Creating a neural network in keras to multiply two input integers - python

I am playing around with Keras v2.0.8 in Python v2.7 (Tensorflow backend) to create small neural networks that calculate simple arithmetic functions (add, subtract, multiply, etc.), and am a bit confused. The below code is my network which generates a random training dataset of integers with the corresponding labels (the two inputs added together):
def create_data(low, high, examples):
train_data = []
label_data = []
a = np.random.randint(low=low, high=high, size=examples, dtype='int')
b = np.random.randint(low=low, high=high, size=examples, dtype='int')
for i in range(0, examples):
train_data.append([a[i], b[i]])
label_data.append((a[i] + b[i]))
train_data = np.array(train_data)
label_data = np.array(label_data)
return train_data, label_data
X, y = create_data(0, 500, 10000)
model = Sequential()
model.add(Dense(3, input_dim=2))
model.add(Dense(5, activation='relu'))
model.add(Dense(3, activation='relu'))
model.add(Dense(5, activation='relu'))
model.add(Dense(1, activation='relu'))
model.compile(optimizer='adam', loss='mean_squared_error', metrics=['accuracy'])
model.fit(X, y, epochs=10, batch_size=10)
test_data, _ = create_data(0, 500, 10)
results = model.predict(test_data, batch_size=2)
sq_error = []
for i in range(0, len(test_data)):
print 'test value:', test_data[i], 'result:', results[i][0], 'error:',\
'%.2f' %(results[i][0] - (test_data[i][0] + test_data[i][1]))
sq_error.append((results[i][0] - (test_data[i][0] + test_data[i][1])))
print '\n total rmse error: ', sqrt(np.sum(np.array(sq_error)))
This trains perfectly well and produces no unexpected results. However, when I create the training data by multiplying the two inputs together the model's loss for each epoch stays around 7,000,000,000 and the model does not converge at all. The data creation function for this is as follows:
def create_data(low, high, examples):
train_data = []
label_data = []
a = np.random.randint(low=low, high=high, size=examples, dtype='int')
b = np.random.randint(low=low, high=high, size=examples, dtype='int')
for i in range(0, examples):
train_data.append([a[i], b[i]])
label_data.append((a[i] * b[i]))
train_data = np.array(train_data)
label_data = np.array(label_data)
return train_data, label_data
I also had the same problem when I had training data of a single input integer and created the label by squaring the input data. However, it worked fine when I only multiplied the single input by a constant value or added/subtracted by a constant.
I have two questions:
1) Why is this the case? I assume it has something to do with the fundamentals of neural networks, but I can't work it out.
2) How could I adapt this code to train a model that multiplies two input numbers together.
The network architecture (2 - 3 - 5 - 3 - 5 - 1) is fairly random right now. I've tried lots of different ones varying in layers and neurons, this one just happened to be on my screen as I write this and got an accuracy of 100% for adding two inputs.

It is due to large gradient updates caused by large numbers in training data. When using a neural network, you should first ensure that the training data falls in a small range (usually [-1,1] or [0,1]) to help the optimization process and prevent disruptive gradient updates. Therefore, you should first normalize data. In this case, one good candidate would be log-normalization.
Further, the 'accuracy' as a metric in Keras is used in case of a classification problem. In a regression problem, using it does not make sense, and instead it's better to use a relevant metric like "mean absolute error" or 'mae'.

Related

Sequence labeling with Keras - ignore first K predictions

I'm trying to create a sequence labeler for some long sequences.
Due to the nature of the problem, I don't expect the network to perform very well at the beginning of the sequence, due to a lack of historical data.
How can I train the network to ignore the first k predictions?
My network strucutre is as follows:
model = Sequential()
model.add(LSTM(10,return_sequences = True, input_shape = (None, 5)))
model.add(LSTM(10,return_sequences = True))
model.add(LSTM(10,return_sequences = True))
model.add(TimeDistributed(Dense(1,activation='sigmoid')))
model.compile(optimizer = adam,loss = 'binary_crossentropy',metrics = ['acc'])
And I train it by doing: model.fit(X,y) where X.shape is (m,n,5) and y.shape is (m,n,1) where m is number of sequences and n is the sequence length

