [Speech] Multichannel Long-Term Streaming Neural Speech Enhancement for Static and Moving Speakers (https://arxiv.org/abs/2403.07675) GitHub

45. [Vision] On the low-shot transferability of [V]-Mamba (https://arxiv.org/abs/2403.10696)

46. [Diffusion Model] ZigMa: Zigzag Mamba Diffusion Model (ECCV 2024) (https://arxiv.org/abs/2403.13802) To-be-updated-GitHub

47. [Scale-up] Jamba: SSM-Transformer Model (https://www.ai21.com/blog/announcing-jamba)

    Total 52B parameters. SSM-Transformer hybrid architecture, 256K context window

48. [Control] State Space Models as Foundation Models: A Control Theoretic Overview (https://arxiv.org/abs/2403.16899) GitHub

49. [3D reconstruction] Gamba: Marry Gaussian Splatting with Mamba for single view 3D reconstruction (https://arxiv.org/abs/2403.18795)

50. MambaMixer: Efficient Selective State Space Models with Dual Token and Channel Selection (https://arxiv.org/abs/2403.19888)

51. [Semantic Segmentation] Sigma: Siamese Mamba Network for Multi-Modal Semantic Segmentation (https://arxiv.org/abs/2404.04256) GitHub

52. [Scale-up] RecurrentGemma: Moving Past Transformers for Efficient Open Language Models (https://storage.googleapis.com/deepmind-media/gemma/recurrentgemma-report.pdf) GitHub

53. HGRN2: Gated Linear RNNs with State Expansion (https://arxiv.org/abs/2404.07904) GitHub

54. [Theory] State-Space Systems as Dynamic Generative Models (https://arxiv.org/abs/2404.08717)

    This paper studies the conditions for stochastic echo state property, which is a generalisation of deterministic case.

55. [Survey] State Space Model for New-Generation Network Alternative to Transformers: A Survey (https://arxiv.org/abs/2404.09516) GitHub

56. [DNA] Caduceus: Bi-Directional Equivariant Long-Range DNA Sequence Modeling (https://arxiv.org/pdf/2403.03234) GitHub

57. [Vision] ViM-UNet: Vision Mamba for Biomedical Segmentation (https://arxiv.org/abs/2404.07705) GitHub

58. Integrating Mamba and Transformer for Long-Short Range Time Series Forecasting (https://arxiv.org/abs/2404.14757) GitHub

59. xLSTM: Extended Long Short-Term Memory (https://arxiv.org/abs/2405.04517)

60. MambaOut: Do We Really Need Mamba for Vision? (https://arxiv.org/abs/2405.07992) GitHub

61. [Transformer_to_Recurrent] Linearizing Large Language Models (https://arxiv.org/abs/2405.06640) GitHub

62. Not All Language Model Features Are Linear (https://arxiv.org/abs/2405.14860)

63. Attention as an RNN (https://arxiv.org/abs/2405.13956)

64. I2I-Mamba: Multi-modal medical image synthesis via selective state space modeling (https://arxiv.org/abs/2405.14022) GitHub

65. There is HOPE to Avoid HiPPOs for Long-memory State Space Models (https://arxiv.org/abs/2405.13975)

66. Understanding the differences in Foundation Models: Attention, State Space Models, and Recurrent Neural Networks (https://arxiv.org/abs/2405.15731) GitHub

67. The Expressive Capacity of State Space Models: A Formal Language Perspective (https://arxiv.org/abs/2405.17394)

68. Efficient Time Series Processing for Transformers and State-Space Models through Token Merging (https://arxiv.org/abs/2405.17951)

69. DiG: Scalable and Efficient Diffusion Models with Gated Linear Attention (https://arxiv.org/abs/2405.18428)

70. ViG: Linear-complexity Visual Sequence Learning with Gated Linear Attention (https://arxiv.org/abs/2405.18425)

71. State Space Models are Comparable to Transformers in Estimating Functions with Dynamic Smoothness (https://arxiv.org/abs/2405.19036)

72. Recurrent neural networks: vanishing and exploding gradients are not the end of the story (https://arxiv.org/abs/2405.21064)

73. Parallelizing Linear Transformers with the Delta Rule over Sequence Length (https://arxiv.org/abs/2406.06484)

74. An Empirical Study of Mamba-based Language Models (https://arxiv.org/abs/2406.07887)

75. Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling (https://arxiv.org/abs/2406.07522)

