Write a custom CUDA kernel to optimize `RePU` (Rectified Power Unit).

Formula: f(x) = max(0, x)^s
This is a generalized activation function where 's' is a hyperparameter (power).

Problem Analysis:
1. Memory Bottleneck: The standard PyTorch implementation typically involves `F.relu(x).pow(s)`. This executes two separate kernels (one for ReLU, one for Pow), requiring an intermediate read/write cycle to global memory. Since activation functions are element-wise and computationally light, they are strictly memory-bound.
2. Overhead: Multiple kernel launches add latency.

Optimization Strategy: Fused Element-wise Kernel with Vectorization

1. Fusion: Combine the Rectification (`max(0, x)`) and Power (`pow(x, s)`) operations into a single kernel pass. This reduces global memory traffic by 50% (from 2 reads/2 writes to 1 read/1 write).

2. Vectorized Loads (float4): Process 4 float elements (128 bits) per thread per iteration using `float4` data types. This maximizes memory bandwidth utilization, which is the critical factor for this operator.

3. In-Register Computation:
   - Load `float4` data from global memory.
   - For each component: Apply `val = fmaxf(val, 0.0f)` followed by `val = powf(val, s)`.
   - Store the result back to global memory.

4. Kernel Configuration: Launch a 1D grid sufficient to cover the flattened input tensor.
  
Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:   
  
```python
import torch
import torch.nn as nn
import torch.nn.functional as F

BATCH_SIZE = 4096
HIDDEN_DIM = 8192
SHAPE = (BATCH_SIZE, HIDDEN_DIM)

S_VALUE = 3.0

class RePU(nn.Module):
    """
    Rectified Power Unit
    From Why Rectified Power (RePU) Activation Functions are Efficient in Deep Learning: A Theoretical Explanation
    f(x) = max(0, x)^s
    """
    def __init__(self, s=3.0):
        super(RePU, self).__init__()
        self.s = s

    def forward(self, x: torch.Tensor) -> torch.Tensor:
        return F.relu(x).pow(self.s)

class Model(nn.Module):
    def __init__(self, s=3.0):
        super(Model, self).__init__()
        self.repu = RePU(s)
    
    def forward(self, x):
        return self.repu(x)

def get_inputs():
    input_tensor = torch.randn(SHAPE, dtype=torch.float32)
    return [input_tensor.contiguous()]

def get_init_inputs():
    return [S_VALUE]