I want to use gradient descent with momentum (keep track of previous gradients) while building a classifier in TensorFlow.
So I don't want to use tensorflow.train.GradientDescentOptimizer but I want to use tensorflow.gradients to calculate gradients and keep track of previous gradients and update the weights based on all of them.
How do I do this in TensorFlow?
TensorFlow has an implementation of gradient descent with momentum.
To answer your general question about implementing your own optimization algorithm, TensorFlow gives you the primitives to calculate the gradients, and update variables using the calculated gradients. In your model, suppose loss designates the loss function, and var_list is a python list of TensorFlow variables in your model (which you can get by calling tf.all_variables or tf.trainable_variables, then you can calculate the gradients w.r.t your variables as follows :
grads = tf.gradients(loss, var_list)
For the simple gradient descent, you would simply subtract the product of the gradient and the learning rate from the variable. The code for that would look as follows :
var_updates = []
for grad, var in zip(grads, var_list):
var_updates.append(var.assign_sub(learning_rate * grad))
train_op = tf.group(*var_updates)
You can train your model by calling sess.run(train_op). Now, you can do all sorts of things before actually updating your variables. For instance, you can keep track of the gradients in a different set of variables and use it for the momentum algorithm. Or, you can clip your gradients before updating the variables. All these are simple TensorFlow operations because the gradient tensors are no different from other tensors that you compute in TensorFlow. Please look at the implementations (Momentum, RMSProp, Adam) of some the fancier optimization algorithms to understand how you can implement your own.
Related
I recently was reading a Pytorch code and came across loss.backward() and optimizer.step() functions, are there any equivalent of these using tensorflow/keras?
loss.backward() equivalent in tensorflow is tf.GradientTape(). TensorFlow provides the tf.GradientTape API for automatic differentiation - computing the gradient of computation with respect to its input variables. Tensorflow "records" all operations executed inside the context of a tf.GradientTape onto a "tape". Tensorflow then uses that tape and the gradients associated with each recorded operation to compute the gradients of a "recorded" computation using reverse mode differentiation.
optimizer.step() equivalent in tensorflow is minimize(). Minimizes the loss by updating the variable list. Calling minimize() takes care of both computing the gradients and applying them to the variables.
If you want to process the gradients before applying them you can instead use the optimizer in three steps:
Compute the gradients with tf.GradientTape.
Process the gradients as you wish.
Apply the processed gradients with apply_gradients().
Hope this answers your question. Happy Learning.
I have a Tensorflow 2.0 tf.keras.Sequential model. Now, my technical specification prescribes using the Levenberg-Marquardt optimizer to fit the model. Tensorflow 2.0 doesn't provide it as an optimizer out of the box, but it is available in the Tensorflow Graphics module.
tfg.math.optimizer.levenberg_marquardt.minimize function accepts residuals ( a residual is a Python callable returning a tensor) and variables (list of tensors corresponding to my model weights) as parameters.
What would be the best way to convert my model into residuals and variables?
If I understand correctly how the minimize function works, I have to provide two residuals. The first residual must call my model for every learning case and aggregate all the results into a tensor. The second residuals must return all labels as a single constant tensor. The problem is that tf.keras.Sequential.predict function returns a numpy array instead of tensor. I believe that if I convert it to a tensor, the minimizer won't be able to calculate jacobians with respect to variables.
The same problem is with variables. It doesn't seem like there's a way to extract all weights from a model into a list of tensors.
There's a major difference between tfg.math.optimizer.levenberg_marquardt.minimize and Keras optimizers from the implementation/API perspective.
Keras optimizers, such as tf.keras.optimizers.Adam consume gradients as input and updates tf.Variables.
In contrast, tfg.math.optimizer.levenberg_marquardt.minimize essentially unrolls the optimization loop in graph mode (using a tf.while_loop construct). It takes initial parameter values and produces updated parameter values, unlike Adam & co, which only apply one iteration and actually change the values of tf.Variables via assign_add.
