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Interactive 3D/Mamba vs Transformer - Complexity and Memory Comparison
FLOPs vs Sequence Length (dim=1024, hw=A100)
1281.024k16.384k131.072kFLOPsAttention O(n²)Mamba O(n)
Attention scales quadratically with sequence length - Mamba's selective scan is linear. Crossover point ~1,024 tokens.
Transformer
Attention FLOPs
O(n²·d)
68.7G
KV Cache memory
2·n·d·layers
0.02GB
Complexity
per layer
O(n²)
Inference memory
bottleneck
Grows with n
Mamba (SSM)
Scan FLOPs
O(n·d)
16.8M
Hidden state
constant in n
0.00GB
Complexity
per layer
O(n)
Inference memory
fixed state size
O(1)
FLOP Ratio at seq=4,096
Mamba speedup
4096×
fewer FLOPs
KV Cache @seqlen
0.02GB
vs fixed 0.00GB
Controls
Sequence Length
Tokens4,096
128128k
Model Dim
Hardware
Mamba advantage: O(1) inference memory (fixed hidden state) vs Transformer's O(n) KV cache. At long sequences, Mamba becomes dramatically faster and cheaper.

Mamba vs Transformer - Complexity and Memory Comparison - Interactive Visualization

Transformer attention scales as O(n²) in FLOPs and O(n) in KV cache memory - both grow with sequence length. Mamba's selective scan is O(n) in FLOPs and O(1) in memory (fixed-size hidden state). At short sequences, transformers win due to better parallelism. At long sequences (beyond ~4k tokens), Mamba becomes dramatically faster and cheaper. The crossover point depends on model dimension and hardware memory bandwidth.

  • Attention FLOPs: 4·n²·d per layer - quadratic in sequence length n
  • Mamba scan FLOPs: 4·n·d per layer - linear in sequence length n
  • KV cache grows with n at inference: 2·n·d·layers bytes - hits memory wall at long contexts
  • Mamba inference memory: fixed O(d²) hidden state regardless of sequence length
  • At 32k tokens, Mamba is ~32x fewer FLOPs than attention for same model dimension

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