Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges

The Mamba-360 framework is a collection of State Space Models in various Domains.

Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequences

Transformers have dominated sequence modeling tasks like Machine Translation, Named Entity Recognition (NER), etc., but they suffer from $O(N^2)$ attention complexity and challenges in handling inductive bias for long sequences.
State Space Models (SSMs) have emerged as promising alternatives for sequence modeling paradigms, especially with the advent of S4 and its variants, such as S4nd, Hippo, Hyena, Diagonal State Spaces (DSS), Gated State Spaces (GSS), Linear Recurrent Unit (LRU), Liquid-S4, Long-Conv, Mega, HGRN, TNN, S5, Mamba, Mamba-former, Mamba-MoE etc.

-In this survey, we categorize foundational SSMs based on three paradigms: Structural architectures, Gating architectures, and Recurrent architectures.

The survey highlights crucial applications of SSMs for Long Sequence context across various domains, including:
- Natural Language Processing (NLP)
- Computer Vision
- Medical Domain (including genomics, drug design)
- Video Domain
- Audio and Speech
- Multi-Modal Domain
- Tabular Domain
- Recommendation System
- Graph Domain
- Time Series forecasting
The work consolidates the performance of SSMs on benchmark datasets in:
- Text Domain: Long Range Arena (LRA), WikiText, Glue, Pile
- Vision Domain: ImageNet1K
- Video Dataset: Kinetics-400, SSTv2, Breakfast, COIN, LVU
- Time Series Datasets: Electricity, Weather, Traffic, ETTh1, ETTh2, ETTm1, and ETTm2.

A Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges

Badri N. Patro, Vijay S. Agneeswaran Microsoft

@article{patro2024mamba,
  title={Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges},
  author={Patro, Badri Narayana and Agneeswaran, Vijay Srinivas},
  journal={arXiv preprint arXiv:2404.16112},
  year={2024}
}

Adavance State Space Models

SSMs for Various Applications

Architectural Evolution

Basic Of SSM.

SSM SOTA on ImageNet-1K dataset with Image size 224 x 224.

This table shows the performance of various SSM models for Image Recognition tasks on the ImageNet1K dataset (Deng et al., 2009).

Table: SSM SOTA on ImageNet-1K. This table shows the performance of various SSM models for Image Recognition tasks on the ImageNet1K dataset. Models are grouped into three categories based on their GFLOPs. This table is adapted from the original source.

Method	Image Size	#Param.	FLOPs	Top-1 acc.
HyenaViT-B	224^2	88M	-	78.5
S4ND-ViT-B	224^2	89M	-	80.4
TNN-T	-	6.4M	-	72.29
TNN-S	-	23.4M	-	79.20
Vim-Ti	224^2	7M	-	76.1
Vim-S	224^2	26M	-	80.5
HGRN-T	-	6.1M	-	74.40
HGRN-S	-	23.7M	-	80.09
PlainMamba-L1	224^2	7M	3.0G	77.9
PlainMamba-L2	224^2	25M	8.1G	81.6
PlainMamba-L3	224^2	50M	14.4G	82.3
Mamba-2D-S	224^2	24M	-	81.7
Mamba-2D-B	224^2	92M	-	83.0
VMamba-T	224^2	22M	5.6G	82.2
VMamba-S	224^2	44M	11.2G	83.5
VMamba-B	224^2	75M	18.0G	83.2
LocalVMamba-T	224^2	26M	5.7G	82.7
LocalVMamba-S	224^2	50M	11.4G	83.7
SiMBA-S(Monarch)	224^2	18.5M	3.6G	81.1
SiMBA-B(Monarch)	224^2	26.9M	6.3G	82.6
SiMBA-L(Monarch)	224^2	42M	10.7G	83.8
ViM2-T	224^2	20M	-	82.7
ViM2-S	224^2	43M	-	83.7
ViM2-B	224^2	74M	-	83.9
SiMBA-S(EinFFT)	224^2	15.3M	2.4G	81.7
SiMBA-B(EinFFT)	224^2	22.8M	5.2G	83.5
SiMBA-L(EinFFT)	224^2	36.6M	9.6G	84.4
SiMBA-S(MLP)	224^2	26.5M	5.0G	84.0
SiMBA-B(MLP)	224^2	40.0M	9.0G	84.7

State of the Art results of various vision models (Convnets, Transformers, SSMs) on ImageNet-1K dataset with Image size 224 x 224.

