As this is an autoencoder, the first step is to build the encoding portion, which will look something like this:

First, we have our two fully connected layers:

w0 := gorgonia.NewMatrix(g, dt, gorgonia.WithShape(784, 256), gorgonia.WithName("w0"), gorgonia.WithInit(gorgonia.GlorotU(1.0)))

w1 := gorgonia.NewMatrix(g, dt, gorgonia.WithShape(256, 128), gorgonia.WithName("w1"), gorgonia.WithInit(gorgonia.GlorotU(1.0)))

We give each layer a ReLU activation:

// Set first layer to be copy of input
l0 = x
log.Printf("l0 shape %v", l0.Shape())

// Encoding - Part 1
if c1, err = gorgonia.Mul(l0, m.w0); err != nil {
   return errors.Wrap(err, "Layer 1 Convolution failed")
}
if l1, err = gorgonia.Rectify(c1); err != nil {
    return errors.Wrap(err, "Layer 1 activation failed")
}
log.Printf("l1 shape %v", l1.Shape())

if c2, err = gorgonia.Mul(l1, m.w1); err != nil {
    return errors.Wrap(err, "Layer 1 Convolution failed")
}
if l2, err = gorgonia.Rectify(c2); err != nil {
    return errors.Wrap(err, "Layer 1 activation failed")
}
log.Printf("l2 shape %v", l2.Shape())

Then, we connect these to our mean and standard deviation layers:

estMean := gorgonia.NewMatrix(g, dt, gorgonia.WithShape(128, 8), gorgonia.WithName("estMean"), gorgonia.WithInit(gorgonia.GlorotU(1.0)))

estSd := gorgonia.NewMatrix(g, dt, gorgonia.WithShape(128, 8), gorgonia.WithName("estSd"), gorgonia.WithInit(gorgonia.GlorotU(1.0)))

These layers are used as they are, so they do not require a specific activation function:

if l3, err = gorgonia.Mul(l2, m.estMean); err != nil {
    return errors.Wrap(err, "Layer 3 Multiplication failed")
}
log.Printf("l3 shape %v", l3.Shape())

if l4, err = gorgonia.HadamardProd(m.floatHalf, gorgonia.Must(gorgonia.Mul(l2, m.estSd))); err != nil {
    return errors.Wrap(err, "Layer 4 Multiplication failed")
}
log.Printf("l4 shape %v", l4.Shape())