Linear Layer

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Specialization of the Layer for Linear Maps. The entries of the previous layer \(\mathbf{z}^{l-1}\in\mathbb{R}^{n_{l-1}}\) are multiplied by a weight matrix \(W\in\mathbb{R}^{n_{l}\times n_{l-1}}\) and a bias \(\mathbf{b}^l\in\mathbb{R}^{n_l}\).

\[\mathbf{z}^l = W^l \mathbf{z}^{l-1}+\mathbf{b}^l\]

If we denote the components of the vectors by \(z_i^{l-1}\) and \(z_j^{l}, b_j^l\) and for the matrix by \(W_{ij}^{l}\) for \(i=1,\dots,n_{l-1}\) and \(j=1,\dots,n_{l}\), this operation can be written as

\[z_j^l = W_{ij}^l z_i^{l-1}+b_j^l\]

Usage

eLayer/Linear"

Configuration

These are settings required by this module.

Output Channels

  • Usage: e[“Output Channels”] = unsigned integer

  • Description: Indicates the size of the output vector produced by the layer.

Weight Scaling

  • Usage: e[“Weight Scaling”] = float

  • Description: Factor that is mutliplied by the layers’ weights.

Engine

  • Usage: e[“Engine”] = string

  • Description: Specifies which Neural Network backend engine to use.

  • Options:

    • “Korali”: Uses Korali’s lightweight NN support. (CPU Sequential - Does not require installing third party software other than Eigen)

    • “OneDNN”: Uses oneDNN as NN support. (CPU Sequential/Parallel - Requires installing oneDNN)

    • “CuDNN”: Uses cuDNN as NN support. (GPU - Requires installing cuDNN)

Mode

  • Usage: e[“Mode”] = string

  • Description: Specifies the execution mode of the Neural Network.

  • Options:

    • “Training”: Use for training. Stores data during forward propagation and allows backward propagation.

    • “Inference”: Use for inference only. Only runs forward propagation. Faster for inference.

Layers

  • Usage: e[“Layers”] = knlohmann::json

  • Description: Complete description of the NN’s layers.

Timestep Count

  • Usage: e[“Timestep Count”] = unsigned integer

  • Description: Provides the sequence length for the input/output data.

Batch Sizes

  • Usage: e[“Batch Sizes”] = List of unsigned integer

  • Description: Specifies the batch sizes.

Default Configuration

These following configuration will be assigned by default. Any settings defined by the user will override the given settings specified in these defaults.

{
"Batch Sizes": [],
"Engine": "Korali",
"Input Values": [],
"Output Channels": 0,
"Uniform Generator": {
    "Maximum": 1.0,
    "Minimum": -1.0,
    "Type": "Univariate/Uniform"
    },
"Weight Scaling": 1.0
}