In this simple toy example, the network leans the XOR operation:
import tensorflow as tf
import numpy as np
from sklearn.metrics import accuracy_score, precision_score, recall_score
model = tf.keras.Sequential(layers=[
tf.keras.layers.Input(shape=(2,)),
tf.keras.layers.Dense(4, activation='relu'),
tf.keras.layers.Dense(1)
])
model.compile(
loss=tf.keras.losses.binary_crossentropy,
optimizer=tf.keras.optimizers.SGD(learning_rate=0.01)
)
x_train = np.random.uniform(-1, 1, (10000, 2))
tmp = x_train > 0
y_train = (tmp[:, 0] ^ tmp[:, 1])
model.fit(x=x_train, y=y_train, epochs=10)
x_test = np.random.uniform(-1, 1, (1000, 2))
tmp = x_test > 0
y_test = (tmp[:, 0] ^ tmp[:, 1])
prediction = model.predict(x_test) > 0.5
print(f'Accuracy: {accuracy_score(y_pred=prediction, y_true=y_test)}')
print(f'recall: {recall_score(y_pred=prediction, y_true=y_test)}')
print(f'precision: {precision_score(y_pred=prediction, y_true=y_test)}')
This example can also be found in the tensorflow playground
When the initial loss is <3, this will quickly converge (in 2-3 epochs). But sometimes the initial conditions lead it to have ~7 loss, in which case it never converges (not even after 1000 epochs).
It's easy to know right after the first epoch if it's going to work or not, but it makes searching for hyper parameters very difficult, since you never know if converged successfully by chance due to initial conditions, or if the hyper parameter is the cause.
Is there a way to make this network less dependent on initial conditions? A different optimizer? Some optimizer hyper parameter? weight regularization?
I've tried changing these, but didn't get consistent improvements.
In the playground example, it never gets stuck at this kind of high loss.
Edit: If you make the training long enough, it might jump to loss 7 even after settling on a good solution with loss < 0.03.
Theoretically, there's no way to be 100% sure if it's the hyper params or the initial config. You'll need to implement something for the case when there's divergence.
Practically though, you could:
Train multiple times, and incorporate how often the network converges into the strategy on selecting the best hyperparameters;.
Find some ranges for which you feel like the model is consistent.
Incorporate the initialization of your weights into your hyperparameter optimization. Right now they are randomly initiliazed, and are the cause of the problem. There's a number of ways to do this. Try playing around with different initilizers, but there's no "one best initiliazers for every ML problem".
Just fix the initial conditions. Fix the random seed that tensorflow uses for initilization using tf.random.set_seed, but that will affect your performance by a lot of course, so I don't think that's really what you want. You could make the claim that you are now sure that a network performs well because of the architecture, but that's only true for that specific random seed, not for all.
According to this blog, adding batchnorm should make the network less sensitive to the initialisation approach.
Related
I have a simple model in tensorflow which is being trained on the first 1000 images in the MNIST datset. From my previous experience the learning rates which I used were of the order of around 0.001, however for my model to converge the learning rate needs to be far heigher, at least larger than 1. The model is shown below.
def gen_model():
return tf.keras.models.Sequential([
tf.keras.Input(shape=(28,28,)),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(128, activation='sigmoid'),
tf.keras.layers.Dense(10, activation='softmax')
])
model = gen_model()
model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=5), loss='mean_squared_error')
model.summary()
model.fit(x_train, y_train, batch_size=1000, epochs=10000)
Is it expected for models of this form to require an extremely high learning rate, or is there something I have missed? When I use a learning rate of around 0.001 the loss changes incredibly slowly.
The dataset was created with the following code:
mnist = tf.keras.datasets.mnist
(x_train, y_train), (x_test, y_test) = mnist.load_data()
x_train = x_train.astype("float32") / 255.0
x_train = x_train.reshape(60000,28,28)[:1000];
y_train = y_train[:1000];
y_train = tf.one_hot(y_train, 10)
Generally speaking, models that require learning rates larger than 1 raise a red flag for me. It seems like your model is a vanilla multilayer perceptron, so there's nothing overly complicated about that, but there are a couple things about your setup that stand out:
The output from your model uses a softmax, which is normally used to represent values from a categorical distribution (i.e., 1-of-k) -- this is typical for a classification model. But the loss you're using is typically used for optimizing Gaussian or regression outputs. You might want to try using a cross-entropy loss to see if that helps.
The output from your model is in probability space, so the values you get out from your model are in [0, 1]. The loss you're using is averaging the squared differences between the model output and the target 1-hot vector (whose values are in {0, 1}). The value you'll get for this loss is always smaller than 1, so with a learning rate less than 1, and multiplying by the existing model weights, the delta that you'll apply to your model weights is always going to be small. Sometimes that's a good thing, but my guess is that in this case -- and particularly at the start of training when the model weights aren't near their optimal values -- this is going to be quite slow.
