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.
Related
As the title suggests I'm looking for a way to copy an arbitrary tensorflow (/keras) model, such that I can run the same computational graph from the model, but have the weights (or different weights or a tensor copy of them) as part of the input of the function, something like the following, where an implementation (or idea how to implement) 'smart_copy_function' is what is missing:
model = some_model() #a TF/Keras Model
model_from_weights = smart_copy_function(model)
x = tf.some_model_input # imagine some random input to the model here, e.g. an mnist image
y_model = model(x) #normal way to call model
y_model_from_weights = model_from_weights(model.trainable_weights, x) #same call to copied model
y_model == y_model_from_weights #should be True
I believe this should be doable in a somewhat easy way, as the respective computational graph does exist in TF anyway already.
'This sounds stupid, why would you do this?': I want to build an analog to the PyTorch MetaLearning Framework higher for TensorFlow, since gradients through calls of TF optimizer 'apply_gradients' and variable 'assign' are not supported. To achieve such gradients through parameter gradient updates the above seems to be the way to go. Such gradients through parameter updates are in turn very important for Meta-Learning Research, with papers like 'Model-Agnostic Meta Learning' and 'Teaching with Commentaries' being somewhat famous examples / use cases.
A question that comes from the fact that I never had to debug my models in TF so deeply.
I'm running a variational inference with a full-rank Gaussian approximation using Tensorflow Probability. I noticed my optimization often explodes. Here is my loss curve.
I suspect numerical issues, as all the losses and the optimization process look reasonable and I don't observe any NaNs.
I use tfp.distributions.MultivariateNormalTriL with a covariance parameter transformed by tfp.bijectors.FillScaleTriL with the default diagonal shift. The condition number of the covariance matrix is reasonable. The variational inference is performed with fit_surrogate_posterior function.
I optimize with an SGD with momentum, using 10 samples per iteration.
Internally in Tensorflow Probability source code, the minimization objective uses a gradient tape:
with tf.GradientTape(watch_accessed_variables=trainable_variables is None) as tape:
for v in trainable_variables or []:
tape.watch(v)
loss = loss_fn()
In order to solve my issue I would like to see the gradient through every operation.
My question is how can I get more insight into which operation is exploding by the gradient computation? How to get the value of gradient at every tensor?
And if any of you faced a similar issue:
Is there a better way to prevent instabilities in the covariance matrix optimization?
Detailed explanations:
I observed that this explosion is caused by one parameter (though it is not always the same parameter that explodes). This can be simply checked by comparing the covariance matrix two iterations before the explosion
and one iteration before the point where the loss explodes
Note the last parameter. When I run the same optimization multiple times, it might happen that one of the "small" parameters (rows from 9 to the last) explodes at some point.
Thanks,
Mateusz
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).
This is my third attempt to get a deep learning project off the ground. I'm working with protein sequences. First I tried TFLearn, then raw TensorFlow, and now I'm trying Keras.
The previous two attempts taught me a lot, and gave me some code and concepts that I can re-use. However there has always been an obstacle, and I've asked questions that the developers can't answer (in the case of TFLearn), or I've simply gotten bogged down (TensorFlow object introspection is tedious).
I have written this TensorFlow loss function, and I know it works:
def l2_angle_distance(pred, tgt):
with tf.name_scope("L2AngleDistance"):
# Scaling factor
count = tgt[...,0,0]
scale = tf.to_float(tf.count_nonzero(tf.is_finite(count)))
# Mask NaN in tgt
tgt = tf.where(tf.is_nan(tgt), pred, tgt)
# Calculate L1 losses
losses = tf.losses.cosine_distance(pred, tgt, -1, reduction=tf.losses.Reduction.NONE)
# Square the losses, then sum, to get L2 scalar loss.
# Divide the loss result by the scaling factor.
return tf.reduce_sum(losses * losses) / scale
My target values (tgt) can include NaN, because my protein sequences are passed in a 4D Tensor, despite the fact that the individual sequences differ in length. Before you ask, the data can't be resampled like an image. So I use NaN in the tgt Tensor to indicate "no prediction needed here." Before I calculate the L2 cosine loss, I replace every NaN with the matching values in the prediction (pred) so the loss for every NaN is always zero.
Now, how can I re-use this function in Keras? It appears that the Keras Lambda core layer is not a good choice, because a Lambda only takes a single argument, and a loss function needs two arguments.
Alternately, can I rewrite this function in Keras? I shouldn't ever need to use the Theano or CNTK backend, so it isn't necessary for me to rewrite my function in Keras. I'll use whatever works.
I just looked at the Keras losses.py file to get some clues. I imported keras.backend and had a look around. I also found https://keras.io/backend/. I don't seem to find wrappers for ANY of the TensorFlow function calls I happen to use: to_float(), count_nonzero(), is_finite(), where(), is_nan(), cosine_distance(), or reduce_sum().
Thanks for your suggestions!
I answered my own question. I'm posting the solution for anyone who may come across this same problem.
I tried using my TF loss function directly in Keras, as was independently suggested by Matias Valdenegro. I did not provoke any errors from Keras by doing so, however, the loss value went immediately to NaN.
Eventually I identified the problem. The calling convention for a Keras loss function is first y_true (which I called tgt), then y_pred (my pred). But the calling convention for a TensorFlow loss function is pred first, then tgt. So if you want to keep a Tensorflow-native version of the loss function around, this fix works:
def keras_l2_angle_distance(tgt, pred):
return l2_angle_distance(pred, tgt)
<snip>
model.compile(loss = keras_l2_angle_distance, optimizer = "something")
Maybe Theano or CNTK uses the same parameter order as Keras, I don't know. But I'm back in business.
You don't need to use keras.backend, as your loss is directly written in TensorFlow, then you can use it directly in Keras. The backend functions are an abstraction layer so you can code a loss/layer that will work with the multiple available backends in Keras.
You just have to put your loss in the model.compile call:
model.compile(loss = l2_angle_distance, optimizer = "something")
I have been using tensorflow to train deep NN acoustic models for speech recognition for a while. The loss function I use is Cross Entropy and the NN models performe very well. Now I want to change the loss function to a more complex one named MMI (Maximum Mutual Information) which is also a classical criterion used in speech recognition domain. I put one paper here which describes this loss function in case that you have interests.
When using this special loss function, the derivatives of the loss function w.r.t. the activations of output layer can be computed by some special algorithms defined in Hidden Markov Model scenario. It means that I can compute the derivatives of the loss function w.r.t. the activations of output layer by myself rather than just write out the loss function and leave Tensorflow to calculate the derivatives automatically.
But based on my poor experiences, I don't know how to backprob the derivatives which I calculate by myself. Is there any way to do this without touching Tensorflow C++ source code?
Probably yes if all the computation involved use existing tensorflow functions.
You just have to set up the chain of operations that compute the gradients from the current variables.
Then you just use tf.assign_add() to the variables with your gradients multiplied by minus the learning rate.
You are thus mimicking what happens in the background in TF usually.
EDIT: If calculations are made in numpy for instance for the gradients you can use.
#perform numpy calculations
a=f(output_npy,variables_npy)
grad_from_user=tf.placeholder(tf.float32, a.shape)
grad_update=tf.assign_add(variables_tf,-lr*grad_from_user)
#and then
sess.run(grad_update,feed_dict={grad_from_user:a,...})