What is `weight_decay` meta parameter in Caffe?

The weight_decay meta parameter govern the regularization term of the neural net.

During training a regularization term is added to the network's loss to compute the backprop gradient. The weight_decay value determines how dominant this regularization term will be in the gradient computation.

As a rule of thumb, the more training examples you have, the weaker this term should be. The more parameters you have (i.e., deeper net, larger filters, larger InnerProduct layers etc.) the higher this term should be.

Caffe also allows you to choose between L2 regularization (default) and L1 regularization, by setting

regularization_type: "L1"

However, since in most cases weights are small numbers (i.e., -1<w<1), the L2 norm of the weights is significantly smaller than their L1 norm. Thus, if you choose to use regularization_type: "L1" you might need to tune weight_decay to a significantly smaller value.

While learning rate may (and usually does) change during training, the regularization weight is fixed throughout.

Weight decay is a regularization term that penalizes big weights. When the weight decay coefficient is big the penalty for big weights is also big, when it is small weights can freely grow.

Look at this answer (not specific to caffe) for a better explanation: Difference between neural net "weight decay" and "learning rate".