architecture-details

Mamba's core innovation is the Selective SSM (S6) layer that makes state space model parameters input-dependent.

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Content

# Mamba Architecture Details

## Selective State Space Mechanism

Mamba's core innovation is the **Selective SSM (S6)** layer that makes state space model parameters input-dependent.

### How S6 Works

**Traditional SSMs** (non-selective):
```python
# Fixed A, B, C matrices for all inputs
h(t) = A * h(t-1) + B * x(t)  # State update
y(t) = C * h(t)                # Output
```

**Mamba's Selective SSM**:
```python
# Input-dependent parameters
B(t) = Linear_B(x(t))  # Selection mechanism
C(t) = Linear_C(x(t))  # Output projection
Δ(t) = Linear_Δ(x(t))  # Discretization step

# Selective state up

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