Stepping back a bit to the theoretical big picture, Levenberg-Marquardt is not a general gradient descent-like solver for any nonlinear optimization problem (such as Adam is). It specifically addresses nonlinear least-squares optimization, so it's not a drop-in replacement for optimizers like Adam. In gradient descent, we compute the gradient of the loss with respect to the parameters. In Levenberg-Marquardt, we compute the Jacobian of the residuals with respect to the parameters. Concretely, it repeatedly solves the linearized problem Jacobian # delta_params = residuals for delta_params using tf.linalg.lstsq (which internally uses Cholesky decomposition on the Gram matrix computed from the Jacobian) and applies delta_params as the update.
Note that this lstsq operation has cubic complexity in the number of parameters, so in case of neural nets it can only be applied for fairly small ones.
Also note that Levenberg-Marquardt is usually applied as a batch algorithm, not a minibatch algorithm like SGD, though there's nothing stopping you from applying the LM iteration on different minibatches in each iteration.
I think you may only be able to get one iteration out of tfg's LM algorithm, through something like
from tensorflow_graphics.math.optimizer.levenberg_marquardt import minimize as lm_minimize
for input_batch, target_batch in dataset:
def residual_fn(trainable_params):
# do not use trainable params, it will still be at its initial value, since we only do one iteration of Levenberg Marquardt each time.
return model(input_batch) - target_batch
new_objective_value, new_params = lm_minimize(residual_fn, model.trainable_variables, max_iter=1)
for var, new_param in zip(model.trainable_variables, new_params):
var.assign(new_param)
In contrast, I believe the following naive method will not work where we assign model parameters before computing the residuals:
from tensorflow_graphics.math.optimizer.levenberg_marquardt import minimize as lm_minimize
dataset_iterator = ...
def residual_fn(params):
input_batch, target_batch = next(dataset_iterator)
for var, param in zip(model.trainable_variables, params):
var.assign(param)
return model(input_batch) - target_batch
final_objective, final_params = lm_minimize(residual_fn, model.trainable_variables, max_iter=10000)
for var, final_param in zip(model.trainable_variables, final_params):
var.assign(final_param)
The main conceptual problem is that residual_fn's output has no gradients wrt its input params, since this dependency goes through a tf.assign. But it might even fail before that due to using constructs that are disallowed in graph mode.
Overall I believe it's best to write your own LM optimizer that works on tf.Variables, since tfg.math.optimizer.levenberg_marquardt.minimize has a very different API that is not really suited for optimizing Keras model parameters since you can't directly compute model(input, parameters) - target_value without a tf.assign.
I watched the Tensorflow Developer's summit video on Eager Execution in Tensorflow, and the presenter gave an introduction to "Gradient Tape." Now I understand that Gradient Tape tracks the automatic differentiation that occurs in a TF model.
I was trying to understand why I would use Gradient Tape? Can anyone explain how Gradient Tape is used as a diagnostic tool? Why would someone use Gradient Tape versus just Tensorboard visualization of weights.
So I get that the automatic differentiation that occurs with a model is to compute the gradients of each node--meaning the adjustment of the weights and biases at each node, given some batch of data. So that is the learning process. But I was under the impression that I can actually use a tf.keras.callback.TensorBoard() call to see the tensorboard visualization of training--so I can watch the weights on each node and determine if there are any dead or oversaturated nodes.
Is the use of Gradient Tape only to see if some gradients go to zero or get really big, etc? Or is there some other use of the Gradient Tape?
With eager execution enabled, Tensorflow will calculate the values of tensors as they occur in your code. This means that it won't precompute a static graph for which inputs are fed in through placeholders. This means to back propagate errors, you have to keep track of the gradients of your computation and then apply these gradients to an optimiser.
This is very different from running without eager execution, where you would build a graph and then simply use sess.run to evaluate your loss and then pass this into an optimiser directly.