Related to the above point, you might try initializing your model weights with a larger range of values than the default. This would help make the gradient values larger, but could also make the model more likely to diverge.
You could also try to replace your softmax output activation with a plain linear activation, in effect converting your model's output to (unnormalized) log-probability space. Then you'd need to change your dataset labels to also represent target log-probability values, which isn't possible exactly, but could get close with something like 1e8 * (1 - one_hot). But if you wanted to go this route, you'd effectively be implementing a cross-entropy loss yourself; see the first point.
I'm using pytorch to implement a simple linear regression model.
The code works perfectly for randomly created datasets, but when it comes to the dataset I wanted to train, it gives significantly wrong results.
Here is the code:
x = torch.linspace(1,100,steps=100)
learn_rate = 0.000001
x_train = x[:100]
x_test = x[100:]
y_train = data[:100]
y_test = data[100:]
# y_train = -0.01*x_train + torch.randn(100)*10 #Code for generating random data.
w = torch.rand(1,requires_grad=True)
b= torch.rand(1,requires_grad=True)
for i in range(1000):
loss = torch.mean((y_train-(w*x_train+b))**2)
if(i%100==0):
print(loss)
loss.backward()
w.data.add_(-w.grad.data*learn_rate)
b.data.add_(-b.grad.data*learn_rate)
w.grad.data.zero_()
b.grad.data.zero_()
The result it gives makes no sense.
However, when I used a randomly generated dataset, it works perfectly:
The dataset actually looks similar. I am not sure for the reason of the inaccuracy of this model.
Code for plotting data:
plt.plot(x_train.numpy(),y_train.numpy())
plt.plot(x_train.numpy(),(w*x_train+b).data.numpy())
plt.show()
--
Now the problem seems to be that weight converges much faster than bias. At the current learning rate, bias will not converge to the optimal. However, if I increase the learning rate just by a little, the weight will simply diverge. I have to set two learning rates.
However, I'm wondering whether setting different learning rate is the best solution for a simple model like this, because I've found out that not much model actually uses different learning rate for different parameters.
Your code seems to be correct, but your model converges slower when there is a large bias in your data (because it now has to update the bias parameter many times before it reaches the correct value).
You could try running it for more iterations or increasing the learning rate.
I'm trying to build a NN with Keras and Tensorflow to predict the final chart position of a song, given a set of 5 features.
After playing around with it for a few days I realised that although my MAE was getting lower, this was because the model had just learned to predict the mean value of my training set for all input, and this was the optimal solution. (This is illustrated in the scatter plot below)
This is a random sample of 50 data points from my testing set vs what the network thinks they should be
At first I realised this was probably because my network was too complicated. I had one input layer with shape (5,) and a single node in the output layer, but then 3 hidden layers with over 32 nodes each.
I then stripped back the excess layers and moved to just a single hidden layer with a couple nodes, as shown here:
self.model = keras.Sequential([
keras.layers.Dense(4,
activation='relu',
input_dim=num_features,
kernel_initializer='random_uniform',
bias_initializer='random_uniform'
),
keras.layers.Dense(1)
])
Training this with a gradient descent optimiser still results in exactly the same prediction being made the whole time.
Then it occurred to me that perhaps the actual problem I'm trying to solve isn't hard enough for the network, that maybe it's linearly separable. Since this would respond better to not having a hidden layer at all, essentially just doing regular linear regression, I tried that. I changed my model to:
inp = keras.Input(shape=(num_features,))
out = keras.layers.Dense(1, activation='relu')(inp)
self.model = keras.Model(inp,out)
This also changed nothing. My MAE, the predicted value are all the same.
I've tried so many different things, different permutations of optimisation functions, learning rates, network configurations, and nothing can help. I'm pretty sure the data is good, but I've included a sample of it just in case.
chartposition,tagcount,dow,artistscore,timeinchart,finalpos
121,3925,5,35128,7,227
131,4453,3,85545,25,130
69,2583,4,17594,24,523
145,1165,3,292874,151,187
96,1679,5,102593,111,540
134,3494,5,1252058,37,370
6,34895,7,6824048,22,5
A sample of my dataset, finalpos is the value I'm trying to predict. Dataset contains ~40,000 records, split 80/20 - training/testing
def __init__(self, validation_split, num_features, should_log):
self.should_log = should_log
self.validation_split = validation_split
inp = keras.Input(shape=(num_features,))
out = keras.layers.Dense(1, activation='relu')(inp)
self.model = keras.Model(inp,out)
optimizer = tf.train.GradientDescentOptimizer(0.01)
self.model.compile(loss='mae',
optimizer=optimizer,
metrics=['mae'])
def train(self, data, labels, plot=False):
early_stop = keras.callbacks.EarlyStopping(monitor='val_loss', patience=20)
history = self.model.fit(data,
labels,
epochs=self.epochs,
validation_split=self.validation_split,
verbose=0,
callbacks = [PrintDot(), early_stop])
if plot: self.plot_history(history)
All code relevant to constructing and training the networ
def normalise_dataset(df, mini, maxi):
return (df - mini)/(maxi-mini)
Normalisation of the input data. Both my testing and training data are normalised to the max and min of the testing set
Graph of my loss vs validation curves with the one hidden layer network with an adamoptimiser, learning rate 0.01
Same graph but with linear regression and a gradient descent optimiser.
