How to interpret increase in both loss and accuracy

I think the top-rated answer is incorrect.

I will assume you are talking about cross-entropy loss, which can be thought of as a measure of 'surprise'.

Loss and accuracy increasing/decreasing simultaneously on the training data tells you nothing about whether your model is overfitting. This can only be determined by comparing loss/accuracy on the validation vs. training data.

If loss and accuracy are both decreasing, it means your model is becoming more confident on its correct predictions, or less confident on its incorrect predictions, or both, hence decreased loss. However, it is also making more incorrect predictions overall, hence the drop in accuracy. Vice versa if both are increasing. That is all we can say.

The loss decreases as the training process goes on, except for some fluctuation introduced by the mini-batch gradient descent and/or regularization techniques like dropout (that introduces random noise).

If the loss decreases, the training process is going well.

The (validation I suppose) accuracy, instead, it's a measure of how good the predictions of your model are.

If the model is learning, the accuracy increases. If the model is overfitting, instead, the accuracy stops to increase and can even start to decrease.

If the loss decreases and the accuracy decreases, your model is overfitting.

If the loss increases and the accuracy increase too is because your regularization techniques are working well and you're fighting the overfitting problem. This is true only if the loss, then, starts to decrease whilst the accuracy continues to increase. Otherwise, if the loss keep growing your model is diverging and you should look for the cause (usually you're using a too high learning rate value).

I'd like to add a possible option here for all those who struggle with a model training right now.

If your validation data is a bit dirty, you might experience that in the beginning of the training the validation loss is low as well as the accuracy, and the more you train your network, the accuracy increases with the loss side by side. The reason why it happens, because it finds the possible outliers of your dirty data and gets a super high loss there. Therefore, your accuracy will grow as it guesses more data right, but the loss grows with it.