I've been running into an issue lately trying to train a simple MLP.
I'm basically trying to get a network to map the XYZ position and RPY orientation of the end-effector of a robot arm (6-dimensional input) to the angle of every joint of the robot arm to reach that position (6-dimensional output), so this is a regression problem.
I've generated a dataset using the angles to compute the current position, and generated datasets with 5k, 500k and 500M sets of values.
My issue is the MLP I'm using doesn't learn anything at all. Using Tensorboard (I'm using Keras), I've realized that the output of my very first layer is always zero (see image 1), no matter what I try.
Basically, my input is a shape (6,) vector and the output is also a shape (6,) vector.
Here is what I've tried so far, without success:
I've tried MLPs with 2 layers of size 12, 24; 2 layers of size 48, 48; 4 layers of size 12, 24, 24, 48.
Adam, SGD, RMSprop optimizers
Learning rates ranging from 0.15 to 0.001, with and without decay
Both Mean Squared Error (MSE) and Mean Absolute Error (MAE) as the loss function
Normalizing the input data, and not normalizing it (the first 3 values are between -3 and +3, the last 3 are between -pi and pi)
Batch sizes of 1, 10, 32
Tested the MLP of all 3 datasets of 5k values, 500k values and 5M values.
Tested with number of epoches ranging from 10 to 1000
Tested multiple initializers for the bias and kernel.
Tested both the Sequential model and the Keras functional API (to make sure the issue wasn't how I called the model)
All 3 of sigmoid, relu and tanh activation functions for the hidden layers (the last layer is a linear activation because its a regression)
Additionally, I've tried the very same MLP architecture on the basic Boston housing price regression dataset by Keras, and the net was definitely learning something, which leads me to believe that there may be some kind of issue with my data. However, I'm at a complete loss as to what it may be as the system in its current state does not learn anything at all, the loss function just stalls starting on the 1st epoch.
Any help or lead would be appreciated, and I will gladly provide code or data if needed!
Thank you
EDIT:
Here's a link to 5k samples of the data I'm using. Columns B-G are the output (angles used to generate the position/orientation) and columns H-M are the input (XYZ position and RPY orientation). https://drive.google.com/file/d/18tQJBQg95ISpxF9T3v156JAWRBJYzeiG/view
Also, here's a snippet of the code I'm using:
df = pd.read_csv('kinova_jaco_data_5k.csv', names = ['state0',
'state1',
'state2',
'state3',
'state4',
'state5',
'pose0',
'pose1',
'pose2',
'pose3',
'pose4',
'pose5'])
states = np.asarray(
[df.state0.to_numpy(), df.state1.to_numpy(), df.state2.to_numpy(), df.state3.to_numpy(), df.state4.to_numpy(),
df.state5.to_numpy()]).transpose()
poses = np.asarray(
[df.pose0.to_numpy(), df.pose1.to_numpy(), df.pose2.to_numpy(), df.pose3.to_numpy(), df.pose4.to_numpy(),
df.pose5.to_numpy()]).transpose()
x_train_temp, x_test, y_train_temp, y_test = train_test_split(poses, states, test_size=0.2)
x_train, x_val, y_train, y_val = train_test_split(x_train_temp, y_train_temp, test_size=0.2)
mean = x_train.mean(axis=0)
x_train -= mean
std = x_train.std(axis=0)
x_train /= std
x_test -= mean
x_test /= std
x_val -= mean
x_val /= std
n_epochs = 100
n_hidden_layers=2
n_units=[48, 48]
inputs = Input(shape=(6,), dtype= 'float32', name = 'input')
x = Dense(units=n_units[0], activation=relu, name='dense1')(inputs)
for i in range(1, n_hidden_layers):
x = Dense(units=n_units[i], activation=activation, name='dense'+str(i+1))(x)
out = Dense(units=6, activation='linear', name='output_layer')(x)
model = Model(inputs=inputs, outputs=out)
optimizer = SGD(lr=0.1, momentum=0.4)
model.compile(optimizer=optimizer, loss='mse', metrics=['mse', 'mae'])
history = model.fit(x_train,
y_train,
epochs=n_epochs,
verbose=1,
validation_data=(x_test, y_test),
batch_size=32)
Edit 2
I've tested the architecture with a random dataset where the input was a (6,) vector where input[i] is a random number and the output was a (6,) vector with output[i] = input[i]² and the network didn't learn anything. I've also tested a random dataset where the input was a random number and the output was a linear function of the input, and the loss converged to 0 pretty quickly. In short, it seems the simple architecture is unable to map a non-linear function.
the output of my very first layer is always zero.
This typically means that the network does not "see" any pattern in the input at all, which causes it to always predict the mean of the target over the entire training set, regardless of input. Your output is in the range of -𝜋 to 𝜋 probably with an expected value of 0, so it checks out.
