A neural network that keeps learning as new training data becomes available I have a text-classification problem with a lot of training data. Running cross-validation takes a lot of time - several days or even weeks. In order to make the system more responsive, I am thinking of the following scheme:


Train a network on instances 1,...,100.
Test it on instances 101,...200; output the accuracy.
Train the existing network on instances 101,...200; 
Test it on instances 201,...300; output the accuracy.
And so on.


Ideally, I would like that:


Training on each additional 100 instances will take a constant time (i.e, I will not have to re-train the network on all previous instances);
The trained network will have the combined "wisdom" of all previous instances (so its accuracy will tend to improve with time).


Is this possible to do with standard deep-learning tools (e.g. dynet)?
You can achieve that by training the network using batches of 100 examples. In this case, you train on a batch and update the neural network parameters, you predict on the second batch to estimate the accuracy and then you use the examples of this second batch to continue training the network and so on and so forth.

Batch training (a form of online learning) is implemented on every framework, see for instances here for Keras.