Table: SOTA on ImageNet-1K}The table shows the performance of various vision backbones on the ImageNet1K dataset for image recognition tasks. $\star$ indicates additionally trained with the Token Labeling for patch encoding. We have grouped the vision models into three categories based on their GFLOPs (Small, Base, and Large). The GFLOP ranges: Small (GFLOPs$<$5), Base (5$\leq$GFLOPs$<$10), and Large (10$\leq$GFLOPs$<$30). This table is adapted from the SiMBA paper.

Method	Image Size	#Param.	FLOPs	Top-1 acc.
Convnets
ResNet-101	$224^2$	45M	-	77.4
RegNetY-8G	$224^2$	39M	8.0G	81.7
ResNet-152	$224^2$	60M	-	78.3
RegNetY-16G	$224^2$	84M	16.0G	82.9
Transformers
DeiT-S	$224^2$	22M	4.6G	79.8
Swin-T	$224^2$	29M	4.5G	81.3
EffNet-B4	$380^2$	19M	4.2G	82.9
WaveViT-H-S$^\star$	$224^2$	22.7M	4.1G	82.9
SpectFormer-H-S$^\star$	$224^2$	22.2M	3.9G	84.3
SVT-H-S$^\star$	$224^2$	22M	3.9G	84.2
SCT-H-S$^\star$	$224^2$	21.7M	4.1G	84.5
EffNet-B5	$456^2$	30M	9.9G	83.6
Swin-S	$224^2$	50M	8.7G	83.0
CMT-B	$224^2$	45M	9.3G	84.5
MaxViT-S	$224^2$	69M	11.7G	84.5
iFormer-B	$224^2$	48M	9.4G	84.6
Wave-ViT-B$^\star$	$224^2$	33M	7.2G	84.8
SpectFormer-H-B$^\star$	$224^2$	33.1M	6.3G	85.1
SVT-H-B$^\star$	$224^2$	32.8M	6.3G	85.2
SCT-H-B$^\star$	$224^2$	32.5M	6.5G	85.2
M2-ViT-b	$224^2$	45M	-	79.5
DeiT-B	$224^2$	86M	17.5G	81.8
Swin-B	$224^2$	88M	15.4G	83.5
M2-Swin-B	$224^2$	50M	-	83.5
EffNet-B6	$528^2$	43M	19.0G	84.0
MaxViT-B	$224^2$	120M	23.4G	85.0
VOLO-D3$^\star$	$224^2$	86M	20.6G	85.4
Wave-ViT-L$^\star$	$224^2$	57M	14.8G	85.5
SpectFormer-H-L$^\star$	$224^2$	54.7M	12.7G	85.7
SVT-H-L$^\star$	$224^2$	54.0M	12.7G	85.7
SCT-H-L$^\star$	$224^2$	54.1M	13.4G	85.9
SSMs
Vim-Ti	$224^2$	7M	-	76.1
PlainMamba-L1	$224^2$	7M	3.0G	77.9
VMamba-T	$224^2$	22M	5.6G	82.2
SiMBA-S(Monarch)	$224^2$	18.5M	3.6G	81.1
Mamba-2D-S	$224^2$	24M	-	81.7
SiMBA-S(EinFFT)	$224^2$	15.3M	2.4G	81.7
LocalVMamba-T	$224^2$	26M	5.7G	82.7
ViM2-T	$224^2$	20M	-	82.7
SiMBA-S(MLP)	$224^2$	26.5M	5.0G	84.0
Vim-S	$224^2$	26M	-	80.5
PlainMamba-L2	$224^2$	25M	8.1G	81.6
SiMBA-B(Monarch)	$224^2$	26.9M	6.3G	82.6
Mamba-2D-B	$224^2$	92M	-	83.0
SiMBA-B(EinFFT)	$224^2$	22.8M	5.2G	83.5
VMamba-S	$224^2$	44M	11.2G	83.5
LocalVMamba-S	$224^2$	50M	11.4G	83.7
ViM2-S	$224^2$	43M	-	83.7
SiMBA-B(MLP)	$224^2$	40.0M	9.0G	84.7
HyenaViT-B	$224^2$	88M	-	78.5
S4ND-ViT-B	$224^2$	89M	-	80.4
PlainMamba-L3	$224^2$	50M	14.4G	82.3
VMamba-B	$224^2$	75M	18.0G	83.2
SiMBA-L(Monarch)	$224^2$	42M	10.7G	83.8
ViM2-B	$224^2$	74M	-	83.9
SiMBA-L(EinFFT)	$224^2$	36.6M	9.6G	84.4

State of the Art results of LRA benchmark tasks (Tay et al., 2020).