So I am pretty sure that your normalization is the issue: You are not normalizing by feature (as is the de-fact industry standard), but across all data.
That means, if you have two different features that have very different orders of magnitude/ranges (in your case, compare timeinchart with artistscore.
Instead, you might want to normalize using something like scikit-learn's StandardScaler. Not only does this normalize per column (so you can pass all features at once), but it also does unit variance (which is some assumption about your data, but can potentially help, too).
To transform your data, use something along these lines
from sklearn.preprocessing import StandardScaler
import numpy as np
raw_data = np.array([[1,40], [2, 80]])
scaler = StandardScaler()
processed_data = scaler.fit_transform(raw_data)
# fit() calculates mean etc, transform() puts it to the new range.
print(processed_data) # returns [[-1, -1], [1,1]]
Note that you have two possibilities to normalize/standardize your training data:
Either scale them together with your training data, and then split afterwards,
or you instead only fit the training data, and then use the same scaler to transform your test data.
Never fit_transform your test set separate from training data!
Since you have potentially different mean/min/max values, you can end up with totally wrong predictions! In a sense, the StandardScaler is your definition of your "data source distribution", which is inherently still the same for your test set, even though they might be a subset not exactly following the same properties (due to small sample size etc.)
Additionally, you might want to use a more advanced optimizer, like Adam, or specify some momentum property (0.9 is a good choice in practic, as a rule of thumb) for your SGD.
Turns out the error was a really stupid and easy to miss bug.
When I was importing my dataset, I shuffle it, however when I performed the shuffling, I was accidentally applying the shuffling only to the labels set, not the whole dataset as a whole.
As a result, each label was being assigned to a completely random feature set, of course the model didn't know what to do with this.
Thanks to #dennlinger for suggesting for me to look in the place where I eventually found this bug.
I am creating a deep convolutional neural network for pixel-wise classification. I am using adam optimizer, softmax with cross entropy.
Github Repository
I asked a similar question found here but the answer I was given did not result in me solving the problem. I also have a more detailed graph of what it going wrong. Whenever I use softmax, the problem in the graph occurs. I have done many things such as adjusting training and epsilon rates, trying different optimizers, etc. The loss never decreases past 500. I do not shuffle my data at the moment. Using sigmoid in place of softmax results in this problem not occurring. However, my problem has multiple classes, so the accuracy of sigmoid is not very good. It should also be mentioned that when the loss is low, my accuracy is only about 80%, I need much better than this. Why would my loss suddenly spike like this?
x = tf.placeholder(tf.float32, shape=[None, 7168])
y_ = tf.placeholder(tf.float32, shape=[None, 7168, 3])
#Many Convolutions and Relus omitted
final = tf.reshape(final, [-1, 7168])
keep_prob = tf.placeholder(tf.float32)
W_final = weight_variable([7168,7168,3])
b_final = bias_variable([7168,3])
final_conv = tf.tensordot(final, W_final, axes=[[1], [1]]) + b_final
cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=final_conv))
train_step = tf.train.AdamOptimizer(1e-5).minimize(cross_entropy)
correct_prediction = tf.equal(tf.argmax(final_conv, 2), tf.argmax(y_, 2))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
You need label smoothing.
I just had the same problem. I was training with tf.nn.sparse_softmax_cross_entropy_with_logits which is the same as if you use tf.nn.softmax_cross_entropy_with_logits with one-hot labels. My dataset predicts the occurrence of rare events so the labels in the training set are 99% class 0 and 1% class 1. My loss would start to fall, then stagnate (but with reasonable predictions), then suddenly explode and then the predictions also went bad.
Using the tf.summary ops to log internal network state into Tensorboard, I observed that the logits were growing and growing in absolute value. Eventually at >1e8, tf.nn.softmax_cross_entropy_with_logits became numerically unstable and that's what generated those weird loss spikes.
In my opinion, the reason why this happens is with the softmax function itself, which is in line with Jai's comment that putting a sigmoid in there before the softmax will fix things. But that will quite surely also make it impossible for the softmax likelihoods to be accurate, as it limits the value range of the logits. But in doing so, it prevents the overflow.