76. Learning to (Learn at Test Time): RNNs with Expressive Hidden States (https://arxiv.org/abs/2407.04620) GitHub

77. Towards a theory of learning dynamics in deep state space models (https://arxiv.org/pdf/2407.07279)

78. Towards Scalable and Stable Parallelization of Nonlinear RNNs (https://arxiv.org/abs/2407.19115)

79. PackMamba: Efficient Processing of Variable-Length Sequences in Mamba training (https://arxiv.org/abs/2408.03865)

80. Long Range Switching Time Series Prediction via State Space Model (https://arxiv.org/pdf/2407.19201)

81. B’MOJO: Hybrid State Space Realizations of Foundation Models with Eidetic and Fading Memory (https://arxiv.org/pdf/2407.06324)

82. FalconMamba (https://huggingface.co/blog/falconmamba)

83. Jamba 1.5 (https://arxiv.org/html/2408.12570v1) https://huggingface.co/ai21labs

84. Shuffle Mamba: State Space Models with Random Shuffle for Multi-Modal Image Fusion (https://arxiv.org/abs/2409.01728)

85. GSA: Gated Slot Attention for Efficient Linear-Time Sequence Modeling (http://arxiv.org/abs/2409.07146)

86. A Diagonal Structured State Space Model on Loihi 2 for Efficient Streaming Sequence Processing (https://arxiv.org/abs/2409.15022)

87. Uncertainty Representations in State-Space Layers for Deep Reinforcement Learning under Partial Observability (https://arxiv.org/abs/2409.16824)

88. [WACV 2025] SUM: Saliency Unification through Mamba for Visual Attention Modeling (https://www.arxiv.org/abs/2406.17815) GitHub

89. Mathematical Formalism for Memory Compression in Selective State Space Models (https://arxiv.org/pdf/2410.03158)

ICLR 2024 submissions

I try to use the most important 2-3 sentences in the abstract to summarize the paper. (https://openreview.net/group?id=ICLR.cc/2024/Conference)

1. FlashFFTConv(https://openreview.net/forum?id=gPKTTAfYBp)

   FlashFFTConv speeds up exact FFT convolutions by up to 8.7 over PyTorch and achieves up to 4.4 speedup end-to-end. GitHub.

2. Variational quantization for state space models(https://openreview.net/forum?id=EAkjVCtRO2)

   In this work, we propose a new forecasting model that combines discrete state space hidden Markov models with recent neural network architectures and training procedures inspired by vector quantized variational autoencoders. We introduce a variational discrete posterior distribution of the latent states given the observations and a two-stage training procedure to alternatively train the parameters of the latent states and of the emission distributions.

3. Efficient Long Sequence Modeling via State Space Augmented Transformer(https://openreview.net/forum?id=xuxYaBMd9F)

   We propose SPADE, short for State Space Augmented Transformer. Specifically, we augment a SSM into the bottom layer of SPADE, and we employ efficient local attention methods for the other layers.

   SSM + Transformer GitHub

4. StableSSM: Alleviating the Curse of Memory in State-space Models through Stable Reparameterization(https://openreview.net/forum?id=BwG8hwohU4)

   Our analysis identifies this ``curse of memory'' as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability.

   Stability, more on parameterisation

5. Robustifying State-space Models for Long Sequences via Approximate Diagonalization(https://openreview.net/forum?id=DjeQ39QoLQ)

   We introduce a generic, backward-stable ''perturb-then-diagonalize'' (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences.

   Robustness, more on initialization

6. From generalization analysis to optimization designs for state space models(https://openreview.net/forum?id=EGjvMcKrrl)

   In this paper, we theoretically study the generalization of SSMs and propose improvements to training algorithms based on the generalization results. Specifically, we give a data-dependent generalization bound for SSMs, showing an interplay between the SSM parameters and the temporal dependencies of the training sequences. Leveraging the generalization bound, we (1) set up a scaling rule for model initialization based on the proposed generalization measure, which significantly improves the robustness of SSMs to different temporal patterns in the sequence data; (2) introduce a new regularization method for training SSMs to enhance the generalization performance. Numerical results are conducted to validate our results.

7. A 2-Dimensional State Space Layer for Spatial Inductive Bias(https://openreview.net/forum?id=BGkqypmGvm)

   We leverage an expressive variation of the multidimensional State Space Model (SSM). Our approach introduces efficient parameterization, accelerated computation, and a suitable normalization scheme. Empirically, we observe that incorporating our layer at the beginning of each transformer block of Vision Transformers (ViT) significantly enhances performance for multiple ViT backbones and across datasets. The new layer is effective even with a negligible amount of additional parameters and inference time.