My guess is that the model is too small to represent the data efficiently. I would suggest that you increase the number of parameters in the model by a factor of 10 or 100 and see if it starts seeing something. Limiting the number of parameters has a regularizing effect on the network, and strong regularization usually leads the the aforementioned derping to the mean.
I'm by no means a robotics expert, but I guess that there are a lot of situations where a small nudge in the output parameters causes a large change of the input. Let's say I'm trying to scratch my back with my left hand - the farther my hand goes to the left, the harder the task becomes, so at some point I might want to switch hands, which is a discontinuous configuration change. A bad analogy, sure, but I hope it demonstrates my hunch that there are certain places in the configuration space where small target changes cause large configuration changes.
Such large changes will cause a very large, very noisy gradient around those points. I'm not sure how well the network will work around these noisy gradients, but I would suggest as an experiment that you try to limit the training dataset to a set of outputs that are connected smoothly to one another in the configuration space of the arm, if that makes sense. Going further, you should remove any points from the dataset that are close to such configuration boundaries. To make up for that at inference time, you might instead want to sample several close-by points and choose the most common prediction as the final result. Hopefully some of those points will land in a smooth configuration area.
Also, adding batch normalization before each dense layer will help smooth the gradient and provide for more reliable training.
As for the rest of your hyperparameters:
A batch size of 32 is good, a very small batch size will make the gradient too noisy
The loss function is not critical, both MSE and MAE should work
The activation functions aren't critical, ReLU is a good default choice.
The default initializers a good enough.
Normalizing is important for Dense layers, so keep it
Train for as many epochs as you need as long as both the training and validation loss are dropping. If the validation loss hasn't dropped for 5-10 epochs you might as well stop early.
Adam is a good default choice. Start with a small learning rate and increase the learning rate at the beginning of training only if the training loss is dropping consistently over several epochs.
Further reading: 37 Reasons why your Neural Network is not working
I ended up replacing the first dense layer with a Conv1D layer and the network now seems to be learning decently. It's overfitting to my data, but that's territory I'm okay with.
I'm closing the thread for now, I'll spend some time playing with the architecture.
TL;DR: you can just skip to the question in yellow box below.
Suppose I have a Encoder-Decoder Neural Network, with weights W_1 and W_2 of the encoder and decoder respectively. Let's denote Z as the output of the encoder. The network is trained with batch size n, and all the gradients will be calculated with respect to the mean loss value over the batch (as shown in image below, the L_hat which is the sum of per-sample loss L).
What I'm trying to achieve is, in the backward pass, to manipulate the gradients of Z before passing it further to the encoder's weights W_1. Suppose is a somehow modified gradients operator, for which the following holds:
The described above, in case of a synchronuous pass (first calculate the modified gradients of Z, then propagate down to W_1) is very easy to implement (the Jacobian multiplication is done using grad_ys of tf.gradients):
def modify_grad(grad_z):
# do some modifications
grad_z = tf.gradients(L_hat, Z)
mod_grad_z = modify_grad(grad_z)
mod_grad_w1 = tf.gradients(Z, W_1, mod_grad_z)
The problem is, I need to accumulate the gradients grad_z of the tensor Z over several batches. As the shape of it is dynamic (with None in one of the dimensions, as in the illustration above), I cannot define a tf.Variable to store it. Furthermore, the batch size n may change during training. How can I store the average of grad_z over several batches?
PS: I just wanted to combine pareto-optimal training of ArXiv:1810.04650, the asynchronous network training of ArXiv:1609.02132, and batch size scheduling of ArXiv:1711.00489.
Recently, I'm working on a project "predicting future trajectories of objects from their past trajectories by using LSTMs in Tensorflow."
(Here, a trajectory means a sequence of 2D positions.)
Input to the LSTM is, of course, 'past trajectories' and output is 'future trajectories'.
The size of mini-batch is fixed when training. However, the number of past trajectories in a mini-batch can be different. For example, let the mini-batch size be 10. If I have only 4 past trajectories for the current training iteration, 6 out of 10 in the mini-batch is padded with zero value.
When calculating the loss for the back-propagation, I let the loss from the 6 be zero so that the only 4 contribute to the back-propagation.
The problem that I concern is..it seems that Tensorflow still calculates gradients for the 6 even if their loss is zero. As a result, the training speed becomes slower as I increase the mini-batch size even if I used the same training data.
I also used tf.where function when calculating the loss. However, the training time does not decrease.
How can I reduce the training time?
Here I attached my pseudo code for training.
# For each frame in a sequence
for f in range(pred_length):
# For each element in a batch
for b in range(batch_size):
with tf.variable_scope("rnnlm") as scope:
if (f > 0 or b > 0):
scope.reuse_variables()
# for each pedestrian in an element
for p in range(MNP):
# ground-truth position
cur_gt_pose = ...