Improve Accuracy for a Siamese Network

I wrote this little model using Keras Functional API to find similarity of a dialogue between two individuals. I am using Gensim's Doc2Vec embeddings for transforming text-data into vectors (vocab size: 4117). My data is equally divided up into 56 positive cases and 64 negative cases. (yes I know the dataset is small - but that's all I have for the time being).
def euclidean_distance(vects):
x, y = vects
sum_square = K.sum(K.square(x - y), axis=1, keepdims=True)
return K.sqrt(K.maximum(sum_square, K.epsilon()))
ch_inp = Input(shape=(38, 200))
csr_inp = Input(shape=(38, 200))
inp = Input(shape=(38, 200))
net = Embedding(int(vocab_size), 16)(inp)
net = Conv2D(16, 1, activation='relu')(net)
net = TimeDistributed(LSTM(8, return_sequences=True))(net)
out = Activation('relu')(net)
sia = Model(inp, out)
x = sia(csr_inp)
y = sia(ch_inp)
sub = Subtract()([x, y])
mul = Multiply()([sub, sub])
mul_x = Multiply()([x, x])
mul_y = Multiply()([y, y])
sub_xy = Subtract()([x, y])
euc = Lambda(euclidean_distance)([x, y])
z = Concatenate(axis=-1)([euc, sub_xy, mul])
z = TimeDistributed(Bidirectional(LSTM(4)))(z)
z = Activation('relu')(z)
z = GlobalMaxPooling1D()(z)
z = Dense(2, activation='relu')(z)
out = Dense(1, activation = 'sigmoid')(z)
model = Model([ch_inp, csr_inp], out)
model.compile(optimizer='rmsprop', loss='binary_crossentropy', metrics=['acc'])
The problem is: my accuracy won't improve from 60.87% - I ran 10 epochs and the accuracy remains constant. Is there something I've done here in my code that's causing that? Or perhaps its an issue with my data?
I also did K-Fold Validation for some Sklearn models and got these results from the dataset:
Additionally, an overview of my dataset is attached below:
I'm definitely struggling with this one - so literally any help here would be appreciated. Thanks!
UPDATE:
I increased my data-size to 1875 train-samples. Its accuracy improved to 70.28%. But its still constant over all iterations.
I see two things that may be important there.
You're using 'relu' after the LSTM. An LSTM in Keras already has 'tanh' as default activation. So, although you're not locking your model, you're making it harder for it to learn, with an activation that constraints the results between as small range plus one that cuts the negative values
You're using 'relu' with very few units! Relu with few units, bad initialization, big learning rates and bad luck will get stuck in the zero region without any gradients.
If your loss completely freezes, it's most probably due to the second point above. And even if it doesn't freeze, it may be using just one unit from the 2 Dense units, for instance, making the layer very poor.
You should do something from below:
Your model is small, so quit using 'relu' and use 'tanh' instead. This will give your model the expected power it should have.
Otherwise, you should definitely increase the number of units, both for the LSTM and for the Dense, so 'relu' doesn't get easily stuck.
You can add a BatchNormalization layer after Dense and before 'relu', this way you guarantee that a good amount units will always be above zero.
In any case, don't use 'relu' after the LSTM.
The other approach would be making the model more powerful.
For instance:
z = TimeDistributed(Bidirectional(LSTM(4)))(z)
z = Conv1D(10, 3, activation = 'tanh')(z) #or 'relu' maybe
z = MaxPooling1D(z)
z = Conv1D(15, 3, activation = 'tanh')(z) #or 'relu' maybe
z = Flatten()(z) #unless the length is variable, then GlobalAveragePooling1D()(z)
z = Dense(10, activation='relu')(z)
out = Dense(1, activation = 'sigmoid')(z)

Regression with LSTM - python and Keras

I am trying to use a LSTM network in Keras to make predictions of timeseries data one step into the future. The data I have is of 5 dimensions, and I am trying to use the previous 3 periods of readings to predict the a future value in the next period. I have normalised the data and removed all NaN etc, and this is the code I am trying to use to train the network:
def Network_ii(IN, OUT, TIME_PERIOD, EPOCHS, BATCH_SIZE, LTSM_SHAPE):
length = len(OUT)
train_x = IN[:int(0.9 * length)]
validation_x = IN[int(0.9 * length):]
train_y = OUT[:int(0.9 * length)]
validation_y = OUT[int(0.9 * length):]
# Define Network & callback:
train_x = train_x.reshape(train_x.shape[0],3, 5)
validation_x = validation_x.reshape(validation_x.shape[0],3, 5)
model = Sequential()
model.add(LSTM(units=128, return_sequences= True, input_shape=(train_x.shape[1],3)))
model.add(LSTM(units=128))
model.add(Dense(units=1))
model.compile(optimizer='adam', loss='mean_squared_error')
train_y = np.asarray(train_y)
validation_y = np.asarray(validation_y)
history = model.fit(train_x, train_y, batch_size=BATCH_SIZE, epochs=EPOCHS, validation_data=(validation_x, validation_y))
# Score model
score = model.evaluate(validation_x, validation_y, verbose=0)
print('Test loss:', score)
# Save model
model.save(f"models/new_model")
I am attempting to roughly follow the steps outlined here- https://machinelearningmastery.com/multivariate-time-series-forecasting-lstms-keras/
However, no matter what adjustments I have made in terms of changing the number of dimensions used to train the network or the length of the time period I cannot get the output of the model to give predictions that are not either 1 or 0. This is even though the target data, in the array 'OUT' is made up of data continuous on [0,1].
I think there may be something wrong with how I am setting up the .Sequential() function, but I cannot see what to adjust. I am relatively new to this so any help would be greatly appreciated.
You are probably using a prediction function that is not the standard. Maybe you are using predict_classes?
The one that is well documented and the standard is model.predict.

