After going through the Caffe tutorial here: http://caffe.berkeleyvision.org/gathered/examples/mnist.html
I am really confused about the different (and efficient) model using in this tutorial, which is defined here: https://github.com/BVLC/caffe/blob/master/examples/mnist/lenet_train_test.prototxt
As I understand, Convolutional layer in Caffe simply calculate the sum of Wx+b for each input, without applying any activation function. If we would like to add the activation function, we should add another layer immediately below that convolutional layer, like Sigmoid, Tanh, or Relu layer. Any paper/tutorial I read on the internet applies the activation function to the neuron units.
It leaves me a big question mark as we only can see the Convolutional layers and Pooling layers interleaving in the model. I hope someone can give me an explanation.
As a site note, another doubt for me is the max_iter in this solver:
https://github.com/BVLC/caffe/blob/master/examples/mnist/lenet_solver.prototxt
We have 60.000 images for training, 10.000 images for testing. So why does the max_iter here only 10.000 (and it still can get > 99% accuracy rate)? What does Caffe do in each iteration?
Actually, I'm not so sure if the accuracy rate is the total correct prediction/test size.
I'm very amazed of this example, as I haven't found any example, framework that can achieve this high accuracy rate in that very short time (only 5 mins to get >99% accuracy rate). Hence, I doubt there should be something I misunderstood.
Thanks.
Caffe uses batch processing. The max_iter is 10,000 because the batch_size is 64. No of epochs = (batch_size x max_iter)/No of train samples. So the number of epochs is nearly 10. The accuracy is calculated on the test data. And yes, the accuracy of the model is indeed >99% as the dataset is not very complicated.
For your question about the missing activation layers, you are correct. The model in the tutorial is missing activation layers. This seems to be an oversight of the tutorial. For the real LeNet-5 model, there should be activation functions following the convolution layers. For MNIST, the model still works surprisingly well without the additional activation layers.
For reference, in Le Cun's 2001 paper, it states:
As in classical neural networks, units in layers up to F6 compute a dot product between their input vector and their weight vector, to which a bias is added. This weighted sum, denoted a_i, for unit i, is then passed through a sigmoid squashing function to produce the state of unit i ...
F6 is the "blob" between the two fully connected layers. Hence the first fully connected layers should have an activation function applied (the tutorial uses ReLU activation functions instead of sigmoid).
MNIST is the hello world example for neural networks. It is very simple to today's standard. A single fully connected layer can solve the problem with accuracy of about 92%. Lenet-5 is a big improvement over this example.
Related
I'm investigating the task of training a neural network to predict one future value given a sinusoidal input. So for example, as seen in the Figure, the input signal is x and the expected output signal y. The model's output is y^. Doing the regression task is fairly straightforward, and there are a lot of choices for this problem. I'm using a simple recurrent neural network with mean-squared error (MSE) loss between y and y^.
Additionally, suppose I know that the sinusoid is made up of N modalities, e.g., at some points, the wave oscillates at 5 Hz, then 10 Hz, then back to 5 Hz, then up to 15 Hz maybe—i.e., N=3.
In this case, I have ground-truth class labels in a vector k and the model does both regression and classification, additionally outputting a vector k^. An example is shown in the Figure. As this is a multi-class problem with exclusivity, I figured binary cross entropy (BCE) loss should be relevant here.
I'm sure there is a lot of research about combining loss functions, but does just adding MSE and BCE make sense? Scaling one up or down by a factor of 10 doesn't seem to change the learning outcome too much. So I was wondering what is considered the standard approach to problems where there is a joint classification and regression objective.
Additionally, on top of just BCE, I want to penalize k^ for quickly jumping around between classes; for example, if the model guesses one class, I'd like it to stay in that one class and switch only when it's necessary. See how in the Figure, there are fast dark blue blips in k^. I would like the same solid bands as seen in k, and naive BCE loss doesn't account for that.
Appreciate any and all advice!
I'm using Resnet50 model to classify images into two classes: normal cells and cancer cells.
so I want to to increase the accuracy but i don't know what to modify.
# we are using resnet50 for transfer learnin here. So we have imported it
from tensorflow.keras.applications import resnet50
# initializing model with weights='imagenet'i.e. we are carring its original weights
model_name='resnet50'
base_model=resnet50.ResNet50(include_top=False, weights="imagenet",input_shape=img_shape, pooling='max')
last_layer=base_model.output # we are taking last layer of the model
# Add flatten layer: we are extending Neural Network by adding flattn layer
flatten=layers.Flatten()(last_layer)
# Add dense layer
dense1=layers.Dense(100,activation='relu')(flatten)
# Add dense layer to the final output layer
output_layer=layers.Dense(class_count,activation='softmax')(flatten)
# Creating modle with input and output layer
model=Model(inputs=base_model.inputs,outputs=output_layer)
model.compile(Adamax(learning_rate=.001), loss='categorical_crossentropy', metrics=['accuracy'])
There were 48 errors in 534 test cases Model accuracy= 91.01 %
Also what do you think about the results of the graph?
this is the classification report
i got good results but is there a possibility to increase accuracy more than that?
This is a broad question as there are many ways one can attempt to generally improve the network's accuracy. some of which may be
Increase the dimension of the layers that are learned in transfer learning (make sure not to overfit)
Use transfer learning with Convolution layers and not MLP
let the optimization algorithm choose the learning rate on its own
Play with additional augmentations to the dataset
and the list goes on.
