mamba ssm代码

### Mamba SSM Framework Code Example The `Mamba` model, as referenced within the Hugging Face Transformers library[^1], is primarily designed for causal language modeling tasks. However, when discussing state-space models (SSMs), these are typically used in time-series analysis and control systems rather than directly tied to transformer architectures like Mamba. Below is an example of how one might implement a basic State-Space Model (SSM) framework using PyTorch. This implementation does not specifically relate to the Mamba architecture but demonstrates general principles that could be adapted or integrated into more complex frameworks: #### Basic Implementation of an SSM Framework ```python import torch import torch.nn as nn class SSMLayer(nn.Module): def __init__(self, input_dim, hidden_dim, output_dim): super(SSMLayer, self).__init__() self.input_dim = input_dim self.hidden_dim = hidden_dim self.output_dim = output_dim # Transition matrix A self.A = nn.Parameter(torch.randn(hidden_dim, hidden_dim)) # Input-to-state matrix B self.B = nn.Parameter(torch.randn(hidden_dim, input_dim)) # Output matrix C self.C = nn.Parameter(torch.randn(output_dim, hidden_dim)) def forward(self, x, h_prev=None): batch_size, seq_len, _ = x.size() if h_prev is None: h_prev = torch.zeros(batch_size, self.hidden_dim).to(x.device) outputs = [] h_t = h_prev for t in range(seq_len): u_t = x[:, t, :] # Current input at time step t # Update hidden state based on transition dynamics h_t = torch.matmul(h_t, self.A) + torch.matmul(u_t, self.B.T) # Compute output from current hidden state y_t = torch.matmul(h_t, self.C.T) outputs.append(y_t.unsqueeze(1)) # Append with sequence dimension return torch.cat(outputs, dim=1), h_t # Example usage if __name__ == "__main__": input_dim = 5 hidden_dim = 10 output_dim = 3 ss_model = SSMLayer(input_dim=input_dim, hidden_dim=hidden_dim, output_dim=output_dim) # Generate random data batch_size = 8 seq_length = 20 inputs = torch.rand((batch_size, seq_length, input_dim)) # Forward pass through the SSM layer outputs, final_hidden_state = ss_model(inputs) print(f"Outputs shape: {outputs.shape}") # Expected: [batch_size, seq_length, output_dim] print(f"Final Hidden State shape: {final_hidden_state.shape}") # Expected: [batch_size, hidden_dim] ``` This code defines a simple State-Space Model (SSM) where matrices \(A\), \(B\), and \(C\) represent the system's internal transitions, external influences, and observation mappings respectively. The provided script initializes parameters randomly; however, they would generally need training via optimization techniques such as gradient descent depending upon specific application requirements.