Keras LSTM appears to be fitting the end of time-series input instead of the prediction target

To preface this, I have plenty of experience with python and moderate experience building and using machine learning networks. That being said, this is the first LSTM I have made aside from some of the cookie-cutter examples available, so any help is appreciated. I feel like this is a problem with a simple solution and that I have just been looking at this code for far too long to see it.
This model is made in a python3.5 venv using Keras with a tensorflow backend.
In short, I am trying to make predictions of some temporal data using the data itself as well as a few mathematical permutations of this data, creating four input features. I am building a time-series input from the prior 60 data points and specifying the prediction target to be 60 data points in the future.
Shape of complete training data (input)(target): (2476224, 60, 4) (2476224)
Shape of single data "point" (input)(target): (1, 60, 4) (1)
What appears to be happening is that the trained model has fit the trailing value of my input time-series (the current value) instead of the target I have provided it (60 cycles in the future).
What is interesting is that the loss function seems to be calculating according to the correct prediction target, yet the model is not converging to the proper solution.
I have no idea why the model should be doing this. My first thought was that I was preprocessing my data incorrectly and feeding it the wrong target. I have tested my input formatting of the data extensively and am pretty confident that I am providing the model with he correct target and input information.
In one instance, I had increased the learning rate a tad such that the model converged to a local minima. This testing loss of this convergence was very similar to the loss of my preferred learning rate (still quite high). But the predictions were still of the "current value". Why is this so?
Here is how I created my model:
def create_model():
lstm_model = Sequential()
lstm_model.add(CuDNNLSTM(100, batch_input_shape=(batch_size, time_step, train_input.shape[2]),
stateful=True, return_sequences=True,
kernel_initializer='random_uniform'))
lstm_model.add(Dropout(0.4))
lstm_model.add(CuDNNLSTM(60))
lstm_model.add(Dropout(0.4))
lstm_model.add(Dense(20, activation='relu'))
lstm_model.add(Dense(1, activation='linear'))
optimizer = optimizers.Adagrad(lr=params["lr"])
lstm_model.compile(loss='mean_squared_error', optimizer=optimizer)
return lstm_model
This is how I am pre-processing the data. The first function, build_timeseries, constructs my input-output pairs. I believe this is working correctly (but please correct me if I am wrong). The second function trims the pairs to fit the batch size. I do the exact same for the test input/target.
train_input, train_target = build_timeseries(train_input, time_step, pred_horiz, 0)
train_input = trim_dataset(train_input, batch_size)
train_target = trim_dataset(train_target, batch_size)
def build_timeseries(mat, TIME_STEPS, PRED_HORIZON, y_col_index):
# y_col_index is the index of column that would act as output column
dim_0 = mat.shape[0] # num datasets
dim_1 = mat.shape[1] # num features
dim_2 = mat.shape[2] # num datapoints
# Reformatted matrix
mat = mat.swapaxes(1, 2)
x = np.zeros((dim_0*(dim_2-PRED_HORIZON), TIME_STEPS, dim_1))
y = np.zeros((dim_0*(dim_2-PRED_HORIZON),))
k = 0
for i in range(dim_0): # Iterate through datasets
for j in range(TIME_STEPS, dim_2-PRED_HORIZON):
x[k] = mat[i, j-TIME_STEPS:j]
y[k] = mat[i, j+PRED_HORIZON, y_col_index]
k += 1
print("length of time-series i/o", x.shape, y.shape)
return x, y
def trim_dataset(mat, batch_size):
no_of_rows_drop = mat.shape[0] % batch_size
if(no_of_rows_drop > 0):
return mat[no_of_rows_drop:]
else:
return mat
Lastly, this is how I call the actual model.
history = model.fit(train_input, train_target, epochs=params["epochs"], verbose=2, batch_size=batch_size,
shuffle=True, validation_data=(test_input, test_target), callbacks=[es, mcp])
As the model converges, I expect it to predict values close to the specified targets I had fed it. However instead, its predictions align much more closely with the trailing value of the time-series data (or the current value). Though, on the other hand, the model appears to be evaluating the loss according to the specified target.... Why is it working this way and how can I fix it? Any help is appreciated.