Table: Test accuracy on the LRA benchmark tasks (Tay et al., 2020). "✗" indicates the model did not exceed random guessing. The results for models ranging from Transformer to Performer are sourced from Tay et al. (2020). We compiled this table using data from the HGRN paper by Qin et al. (2023) and the S5 paper by Smith et al. (2022), consolidating the results into a unified presentation below.

Model	ListOps	Text	Retrieval	Image	Pathfinder	Path-X	Avg.
Transformer	36.37	64.27	57.46	42.44	71.40	✗	53.66
Local Attention	15.82	52.98	53.39	41.46	66.63	✗	46.71
Sparse Trans.	17.07	63.58	59.59	44.24	71.71	✗	51.03
Longformer	35.63	62.85	56.89	42.22	69.71	✗	52.88
Linformer	35.70	53.94	52.27	38.56	76.34	✗	51.14
Reformer	37.27	56.10	53.40	38.07	68.50	✗	50.56
Sinkhorn Trans.	33.67	61.20	53.83	41.23	67.45	✗	51.23
Synthesizer	36.99	61.68	54.67	41.61	69.45	✗	52.40
BigBird	36.05	64.02	59.29	40.83	74.87	✗	54.17
Linear Trans.	16.13	65.90	53.09	42.34	75.30	✗	50.46
Performer	18.01	65.40	53.82	42.77	77.05	✗	51.18
cosFormer	36.50	67.70	83.15	51.23	71.96	-	51.76
FLASH	38.70	64.10	86.10	47.40	70.25	-	51.09
FNet	35.33	65.11	59.61	38.67	77.80	✗	54.42
Nyströmformer	37.15	65.52	79.56	41.58	70.94	✗	57.46
Luna-256	37.25	64.57	79.29	47.38	77.72	✗	59.37
H-Transformer-1D	49.53	78.69	63.99	46.05	68.78	✗	61.41
CCNN	43.60	84.08	✗	88.90	91.51	✗	68.02
S4	58.35	76.02	87.09	87.26	86.05	88.10	80.48
DSSEXP	59.70	84.60	87.60	84.90	84.70	85.60	81.18
DSS(SOFTMAX)	60.60	84.80	87.80	85.70	84.60	87.80	81.88
S4D-LegS	60.47	86.18	89.46	88.19	93.06	91.95	84.89
Mega-chunk	58.76	90.19	90.97	85.80	94.41	93.81	85.66
S4-LegS	59.60	86.82	90.90	88.65	94.20	96.35	86.09
TNN	61.04	87.90	90.97	88.24	93.00	96.10	86.21
LRU	60.20	89.40	89.90	89.00	95.10	94.20	86.30
HGRN	59.95	88.14	94.23	88.69	92.92	97.50	86.91
SGConv	61.45	89.2	91.11	87.97	95.46	97.83	87.17
Liquid-S4	62.75	89.02	91.20	89.50	94.8	96.66	87.32
S5	62.15	89.31	91.40	88.00	95.33	98.58	87.46
Mega	63.14	90.43	91.25	90.44	96.01	97.98	88.21

Multivariate Time series benchmark Datasets

Table: Multivariate long-term forecasting results: It uses prediction lengths (T \in {96, 192, 336, 720}) for all the datasets for lookup window 96. The best results are in bold and the second best is underlined. This table is adapted from the SiMBA paper [@patro2024simba].