# loss mask
loss_mask_ped = ... # '1' or '0'
# go through RNN decoder
output_states_dec_list[b][p], zero_states_dec_list[b][p] = cell_dec(cur_embed_frm_dec,
zero_states_dec_list[b][p])
# fully connected layer for output
cur_pred_pose_dec = tf.nn.xw_plus_b(output_states_dec_list[b][p], output_wd, output_bd)
# go through embedding function for the next input
prev_embed_frms_dec_list[b][p] = tf.reshape(tf.nn.relu(tf.nn.xw_plus_b(cur_pred_pose_dec, embedding_wd, embedding_bd)), shape=(1, rnn_size))
# calculate MSE loss
mse_loss = tf.reduce_sum(tf.pow(tf.subtract(cur_pred_pose_dec, cur_gt_pose_dec), 2.0))
# only valid ped's traj contributes to the loss
self.loss += tf.multiply(mse_loss, loss_mask_ped)
I think you're looking for the function tf.stop_gradient. Using this, you could do something like tf.where(loss_mask, tensor, tf.stop_gradient(tensor)) to achieve the desired result, assuming that the dimensions are correct.
However, it looks like this is probably not your issue. It seems as though for each item in your dataset, you are defining new graph nodes. This is not how TensorFlow is supposed to function, you should only have one graph, built beforehand that performs some fixed function, regardless of the batch size. You should definitely not be defining new nodes for every element in the batch, since that cannot efficiently take advantage of parallelism.
Specifically, within one step, how does it training the model? What is the quitting condition for the gradient descent and back propagation?
Docs here: https://www.tensorflow.org/api_docs/python/tf/estimator/Estimator#train
e.g.
mnist_classifier = tf.estimator.Estimator(model_fn=cnn_model_fn)
train_input_fn = tf.estimator.inputs.numpy_input_fn(
x={"x": X_train},
y=y_train,
batch_size=50,
num_epochs=None,
shuffle=True)
mnist_classifier.train(
input_fn=train_input_fn,
steps=100,
hooks=[logging_hook])
I understand that training one step means that we feed the neural network model with batch_size many data points once. My questions is, within this one step, how many times does it perform gradient descent? Does it do back propagation and gradient descent just once or does it keep performing gradient descent until the model weights reach a optimal for this batch of data?
In addition to #David Parks answer, using batches for performing gradient descent is referred to as stochastic gradient descent. Instead of updating the weights after each training sample, you average over the sum of gradients of the batch and use this new gradient to update your weights.
For example, if you have 1000 trainings samples and use batches of 200, you calculate the average gradient for 200 samples, and update your weights with it. That means that you only perform 5 updates overall instead of updating your weights 1000 times. On sufficiently big data sets, you will experience a much faster training process.
Michael Nielsen has a really nice way to explain this concept in his book.
1 step = 1 gradient update. And each gradient update step requires one forward pass and one backward pass.
The stopping condition is generally left up to you and is arguably more art than science. Commonly you will plot (tensorboard is handy here) your cost, training accuracy, and periodically your validation set accuracy. The low point on validation accuracy is generally a good point to stop. Depending on your dataset validation accuracy may drop and at some point increase again, or it may simply flatten out, at which point the stopping condition often correlates with the developer's degree of impatience.
Here's a nice article on stopping conditions, a google search will turn up plenty more.
https://stats.stackexchange.com/questions/231061/how-to-use-early-stopping-properly-for-training-deep-neural-network
Another common approach to stopping is to drop the learning rate every time you compute that no change has occurred to validation accuracy for some "reasonable" number of steps. When you've effectively hit 0 learning rate, you call it quits.
The input function emits batches (when num_epochs=None, num_batches is infinite):
num_batches = num_epochs * (num_samples / batch_size)
One step is processing 1 batch, if steps > num_batches, the training will stop after num_batches.
I am using Tensorflow in an online learning environment.
As cost function is implemented:
cost = tf.sqrt(tf.reduce_mean(tf.square(tf.sub(Y, output))))
Optimization is done like:
train_op = tf.train
.GradientDescentOptimizer(0.0001)
.minimize(cost,name="GradientDescent")
And I run Stochastic Gradient Descent like:
m, i = sess.run([merged, train_op], feed_dict={X: input_batch,Y:label_batch})
Whereby input_batch and label_batch contain only one vector each.
So how can I interpret a cost function like:
Is this a good progress for a stochastic approach?
Why the gap gets bigger?
I train the network 50'000 times with the same 50 training examples.
So each example is used for training 10'000 times every 51th step.
I tried already to change the learning rate by factor 10 in both ways.
This question is related to my other question from: Does Stochastic Gradient Descent even work with TensorFlow?
Thanks for any hints.