Project: s41467-024-54375-y | Function: _DenseLayer.forward (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Implements a dense layer with skip connections for the DenseNet-based twin neural network architecture, combining features through concatenation to enable deep metric learning

**KEY TERMS:** {
  "new_features": "learned features from dense block",
  "x": "input features",
  "drop_rate": "dropout rate for regularization",
  "growth_rate": "number of new channels added"
}

**CONTEXT CODE:** import torch
import torch.nn as nn
import torch.nn.functional as F
from collections import OrderedDict

class _DenseLayer(nn.Sequential):
    def __init__(self, num_input_features, growth_rate, bn_size, drop_rate):
        super(_DenseLayer, self).__init__()
        self.add_module('norm1', nn.BatchNorm1d(num_input_features)),
        self.add_module('relu1', nn.ReLU(inplace=True)),
        self.add_module('conv1', nn.Conv1d(num_input_features, bn_size *
                                           growth_rate, kernel_size=1, stride=1,
                                           bias=False)),
        self.add_module('norm2', nn.BatchNorm1d(bn_size * growth_rate)),
        self.add_module('relu2', nn.ReLU(inplace=True)),
        self.add_module('conv2', nn.Conv1d(bn_size * growth_rate, growth_rate,
                                           kernel_size=3, stride=1, padding=1,
                                           bias=False)),
        self.drop_rate = drop_rate

    def forward(self, x):
        """Forward pass through dense layer with skip connections"""
        raise NotImplementedError("Function implementation has been masked")

class _DenseBlock(nn.Sequential):
    def __init__(self, num_layers, num_input_features, bn_size, growth_rate, drop_rate):
        super(_DenseBlock, self).__init__()
        for i in range(num_layers):
            layer = _DenseLayer(num_input_features + i * growth_rate, growth_rate,
                                bn_size, drop_rate)
            self.add_module('denselayer%d' % (i + 1), layer)
            
class _Transition(nn.Sequential):
    def __init__(self, num_input_features, num_output_features):
        super(_Transition, self).__init__()
        self.add_module('norm', nn.BatchNorm1d(num_input_features))
        self.add_module('relu', nn.ReLU(inplace=True))
        self.add_module('conv', nn.Conv1d(num_input_features, num_output_features,
                                          kernel_size=1, stride=2, bias=False, padding = 1))

class Flatten(nn.Module):
    def forward(self, x):
        x = x.view(-1, 635)
        return x

class PrintOutput(nn.Module):
    def forward(self,x):
        print('printing shape',x.shape)
        return x
    
class TwinDN(nn.Module):
    r"""Densenet-BC model class, based on
    `"Densely Connected Convolutional Networks" <https://arxiv.org/pdf/1608.06993.pdf>`_
    Args:
        growth_rate (int) - how many filters to add each layer (`k` in paper)
        block_config (list of 4 ints) - how many layers in each pooling block
        num_init_features (int) - the number of filters to learn in the first convolution layer
        bn_size (int) - multiplicative factor for number of bottle neck layers
          (i.e. bn_size * k features in the bottleneck layer)
        drop_rate (float) - dropout rate after each dense layer
        num_classes (int) - number of classification classes
    """
    block_config=(6,9,12,6)
    
    def __init__(self, growth_rate=32, block_config=block_config, num_input_channels = 1,
                 num_init_features=64, bn_size=4, drop_rate=0):

        super(TwinDN, self).__init__()

        # First convolution
        self.features = nn.Sequential(OrderedDict([
            ('conv0', nn.Conv1d(num_input_channels, num_init_features, kernel_size=3, stride=2,
                                padding=1, bias=False)),
        ]))

        # Each denseblock
        num_features = num_init_features
        for i, num_layers in enumerate(block_config):
            
            block = _DenseBlock(num_layers=num_layers, num_input_features=num_features,
                                bn_size=bn_size, growth_rate=growth_rate,
                                drop_rate=drop_rate)
            self.features.add_module('denseblock%d' % (i + 1), block)
            num_features = num_features + num_layers * growth_rate
            
            if i != len(block_config) - 1:
                trans = _Transition(num_input_features=num_features,
                                    num_output_features=num_features // 2)
                self.features.add_module('transition%d' % (i + 1), trans)
                num_features = num_features // 2
        
        # Final batch norm
        self.features.add_module('norm_preprelast', nn.BatchNorm1d(num_features))
        
        self.features.add_module('relu_preprelast', nn.ReLU(inplace=True))
        # Final conv 
        
        self.features.add_module('conv_prelast', nn.Conv1d(num_features,num_init_features, kernel_size=1, stride=2,
                                padding=1, bias=False))
        self.features.add_module('norm_prelast', nn.BatchNorm1d(num_init_features))
        
        self.features.add_module('relu_prelast', nn.ReLU(inplace=True))
        
        self.features.add_module('conv_last', nn.Conv1d(num_init_features,1, kernel_size=1, stride=1,
                                padding=0, bias=False))
            
        self.features.add_module('flatten',Flatten())
        self.features.add_module('fc2', nn.Linear(635,100))
        self.features.add_module('bc_last', nn.BatchNorm1d(100))
        self.features.add_module('relu_last', nn.ReLU(inplace=True))
        self.features.add_module('fc3', nn.Linear(100,10))
        
        # Official init from torch repo.
        for m in self.modules():
            if isinstance(m, nn.Conv1d):
                nn.init.kaiming_normal_(m.weight)
            elif isinstance(m, nn.BatchNorm1d):
                nn.init.constant_(m.weight, 1)
                nn.init.constant_(m.bias, 0)
            elif isinstance(m, nn.Linear):


Complete the function implementation replacing "raise NotImplementedError".