Datasets	Models	Simba		TimesNet		Crossformer		PatchTST		ETSFormer		DLinear		FEDFormer		Autoformer		Pyraformer		MTGNN
	Metric	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTm1	96	0.324	0.360	0.338	0.375	0.349	0.395	0.339	0.377	0.375	0.398	0.345	0.372	0.379	0.419	0.505	0.475	0.543	0.510	0.379	0.446
	192	0.363	0.382	0.374	0.387	0.405	0.411	0.376	0.392	0.408	0.410	0.380	0.389	0.426	0.441	0.553	0.496	0.557	0.537	0.470	0.428
	336	0.395	0.405	0.410	0.411	0.432	0.431	0.408	0.417	0.435	0.428	0.413	0.413	0.445	0.459	0.621	0.537	0.754	0.655	0.473	0.430
	720	0.451	0.437	0.478	0.450	0.487	0.463	0.499	0.461	0.499	0.462	0.474	0.453	0.543	0.490	0.671	0.561	0.908	0.724	0.553	0.479
ETTm2	96	0.177	0.263	0.187	0.267	0.208	0.292	0.192	0.273	0.189	0.280	0.193	0.292	0.203	0.287	0.255	0.339	0.435	0.507	0.203	0.299
	192	0.245	0.306	0.249	0.309	0.263	0.332	0.252	0.314	0.253	0.319	0.284	0.362	0.269	0.328	0.281	0.340	0.730	0.673	0.265	0.328
	336	0.304	0.343	0.321	0.351	0.337	0.369	0.318	0.357	0.314	0.357	0.369	0.427	0.325	0.366	0.339	0.372	1.201	0.845	0.365	0.374
	720	0.400	0.399	0.408	0.403	0.429	0.430	0.413	0.416	0.414	0.413	0.554	0.522	0.421	0.415	0.433	0.432	3.625	1.451	0.461	0.459
ETTh1	96	0.379	0.395	0.384	0.402	0.384	0.428	0.385	0.408	0.494	0.479	0.386	0.400	0.376	0.419	0.449	0.459	0.664	0.612	0.515	0.517
	192	0.432	0.424	0.436	0.429	0.438	0.452	0.431	0.432	0.538	0.504	0.437	0.432	0.420	0.448	0.500	0.482	0.790	0.681	0.553	0.522
	336	0.473	0.443	0.491	0.469	0.495	0.483	0.485	0.462	0.574	0.521	0.481	0.459	0.459	0.465	0.521	0.496	0.891	0.738	0.612	0.577
	720	0.483	0.469	0.521	0.500	0.522	0.501	0.497	0.483	0.562	0.535	0.519	0.516	0.506	0.507	0.514	0.512	0.963	0.782	0.609	0.597
ETTh2	96	0.290	0.339	0.340	0.374	0.347	0.391	0.343	0.376	0.340	0.391	0.333	0.387	0.358	0.397	0.346	0.388	0.645	0.597	0.354	0.454
	192	0.373	0.390	0.402	0.414	0.419	0.427	0.405	0.417	0.430	0.439	0.477	0.476	0.429	0.439	0.456	0.452	0.788	0.683	0.457	0.464
	336	0.376	0.406	0.452	0.452	0.449	0.465	0.448	0.453	0.485	0.479	0.594	0.541	0.496	0.487	0.482	0.486	0.907	0.747	0.515	0.540
	720	0.407	0.431	0.462	0.468	0.479	0.505	0.464	0.483	0.500	0.497	0.831	0.657	0.463	0.474	0.515	0.511	0.963	0.783	0.532	0.576
Electricity	96	0.165	0.253	0.168	0.272	0.185	0.288	0.159	0.268	0.187	0.304	0.197	0.282	0.193	0.308	0.201	0.317	0.386	0.449	0.217	0.318
	192	0.173	0.262	0.198	0.300	0.211	0.312	0.195	0.296	0.212	0.329	0.209	0.301	0.214	0.329	0.231	0.338	0.376	0.443	0.260	0.348
	336	0.188	0.277	0.198	0.300	0.211	0.312	0.195	0.296	0.212	0.329	0.209	0.301	0.214	0.329	0.231	0.338	0.376	0.443	0.260	0.348
	720	0.214	0.305	0.220	0.320	0.223	0.335	0.215	0.317	0.233	0.345	0.245	0.333	0.246	0.355	0.254	0.361	0.376	0.445	0.290	0.369
Traffic	96	0.468	0.268	0.593	0.321	0.591	0.329	0.583	0.319	0.607	0.392	0.650	0.396	0.587	0.366	0.613	0.388	0.867	0.468	0.660	0.437
	192	0.413	0.317	0.617	0.336	0.607	0.345	0.591	0.331	0.621	0.399	0.598	0.370	0.604	0.373	0.616	0.382	0.869	0.467	0.649	0.438
	336	0.529	0.284	0.629	0.336	0.613	0.339	0.599	0.332	0.622	0.396	0.605	0.373	0.621	0.383	0.622	0.337	0.881	0.469	0.653	0.472
	720	0.564	0.297	0.640	0.350	0.620	0.348	0.601	0.341	0.632	0.396	0.645	0.394	0.626	0.382	0.660	0.408	0.896	0.473	0.639	0.437
Weather	96	0.176	0.219	0.172	0.220	0.191	0.251	0.171	0.230	0.197	0.281	0.196	0.255	0.217	0.296	0.266	0.336	0.622	0.556	0.230	0.329
	192	0.222	0.260	0.219	0.261	0.219	0.279	0.219	0.271	0.237	0.312	0.237	0.296	0.276	0.336	0.307	0.367	0.739	0.624	0.263	0.322
	336	0.275	0.297	0.280	0.306	0.287	0.332	0.277	0.321	0.298	0.353	0.283	0.335	0.339	0.380	0.359	0.395	1.004	0.753	0.354	0.396
	720	0.350	0.349	0.365	0.359	0.368	0.378	0.365	0.367	0.352	0.288	0.345	0.381	0.403	0.428	0.419	0.428	1.420	0.934	0.409	0.371

