Mamba - Selective State Space Models

Mamba - Selective State Space Models

Quick start

Mamba is a state-space model architecture achieving O(n) linear complexity for sequence modeling.

Installation:

# Install causal-conv1d (optional, for efficiency)
pip install causal-conv1d>=1.4.0

# Install Mamba
pip install mamba-ssm
# Or both together
pip install mamba-ssm[causal-conv1d]

Prerequisites: Linux, NVIDIA GPU, PyTorch 1.12+, CUDA 11.6+

Basic usage (Mamba block):

import torch
from mamba_ssm import Mamba

batch, length, dim = 2, 64, 16
x = torch.randn(batch, length, dim).to("cuda")

model = Mamba(
    d_model=dim,      # Model dimension
    d_state=16,       # SSM state dimension
    d_conv=4,         # Conv1d kernel size
    expand=2          # Expansion factor
).to("cuda")

y = model(x)  # O(n) complexity!
assert y.shape == x.shape

Common workflows

Workflow 1: Language model with Mamba-2

Complete LM with generation:

from mamba_ssm.models.mixer_seq_simple import MambaLMHeadModel
from mamba_ssm.models.config_mamba import MambaConfig
import torch

# Configure Mamba-2 LM
config = MambaConfig(
    d_model=1024,           # Hidden dimension
    n_layer=24,             # Number of layers
    vocab_size=50277,       # Vocabulary size
    ssm_cfg=dict(
        layer="Mamba2",     # Use Mamba-2
        d_state=128,        # Larger state for Mamba-2
        headdim=64,         # Head dimension
        ngroups=1           # Number of groups
    )
)

model = MambaLMHeadModel(config, device="cuda", dtype=torch.float16)

# Generate text
input_ids = torch.randint(0, 1000, (1, 20), device="cuda", dtype=torch.long)
output = model.generate(
    input_ids=input_ids,
    max_length=100,
    temperature=0.7,
    top_p=0.9
)

Workflow 2: Use pretrained Mamba models

Load from HuggingFace:

from transformers import AutoTokenizer
from mamba_ssm.models.mixer_seq_simple import MambaLMHeadModel

# Load pretrained model
model_name = "state-spaces/​mamba-2.8b"
tokenizer = AutoTokenizer.from_pretrained("EleutherAI/​gpt-neox-20b")  # Use compatible tokenizer
model = MambaLMHeadModel.from_pretrained(model_name, device="cuda", dtype=torch.float16)

# Generate
prompt = "The future of AI is"
input_ids = tokenizer(prompt, return_tensors="pt").input_ids.to("cuda")
output_ids = model.generate(
    input_ids=input_ids,
    max_length=200,
    temperature=0.7,
    top_p=0.9,
    repetition_penalty=1.2
)
generated_text = tokenizer.decode(output_ids[0])
print(generated_text)

Available models:

• state-spaces/​mamba-130m
• state-spaces/​mamba-370m
• state-spaces/​mamba-790m
• state-spaces/​mamba-1.4b
• state-spaces/​mamba-2.8b

Workflow 3: Mamba-1 vs Mamba-2

Mamba-1 (smaller state):

from mamba_ssm import Mamba

model = Mamba(
    d_model=256,
    d_state=16,      # Smaller state dimension
    d_conv=4,
    expand=2
).to("cuda")

Mamba-2 (multi-head, larger state):

from mamba_ssm import Mamba2

model = Mamba2(
    d_model=256,
    d_state=128,     # Larger state dimension
    d_conv=4,
    expand=2,
    headdim=64,      # Head dimension for multi-head
    ngroups=1        # Parallel groups
).to("cuda")

Key differences:

• State size: Mamba-1 (d_state=16) vs Mamba-2 (d_state=128)
• Architecture: Mamba-2 has multi-head structure
• Normalization: Mamba-2 uses RMSNorm
• Distributed: Mamba-2 supports tensor parallelism

Workflow 4: Benchmark vs Transformers

Generation speed comparison:

# Benchmark Mamba
python benchmarks/​benchmark_generation_mamba_simple.py \
  --model-name "state-spaces/​mamba-2.8b" \
  --prompt "The future of machine learning is" \
  --topp 0.9 --temperature 0.7 --repetition-penalty 1.2

# Benchmark Transformer
python benchmarks/​benchmark_generation_mamba_simple.py \
  --model-name "EleutherAI/​pythia-2.8b" \
  --prompt "The future of machine learning is" \
  --topp 0.9 --temperature 0.7 --repetition-penalty 1.2

Expected results:

• Mamba: 5× faster inference
• Memory: No KV cache needed
• Scaling: Linear with sequence length

When to use vs alternatives

Use Mamba when:

• Need long sequences (100K+ tokens)
• Want faster inference than Transformers
• Memory-constrained (no KV cache)
• Building streaming applications
• Linear scaling important

Advantages:

• O(n) complexity: Linear vs quadratic
• 5× faster inference: No attention overhead
• No KV cache: Lower memory usage
• Million-token sequences: Hardware-efficient
• Streaming: Constant memory per token

Use alternatives instead:

• Transformers: Need best-in-class performance, have compute
• RWKV: Want RNN+Transformer hybrid
• RetNet: Need retention-based architecture
• Hyena: Want convolution-based approach

Common issues

Issue: CUDA out of memory

Reduce batch size or use gradient checkpointing:

model = MambaLMHeadModel(config, device="cuda", dtype=torch.float16)
model.gradient_checkpointing_enable()  # Enable checkpointing

Issue: Slow installation

Install binary wheels (not source):

pip install mamba-ssm --no-build-isolation

Issue: Missing causal-conv1d

Install separately:

pip install causal-conv1d>=1.4.0

Issue: Model not loading from HuggingFace

Use MambaLMHeadModel.from_pretrained (not AutoModel):

from mamba_ssm.models.mixer_seq_simple import MambaLMHeadModel
model = MambaLMHeadModel.from_pretrained("state-spaces/​mamba-2.8b")

Advanced topics

Selective SSM: See references/​selective-ssm.md for mathematical formulation, state-space equations, and how selectivity enables O(n) complexity.

Mamba-2 architecture: See references/​mamba2-details.md for multi-head structure, tensor parallelism, and distributed training setup.

Performance optimization: See references/​performance.md for hardware-aware design, CUDA kernels, and memory efficiency techniques.

Hardware requirements

• GPU: NVIDIA with CUDA 11.6+
• VRAM:
  • 130M model: 2GB
  • 370M model: 4GB
  • 790M model: 8GB
  • 1.4B model: 14GB
  • 2.8B model: 28GB (FP16)
• Inference: 5× faster than Transformers
• Memory: No KV cache (lower than Transformers)

Performance (vs Transformers):

• Speed: 5× faster inference
• Memory: 50% less (no KV cache)
• Scaling: Linear vs quadratic

Resources

• Paper (Mamba-1): https://arxiv.org/abs/2312.00752 (Dec 2023)
• Paper (Mamba-2): https://arxiv.org/abs/2405.21060 (May 2024)
• GitHub: https://github.com/state-spaces/mamba ⭐ 13,000+
• Models: https://huggingface.co/state-spaces
• Docs: Repository README and wiki