Neural Network Trainable Parameter Counter

Understanding the number of trainable parameters in a neural network is crucial for deep learning practitioners. The parameter count directly impacts memory requirements, computational costs, training time, and the model's capacity to learn complex patterns. This metric is essential for model architecture design, deployment optimization, and resource planning.

Given a neural network's architectural specification as a list of layer configurations, your task is to compute the total count of trainable parameters across all layers.

Supported Layer Types:

1. Dense (Fully Connected) Layer

A dense layer connects every input neuron to every output neuron through learnable weights.

Configuration Keys:

• "type": "dense"
• "input_size": Number of input features (integer)
• "output_size": Number of output neurons (integer)
• "use_bias": Whether to include a bias term (boolean)

Parameter Calculation: $$\text{Parameters} = (\text{input_size} \times \text{output_size}) + \begin{cases} \text{output_size} & \text{if use_bias is True} \ 0 & \text{otherwise} \end{cases}$$

The weight matrix has dimensions (input_size × output_size), and the optional bias vector has length output_size.

2. Conv2D (2D Convolutional) Layer

A convolutional layer applies learnable filters across spatial dimensions of the input.

Configuration Keys:

• "type": "conv2d"
• "in_channels": Number of input channels/feature maps (integer)
• "out_channels": Number of filters/output channels (integer)
• "kernel_size": Spatial dimensions of each filter (integer for square kernels, or tuple for non-square)
• "use_bias": Whether to include a bias term per output channel (boolean)

Parameter Calculation: $$\text{Parameters} = (\text{kernel_height} \times \text{kernel_width} \times \text{in_channels} \times \text{out_channels}) + \begin{cases} \text{out_channels} & \text{if use_bias is True} \ 0 & \text{otherwise} \end{cases}$$

Each filter has spatial dimensions (kernel_height × kernel_width) with depth equal to in_channels.

3. Embedding Layer

An embedding layer maps discrete indices to dense vector representations through a learnable lookup table.

Configuration Keys:

• "type": "embedding"
• "num_embeddings": Size of the vocabulary/dictionary (integer)
• "embedding_dim": Dimension of each embedding vector (integer)

Parameter Calculation: $$\text{Parameters} = \text{num_embeddings} \times \text{embedding_dim}$$

The embedding matrix has dimensions (num_embeddings × embedding_dim).

Your Task: Implement a function that iterates through the layer specifications and computes the cumulative parameter count for the entire network architecture.