Fundamentally, because tensors are evaluated immediately, you don't have a graph to calculate gradients and so you need a gradient tape. It is not so much that it is just used for visualisation, but more that you cannot implement a gradient descent in eager mode without it.
Obviously, Tensorflow could just keep track of every gradient for every computation on every tf.Variable. However, that could be a huge performance bottleneck. They expose a gradient tape so that you can control what areas of your code need the gradient information. Note that in non-eager mode, this will be statically determined based on the computational branches that are descendants of your loss but in eager mode there is no static graph and so no way of knowing.
Having worked on this for a while, after posting the initial question, I have a better sense of where Gradient Tape is useful. Seems like the most useful application of Gradient Tap is when you design a custom layer in your keras model for example--or equivalently designing a custom training loop for your model.
If you have a custom layer, you can define exactly how the operations occur within that layer, including the gradients that are computed and also calculating the amount of loss that is accumulated.
So Gradient tape will just give you direct access to the individual gradients that are in the layer.
Here is an example from Aurelien Geron's 2nd edition book on Tensorflow.
Say you have a function you want as your activation.
def f(w1, w2):
return 3 * w1 ** 2 + 2 * w1 * w2
Now if you want to take derivatives of this function with respec to w1 and w2:
w1, w2 = tf.Variable(5.), tf.Variable(3.)
with tf.GradientTape() as tape:
z = f(w1, w2)
gradients = tape.gradient(z, [w1, w2])
So the optimizer will calculate the gradient and give you access to those values. Then you can double them, square them, triple them, etc., whatever you like. Whatever you choose to do, then you can add those adjusted gradients to the loss calculation for the backpropagation step, etc.
I think the most important thing to say in answer to this question is simply that GradientTape is not a diagnostic tool. That's the misconception here.
GradientTape is a mathematical tool for automatic differentiation (autodiff), which is the core functionality of TensorFlow. It does not "track" the autodiff, it is a key part of performing the autodiff.
As the other answers describe, it is used to record ("tape") a sequence of operations performed upon some input and producing some output, so that the output can be differentiated with respect to the input (via backpropagation / reverse-mode autodiff) (in order to then perform gradient descent optimisation).
when I try to fine-tune a VGG network, I only want to update the weights after 5th convolution layers ,in caffe , we can cancel BP in configure file. What should I do in tensorflow ? thanks !
Just use tf.stop_gradient() on the input of your 5th layer. Tensorflow will not backpropagate the error below. tf.stop_gradient() is an operation that acts as the identity function in the forward direction, but stops the gradient in the backward direction.
From documentation:
tf.stop_gradient
Stops gradient computation.
When executed in a graph, this op outputs its input tensor as-is.
When building ops to compute gradients, this op prevents the
contribution of its inputs to be taken into account. Normally, the
gradient generator adds ops to a graph to compute the derivatives of a
specified 'loss' by recursively finding out inputs that contributed to
its computation. If you insert this op in the graph it inputs are
masked from the gradient generator. They are not taken into account
for computing gradients.
Otherwise you can use optimizer.minimize(loss, variables_of_fifth_layer). Here you are running backpropagation and updating only on the variables of your 5th layer.
For a fast selection of the variables of interest you could:
Define as trainable=False all the variables that you don't want to update, and use variables_of_fifth_layer=tf.trainable_variables().
Divide layers by defining specific scopes and then variables_of_fifth_layer = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,"scope/of/fifth/layer")
The tensorflow documentation states that:
Calling minimize() takes care of both computing the gradients and
applying them to the variables. If you want to process the gradients
before applying them you can instead use the optimizer in three steps:
Compute the gradients with compute_gradients(). Process the gradients
as you wish. Apply the processed gradients with apply_gradients().
However the example given is for vanilla SGD.
Does this two step process work for other types of optimizers (like momentum, adam etc), which don't use the gradients directly but instead use other derived descent directions ?
If so, where do the various intermediate variables and the final descent direction get computed - in compute_gradients or apply_gradients ?
Thanks.