Keras network producing inverse predictions

I have a timeseries dataset and I am trying to train a network so that it overfits (obviously, that's just the first step, I will then battle the overfitting).
The network has two layers:
LSTM (32 neurons) and Dense (1 neuron, no activation)
Training/model has these parameters:
epochs: 20, steps_per_epoch: 100, loss: "mse", optimizer: "rmsprop".
TimeseriesGenerator produces the input series with: length: 1, sampling_rate: 1, batch_size: 1.
I would expect the network would just memorize such a small dataset (I have tried even much more complicated network to no avail) and the loss on training dataset would be pretty much zero. It is not and when I visualize the results on the training set like this:
y_pred = model.predict_generator(gen)
plot_points = 40
epochs = range(1, plot_points + 1)
pred_points = numpy.resize(y_pred[:plot_points], (plot_points,))
target_points = gen.targets[:plot_points]
plt.plot(epochs, pred_points, 'b', label='Predictions')
plt.plot(epochs, target_points, 'r', label='Targets')
plt.legend()
plt.show()
I get:
The predictions have somewhat smaller amplitude but are precisely inverse to the targets. Btw. this is not memorized, they are inversed even for the test dataset which the algorithm hasn't trained on at all.It appears that instead of memorizing the dataset, my network just learned to negate the input value and slightly scale it down. Any idea why this is happening? It doesn't seem like the solution the optimizer should have converged to (loss is pretty big).
EDIT (some relevant parts of my code):
train_gen = keras.preprocessing.sequence.TimeseriesGenerator(
x,
y,
length=1,
sampling_rate=1,
batch_size=1,
shuffle=False
)
model = Sequential()
model.add(LSTM(32, input_shape=(1, 1), return_sequences=False))
model.add(Dense(1, input_shape=(1, 1)))
model.compile(
loss="mse",
optimizer="rmsprop",
metrics=[keras.metrics.mean_squared_error]
)
history = model.fit_generator(
train_gen,
epochs=20,
steps_per_epoch=100
)
EDIT (different, randomly generated dataset):
I had to increase number of LSTM neurons to 256, with the previous setting (32 neurons), the blue line was pretty much flat. However, with the increase the same pattern arises - inverse predictions with somewhat smaller amplitude.
EDIT (targets shifted by +1):
Shifting the targets by one compared to predictions doesn't produce much better fit. Notice the highlighted parts where the graph isn't just alternating, it's more apparent there.
EDIT (increased length to 2 ... TimeseriesGenerator(length=2, ...)):
With length=2 the predictions stop tracking the targets so closely but the overall pattern of inversion still stands.
You say that your network "just learned to negate the input value and slightly scale it down". I don't think so. It is very likely that all you are seeing is the network performing poorly, and just predicting the previous value (but scaled as you say). This issue is something I've seen again and again. Here is another example, and another, of this issue. Also, remember it is very easy to fool yourself by shifting the data by one. It is very likely you are simply shifting the poor prediction back in time and getting an overlap.
EDIT: After author's comments I do not believe this is the correct answer but I will keep it posted for posterity.
Great question and the answer is due to how the Time_generator works! Apparently instead of grabbing x,y pairs with the same index (e.g input x[0] to output target y[0]) it grabs target with offset 1 (so x[0] to y[1]).
Thus plotting y with offset 1 will produce the desired fit.
Code to simulate:
import keras
import matplotlib.pyplot as plt
x=np.random.uniform(0,10,size=41).reshape(-1,1)
x[::2]*=-1
y=x[1:]
x=x[:-1]
train_gen = keras.preprocessing.sequence.TimeseriesGenerator(
x,
y,
length=1,
sampling_rate=1,
batch_size=1,
shuffle=False
)
model = keras.models.Sequential()
model.add(keras.layers.LSTM(100, input_shape=(1, 1), return_sequences=False))
model.add(keras.layers.Dense(1))
model.compile(
loss="mse",
optimizer="rmsprop",
metrics=[keras.metrics.mean_squared_error]
)
model.optimizer.lr/=.1
history = model.fit_generator(
train_gen,
epochs=20,
steps_per_epoch=100
)
Proper plotting:
y_pred = model.predict_generator(train_gen)
plot_points = 39
epochs = range(1, plot_points + 1)
pred_points = np.resize(y_pred[:plot_points], (plot_points,))
target_points = train_gen.targets[1:plot_points+1] #NOTICE DIFFERENT INDEXING HERE
plt.plot(epochs, pred_points, 'b', label='Predictions')
plt.plot(epochs, target_points, 'r', label='Targets')
plt.legend()
plt.show()
Output, Notice how the fit is no longer inverted and is mostly very accurate:
This is how it looks when the offset is incorrect:

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