Comparison with SoTA methods on 8 benchmark datasets for Multimodal Applications

Benchmark names are abbreviated due to space limits. VQA-v2 (Goyal et al., 2017); GQA (Hudson and Manning, 2019); SQA-I: ScienceQA-IMG (Anonymous, 2022); VQA-T: TextVQA (Singh et al., 2019); POPE (Li et al., 2023); MME (Yin et al., 2023); MMB: MMBench (Liu et al., 2023); MM-Vet (Yu et al., 2023). PT and IT indicate the number of samples in the pretraining and instruction tuning stages, respectively.

Table: Comparison with State-of-the-Art (SoTA) methods on 8 benchmarks. Benchmark names are abbreviated for space considerations. PT and IT indicate the number of samples in the pretraining and instruction tuning stages, respectively. This table is adapted from the VL-Mamba paper (Qiao et al., 2024).

Method	LLM	PT	IT	VQA-v2	GQA	SQA-I	VQA-T	POPE	MME	MMB	MM-Vet
BLIP-2	Vicuna-13B	129M	-	41.0	41.0	61.0	42.5	85.3	1293.8	--	22.4
MiniGPT-4	Vicuna-7B	5M	5K	-	32.2	-	-	-	581.7	23.0	-
InstructBLIP	Vicuna-7B	129M	1.2M	--	49.2	60.5	50.1	--	--	36	26.2
InstructBLIP	Vicuna-13B	129M	1.2M	--	49.5	63.1	50.7	78.9	1212.8	--	25.6
Shikra	Vicuna-13B	600K	5.5M	77.4	--	--	--	--	--	58.8	--
Otter	LLaMA-7B	-	-	-	-	-	-	-	1292.3	48.3	24.6
mPLUG-Owl	LLaMA-7B	2.1M	102K	-	-	-	-	-	967.3	49.4	-
IDEFICS-9B	LLaMA-7B	353M	1M	50.9	38.4	--	25.9	--	--	48.2	--
IDEFICS-80B	LLaMA-65B	353M	1M	60.0	45.2	--	30.9	--	--	54.5	--
Qwen-VL	Qwen-7B	1.4B	50M	78.8	59.3	67.1	63.8	--	--	38.2	--
Qwen-VL-Chat	Qwen-7B	1.4B	50M	78.2	57.5	68.2	61.5	--	1487.5	60.6	--
LLaVA-1.5	Vicuna-7B	558K	665K	78.5	62.0	66.8	58.2	85.9	1510.7	64.3	30.5
LLaVA-1.5	Vicuna-13B	558K	665K	80.0	63.3	71.6	61.3	85.9	1531.3	67.7	35.4
LLaVA-Phi	Phi-2-2.7B	558K	665K	71.4	-	68.4	48.6	85.0	1335.1	59.8	28.9
MobileVLM-3B	MobileLLaMA-2.7B	558K	665K	-	59.0	61.2	47.5	84.9	1288.9	59.6	-
Cobra	Mamba-2.8B	-	-	75.9	58.5	-	46.0	88.0	-	-	-
VL-Mamba	Mamba LLM-2.8B	558K	665K	76.6	56.2	65.4	48.9	84.4	1369.6	57.0	32.6

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Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges

Contents

Adavance State Space Models

SSMs for Various Applications

Architectural Evolution

Basic Of SSM.

SSM SOTA on ImageNet-1K dataset with Image size 224 x 224.

State of the Art results of various vision models (Convnets, Transformers, SSMs) on ImageNet-1K dataset with Image size 224 x 224.

State of the Art results of LRA benchmark tasks (Tay et al., 2020).

Multivariate Time series benchmark Datasets

Comparison with SoTA methods on 8 benchmark datasets for Multimodal Applications

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Mamba-360: Survey of State Space Models as Transformer Alternative for Long Sequence Modelling: Methods, Applications, and Challenges

Contents

Adavance State Space Models

SSMs for Various Applications

Architectural Evolution

Basic Of SSM.

SSM SOTA on ImageNet-1K dataset with Image size 224 x 224.

State of the Art results of various vision models (Convnets, Transformers, SSMs) on ImageNet-1K dataset with Image size 224 x 224.

State of the Art results of LRA benchmark tasks (Tay et al., 2020).

Multivariate Time series benchmark Datasets

Comparison with SoTA methods on 8 benchmark datasets for Multimodal Applications

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