   Vision task

8. Hieros: Hierarchical Imagination on Structured State Space Sequence World Models(https://openreview.net/forum?id=5j6wtOO6Fk)

   We propose HIEROS, a hierarchical policy that learns time abstracted world representations and imagines trajectories at multiple time scales in latent space. HIEROS uses an S5 layer-based world model, which predicts next world states in parallel during training and iteratively during environment interaction. Due to the special properties of S5 layers, our method can train in parallel and predict next world states iteratively during imagination. This allows for more efficient training than RNN-based world models and more efficient imagination than Transformer-based world models.

   Reinforcement Learning (Use SSM instead of Transformer)

9. S4++: Elevating Long Sequence Modeling with State Memory Reply(https://openreview.net/forum?id=bdnw4qjfH9)

   1. Non-Stable-States (NSS): Significant state variance discrepancies arise among discrete sampling steps, occasionally resulting in divergence.
   2. Dependency Bias: The unidirectional state space dependency in SSM impedes the effective modeling of intricate dependencies. In this paper, we conduct theoretical analysis of SSM from the even-triggered control (ETC) theory perspective and first propose the presence of NSS Phenomenon.

   Our findings indicate that NSS primarily results from the sampling steps, and the integration of multi-state inputs into the current state significantly contributes to the mitigation of NSS. Building upon these theoretical analyses and findings, we propose a simple, yet effective, theoretically grounded State Memory Reply (SMR) mechanism that leverages learnable memories to incorporate multi-state information into the current state.

   Stability

10. Mamba: Linear-Time Sequence Modeling with Selective State Spaces(https://openreview.net/forum?id=AL1fq05o7H)

    Many subquadratic-time architectures such as linear attention, gated convolution and recurrent models, and structured state space models (SSMs) have been developed to address Transformers' computational inefficiency on long sequences, but they have not performed as well as attention on important modalities such as language. We identify that a key weakness of such models is their inability to perform content-based reasoning, and make several improvements. First, simply letting the SSM parameters be functions of the input addresses their weakness with discrete modalities, allowing the model to selectively propagate or forget information along the sequence length dimension depending on the current token. Second, even though this change prevents the use of efficient convolutions, we design a hardware-aware parallel algorithm in recurrent mode. We integrate these selective SSMs into a simplified end-to-end neural network architecture without attention or even MLP blocks (Mamba).

    Time-dependent or input-dependent state-space models + Hardware acceleration

    A very nice analysis in Chinese: https://zhuanlan.zhihu.com/p/661237120.

11. Gated recurrent neural networks discover attention(https://openreview.net/forum?id=rfSfDSFrRL)

    These modern RNNs feature a prominent design pattern: linear recurrent layers interconnected by feedforward paths with multiplicative gating. Here, we show how RNNs equipped with these two design elements can exactly implement (linear) self-attention, the main building block of Transformers.

    By reverse-engineering a set of trained RNNs, we find that gradient descent in practice discovers our construction. In particular, we examine RNNs trained to solve simple in-context learning tasks on which Transformers are known to excel and find that gradient descent instills in our RNNs the same attention-based in-context learning algorithm used by Transformers.

    Naive question: What's the difference in contribution sense against Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention.

    Universality of SSM + Optimization verification over ICL

12. GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling(https://openreview.net/forum?id=02Ug9N8DCI)

    We develop GateLoop, a foundational sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet, by employing data-controlled state transitions. Furthermore, we derive an $O(l^2)$ surrogate-attention mode, revealing remarkable implications for Transformer and recently proposed architectures. While many existing models solely rely on data-controlled cumulative sums for context aggregation, our findings suggest that incorporating data-controlled complex cumulative products may be a crucial step towards more powerful sequence models.

    Data-controlled state transitions sound similar to 9, TODO comparison Official GitHub Unofficial GitHub

13. Never Train from Scratch: Fair Comparison of Long-Sequence Models Requires Data-Driven Priors (https://openreview.net/forum?id=PdaPky8MUn)

    In this work, we show that random initialization leads to gross overestimation of the differences between architectures and that pretraining with standard denoising objectives, using only the downstream task data, leads to dramatic gains across multiple architectures and to very small gaps between Transformers and state space models (SSMs). In stark contrast to prior works, we find vanilla Transformers to match the performance of S4 on Long Range Arena when properly pretrained, and we improve the best reported results of SSMs on the PathX-256 task by 20 absolute points. Subsequently, we analyze the utility of previously-proposed structured parameterizations for SSMs and show they become mostly redundant in the presence of data-driven initialization obtained through pretraining. Our work shows that, when evaluating different architectures on supervised tasks, incorporation of data-driven priors via pretraining is essential for reliable performance estimation, and can be done efficiently.

