Frequently Asked Questions¶
How to update a subset of weights?¶
If you want to update only a subset of a weight matrix (such as some rows or some columns) that are used in the forward propagation of each iteration, then the cost function should be defined in a way that it only depends on the subset of weights that are used in that iteration.
For example if you want to learn a lookup table, e.g. used for word embeddings, where each row is a vector of weights representing the embedding that the model has learned for a word, in each iteration, the only rows that should get updated are those containing embeddings used during the forward propagation. Here is how the aesara function should be written:
Defining a shared variable for the lookup table
lookup_table = aesara.shared(matrix_ndarray)
Getting a subset of the table (some rows or some columns) by passing an integer vector of indices corresponding to those rows or columns.
subset = lookup_table[vector_of_indices]
From now on, use only ‘subset’. Do not call lookup_table[vector_of_indices] again. This causes problems with grad as this will create new variables.
Defining cost which depends only on subset and not the entire lookup_table
cost = something that depends on subset g = aesara.grad(cost, subset)
There are two ways for updating the parameters: Either use inc_subtensor or set_subtensor. It is recommended to use inc_subtensor. Some aesara optimizations do the conversion between the two functions, but not in all cases.
updates = inc_subtensor(subset, g*lr)
updates = set_subtensor(subset, subset + g*lr)
Currently we just cover the case here, not if you use inc_subtensor or set_subtensor with other types of indexing.
Defining the aesara function
f = aesara.function(..., updates=[(lookup_table, updates)])
Note that you can compute the gradient of the cost function w.r.t. the entire lookup_table, and the gradient will have nonzero rows only for the rows that were selected during forward propagation. If you use gradient descent to update the parameters, there are no issues except for unnecessary computation, e.g. you will update the lookup table parameters with many zero gradient rows. However, if you want to use a different optimization method like rmsprop or Hessian-Free optimization, then there will be issues. In rmsprop, you keep an exponentially decaying squared gradient by whose square root you divide the current gradient to rescale the update step component-wise. If the gradient of the lookup table row which corresponds to a rare word is very often zero, the squared gradient history will tend to zero for that row because the history of that row decays towards zero. Using Hessian-Free, you will get many zero rows and columns. Even one of them would make it non-invertible. In general, it would be better to compute the gradient only w.r.t. to those lookup table rows or columns which are actually used during the forward propagation.