What is Train loss, Valid loss, and Train/Val mean in NNs

Question

I'm currently learning about Convolutional Neural Networks by studying examples like the MNIST examples. During the training of a neural network, I often see output like:

 Epoch  |  Train loss  |  Valid loss  |  Train / Val
--------|--------------|--------------|---------------
    50  |    0.004756  |    0.007043  |     0.675330
   100  |    0.004440  |    0.005321  |     0.834432
   250  |    0.003974  |    0.003928  |     1.011598
   500  |    0.002574  |    0.002347  |     1.096366
  1000  |    0.001861  |    0.001613  |     1.153796
  1500  |    0.001558  |    0.001372  |     1.135849
  2000  |    0.001409  |    0.001230  |     1.144821
  2500  |    0.001295  |    0.001146  |     1.130188
  3000  |    0.001195  |    0.001087  |     1.099271

Besides the epochs, can someone give me an explanation on what exactly each column represents and what the values mean? I see a lot of tutorials on basic cnn's, but I haven't run into one that explains this in detail.

Solution

It appears that a held-out set of data is being used, in addition to that used to train the network. Training loss is the error on the training set of data. Validation loss is the error after running the validation set of data through the trained network. Train/valid is the ratio between the two.

Unexpectedly, as the epochs increase both validation and training error drop. At a certain point though, while the training error continues to drop (the network learns the data better and better) the validation error begins to rise -- this is overfitting!