Softmax is defined as likelihood[i] = tf.exp(logit[i]) / tf.reduce_sum(tf.exp(logit[!=i])). Cross-entropy is defined as tf.reduce_sum(-label_likelihood[i] * tf.log(likelihood[i]) so if your labels are one-hot, that reduces to just the negative logarithm of your target likelihood. In practice, that means you're pushing likelihood[true_class] as close to 1.0 as you can. And due to the softmax, the only way to do that is if tf.exp(logit[!=true_class]) becomes as close to 0.0 as possible.
So in effect, you have asked the optimizer to produce tf.exp(x) == 0.0 and the only way to do that is by making x == - infinity. And that's why you get numerical instability.
The solution is to "blur" the labels so instead of [0,0,1] you use [0.01,0.01,0.98]. Now the optimizer works to reach tf.exp(x) == 0.01 which results in x == -4.6 which is safely inside the numerical range where GPU calculations are accurate and reliably.
Not sure, what it causes it exactly. I had the same issue a few times. A few things generally help: You might reduce the learning rate, ie. the bound of the learning rate for Adam (eg. 1e-5 to 1e-7 or so) or try stochastic gradient descent. Adam tries to estimate learning rates which can lead to instable training: See Adam optimizer goes haywire after 200k batches, training loss grows
Once I also removed batchnorm and that actually helped, but this was for a "specially" designed network for stroke data (= point sequences), which was not very deep with Conv1d layers.
I'm trying to understand how to implement neural networks. So I made my own dataset. Xtrain is numpy.random floats. Ytrain is sign(sin(1/x^3).
Try to implement neural networks gave me very poor results. 30%accuracy. Random Forest with 100 trees give 97%. But I heard that NN can approximate any function. What is wrong in my understanding?
import numpy as np
import keras
import math
from sklearn.ensemble import RandomForestClassifier as RF
train = np.random.rand(100000)
test = np.random.rand(100000)
def g(x):
if math.sin(2*3.14*x) > 0:
if math.cos(2*3.14*x) > 0:
return 0
else:
return 1
else:
if math.cos(2*3.14*x) > 0:
return 2
else:
return 3
def f(x):
x = (1/x) ** 3
res = [0, 0, 0, 0]
res[g(x)] = 1
return res
ytrain = np.array([f(x) for x in train])
ytest = np.array([f(x) for x in test])
train = np.array([[x] for x in train])
test = np.array([[x] for x in test])
from keras.models import Sequential
from keras.layers import Dense, Activation, Embedding, LSTM
model = Sequential()
model.add(Dense(100, input_dim=1))
model.add(Activation('sigmoid'))
model.add(Dense(100))
model.add(Activation('sigmoid'))
model.add(Dense(100))
model.add(Activation('sigmoid'))
model.add(Dense(4))
model.add(Activation('softmax'))
model.compile(optimizer='sgd',
loss='categorical_crossentropy',
metrics=['accuracy'])
P.S. I tried out many layers, activation functions, loss functions, optimizers, but never got more than 30% accuracy :(
I suspect that the 30% accuracy is a combination of small learning rate setting and a small training-step setting.
I ran your code snippet with model.fit(train, ytrain, nb_epoch=5, batch_size=32), after 5 epoch's training it yields about 28% accuracy. With the same setting but increasing the training steps to nb_epoch=50, the loss drops to ~1.157 ish and the accuracy raises to 40%. Further increase training steps should lead the model to further converging. Other than that, you can also try to configure the model with a larger learning rate setting which could make the converging faster :
model.compile(loss='categorical_crossentropy', optimizer=SGD(lr=0.1, momentum=0.9, nesterov=True), metrics=['accuracy'])
Although be careful don't set the learning rate to be too large otherwise your loss could blow up.
EDIT:
NN is known for having the potential for modeling extremely complex function, however, whether or not the model actually produce a good performance is a matter of how the model is designed, trained, and many other matters related to the specific application.
Zhongyu Kuang's answer is correct in stating that you may need to train it longer or with a different learning rate.
I'll add that the deeper your network, the longer you'll need to train it before it converges. For a relatively simple function like sign(sin(1/x^3)), you may be able to get away with a smaller network than the one you're using.
Additionally, softmax probably isn't the best output layer. You just need to yield -1 or 1. A single tanh unit seems like it would do well. softmax is generally used when you want to learn a probability distribution over a finite set. (You'll probably want to switch your error function from cross entropy to mean square error for similar reasons.)
Try a network with one sigmoidal hidden layer and an output layer with just one tanh unit. Then play around with the layer size and learning rate. Maybe add a second hidden layer if you can't get results with just one, but I wouldn't be surprised if it's unnecessary.
Addendum: In this approach, you'll replace f(x) with a direct calculation of the target function instead of the one-hot vector you're using currently.