    GitHub

14. Mastering Memory Tasks with World Models (https://openreview.net/forum?id=1vDArHJ68h)

    To improve temporal coherence, we integrate a new family of state space models (SSMs) in world models of MBRL agents to present a new method, Recall to Imagine (R2I). This integration aims to enhance both long-term memory and long-horizon credit assignment. Through a diverse set of illustrative tasks, we systematically demonstrate that R2I establishes a new state-of-the-art performance in challenging memory and credit assignment RL tasks, such as Memory Maze, BSuite, and POPGym. We also show that R2I is faster than the state-of-the-art MBRL method, DreamerV3, resulting in faster wall-time convergence.

    Reinforcement Learning GitHub

Arxiv

1. RWKV (https://arxiv.org/abs/2305.13048): GitHub

2. RetNet (https://arxiv.org/abs/2307.08621) GitHub

3. Zoology (https://arxiv.org/abs/2312.04927) GitHub

4. Structured state-space models are deep Wiener models (https://arxiv.org/abs/2312.06211)

NeurIPS 2023

1. State-space Models with Layer-wise Nonlinearity are Universal Approximators with Exponential Decaying Memory (https://arxiv.org/abs/2309.13414)

   The authors show that the layer-wise nonlinearity is enough to achieve the universality when the state-space models are multi-layer.

   It is also shown that similar to traditional nonlinear recurrent neural networks, SSMs also suffer from the aymptotically exponential memory decay.

2. Sparse Modular Activation for Efficient Sequence Modeling (SMA) (https://arxiv.org/abs/2306.11197) GitHub

   SSM + Attention, SOTA at LRA.

   We design a novel neural architecture, SeqBoat, which employs SMA to sparsely activate a Gated Attention Unit (GAU) based on the state representations learned from an SSM.

3. Laughing Hyena Distillery: Extracting Compact Recurrences from Convolutions (https://arxiv.org/abs/2310.18780)

   Given a convolution-based Hyena model, the authors want to extract the recurrent weights for the convolution kernel so that the convolution model can be converted into a recurrent models. Method used are based on Hankel matrix SVD.

4. Structured State Space Models for In-Context Reinforcement Learning (https://arxiv.org/abs/2303.03982) GitHub

   We propose a modification to a variant of S4 that enables us to initialise and reset the hidden state in parallel, allowing us to tackle reinforcement learning tasks. We show that our modified architecture runs asymptotically faster than Transformers in sequence length and performs better than RNN's on a simple memory-based task.

5. Convolutional State Space Models for Long-Range Spatiotemporal Modeling (https://arxiv.org/abs/2310.19694) GitHub

6. Hierarchically Gated Recurrent Neural Network for Sequence Modeling (https://paperswithcode.com/paper/hierarchically-gated-recurrent-neural-network) GitHub

ICML 2023

1. Resurrecting Recurrent Neural Networks for Long Sequences (https://icml.cc/virtual/2023/oral/25438)

2. Hyena Hierarchy: Towards Larger Convolutional Language Models (https://arxiv.org/abs/2302.10866) GitHub

3. Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Series (https://icml.cc/virtual/2023/oral/25554) GitHub

Before 2023

1. See github repo State-spaces for S4, including HiPPO, LSSL, SaShiMi, DSS, HTTYH, S4D, and S4ND, GSS

2. [S5] Simplified State Space Layers for Sequence Modeling (ICLR 2023) (https://openreview.net/forum?id=Ai8Hw3AXqks) GitHub

3. [Liquid SSM] Liquid Structural State-Space Models (ICLR 2023) (https://openreview.net/forum?id=g4OTKRKfS7R) GitHub

4. [Parallel scan] Parallelizing Linear Recurrent Neural Nets Over Sequence Length (ICLR 2018) (https://openreview.net/forum?id=HyUNwulC-) GitHub

5. Bayesian state-space models GitHub.

   Another very good note is: http://personal.strath.ac.uk/gary.koop/GSE_Bayesian/Bayesian_State_Space_Methods.pdf

6. Mega: Moving Average Equipped Gated Attention (Mega) GitHub

7. Annotated S4 By Sasha Rush and Sidd Karamcheti GitHub

8. The State Space of Complex Systems (thesis by Frank Heilmann) https://d-nb.info/1212365704/34

Star History