Matrix Multiplication with Swish Activation

Perform matrix multiplication followed by Swish activation and scaling:

$$\text{output} = \text{scaling\_factor} \cdot (\text{input} \cdot \text{weight}^T + \text{bias}) \cdot \sigma((\text{input} \cdot \text{weight}^T + \text{bias}))$$

where $\sigma(x)$ is the sigmoid function:

$$\sigma(x) = \frac{1}{1 + e^{-x}}$$

The operation consists of three main steps:

1. Linear transformation: $z = \text{input} \cdot \text{weight}^T + \text{bias}$
2. Swish activation: $\text{swish}(z) = z \cdot \sigma(z)$
3. Scaling: $\text{output} = \text{scaling\_factor} \cdot \text{swish}(z)$

Input:

• Matrix input_matrix of size $\text{batch\_size} \times \text{in\_features}$
• Matrix weight_matrix of size $\text{out\_features} \times \text{in\_features}$
• Vector bias of size $\text{out\_features}$
• Scalar scaling_factor for final scaling

Output:

• Matrix output of size $\text{batch\_size} \times \text{out\_features}$

Notes:

• All matrices are stored in row-major order
• This problem is adapted from KernelBench