Also, if possible, I would suggest comparing your results to other publicly available benchmarks - by doing so you might understand the upper bounds of the accuracies better
I am training a large neural network model (1 module Hourglass) for a facial landmark recognition task. Database used for training is WFLW.
Loss function used is MSELoss() between the predicted output heatmaps, and the ground-truth heatmaps.
- Batch size = 32
- Adam Optimizer
- Learning rate = 0.0001
- Weight decay = 0.0001
As I am building a baseline model, I have launched a basic experiment with the parameters shown above. I previously had executed a model with the same exact parameters, but with weight-decay=0. The model converged successfully. Thus, the problem is with the weight-decay new value.
I was expecting to observe a smooth loss function that slowly decreased. As it can be observed in the image below, the loss function has a very very wierd shape.
This will probably be fixed by changing the weight decay parameter (decreasing it, maybe?).
I would highly appreciate if someone could provide a more in-depth explanation into the strange shape of this loss function, and its relation with the weight-decay parameter.
In addition, to explain why this premature convergence into a very specific value of 0.000415 with a very narrow standard deviation? Is it a strong local minimum?
Thanks in advance.
Loss should not consistently increase when using gradient descent. It does not matter if you use weight decay or not, there is either a bug in your code (e.g. worth checking what happens with normal gradient descent, not Adam, as there are ways in which one can wrongly implement weight decay with Adam), or your learning rate is too large.
I am getting started with deep learning and have a basic question on CNN's.
I understand how gradients are adjusted using backpropagation according to a loss function.
But I thought the values of the convolving filter matrices (in CNN's) needs to be determined by us.
I'm using Keras and this is how (from a tutorial) the convolution layer was defined:
classifier = Sequential()
classifier.add(Conv2D(32, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))
There are 32 filter matrices with dimensions 3x3 is used.
But, how are the values for these 32x3x3 matrices are determined?
It's not the gradients that are adjusted, the gradient calculated with the backpropagation algorithm is just the group of partial derivatives with respect to each weight in the network, and these components are in turn used to adjust the network weights in order to minimize the loss.
Take a look at this introductive guide.
The weights in the convolution layer in your example will be initialized to random values (according to a specific method), and then tweaked during training, using the gradient at each iteration to adjust each individual weight. Same goes for weights in a fully connected layer, or any other layer with weights.
EDIT: I'm adding some more details about the answer above.
Let's say you have a neural network with a single layer, which has some weights W. Now, during the forward pass, you calculate your output yHat for your network, compare it with your expected output y for your training samples, and compute some cost C (for example, using the quadratic cost function).
Now, you're interested in making the network more accurate, ie. you'd like to minimize C as much as possible. Imagine you want to find the minimum value for simple function like f(x)=x^2. You can start at some random point (as you did with your network), then compute the slope of the function at that point (ie, the derivative) and move down that direction, until you reach a minimum value (a local minimum at least).
With a neural network it's the same idea, with the difference that your inputs are fixed (the training samples), and you can see your cost function C as having n variables, where n is the number of weights in your network. To minimize C, you need the slope of the cost function C in each direction (ie. with respect to each variable, each weight w), and that vector of partial derivatives is the gradient.
Once you have the gradient, the part where you "move a bit following the slope" is the weights update part, where you update each network weight according to its partial derivative (in general, you subtract some learning rate multiplied by the partial derivative with respect to that weight).
A trained network is just a network whose weights have been adjusted over many iterations in such a way that the value of the cost function C over the training dataset is as small as possible.
This is the same for a convolutional layer too: you first initialize the weights at random (ie. you place yourself on a random position on the plot for the cost function C), then compute the gradients, then "move downhill", ie. you adjust each weight following the gradient in order to minimize C.
The only difference between a fully connected layer and a convolutional layer is how they calculate their outputs, and how the gradient is in turn computed, but the part where you update each weight with the gradient is the same for every weight in the network.
So, to answer your question, those filters in the convolutional kernels are initially random and are later adjusted with the backpropagation algorithm, as described above.
Hope this helps!
Sergio0694 states ,"The weights in the convolution layer in your example will be initialized to random values". So if they are random and say I want 10 filters. Every execution algorithm could find different filter. Also say I have Mnist data set. Numbers are formed of edges and curves. Is it guaranteed that there will be a edge filter or curve filter in 10?
I mean is first 10 filters most meaningful most distinctive filters we can find.
best
Link to paper
I'm trying to understand the region proposal network in faster rcnn. I understand what it's doing, but I still don't understand how training exactly works, especially the details.
Let's assume we're using VGG16's last layer with shape 14x14x512 (before maxpool and with 228x228 images) and k=9 different anchors. At inference time I want to predict 9*2 class labels and 9*4 bounding box coordinates. My intermediate layer is a 512 dimensional vector.
(image shows 256 from ZF network)
In the paper they write
"we randomly sample 256 anchors in an image to compute the loss
function of a mini-batch, where the sampled positive and negative
anchors have a ratio of up to 1:1"
That's the part I'm not sure about. Does this mean that for each one of the 9(k) anchor types the particular classifier and regressor are trained with minibatches that only contain positive and negative anchors of that type?
Such that I basically train k different networks with shared weights in the intermediate layer? Therefore each minibatch would consist of the training data x=the 3x3x512 sliding window of the conv feature map and y=the ground truth for that specific anchor type.
And at inference time I put them all together.
I appreciate your help.
Not exactly. From what I understand, the RPN predicts WHk bounding boxes per feature map, and then 256 are randomly sampled per the 1:1 criteria, and these are used as part of the computation for the loss function of that particular mini-batch. You're still only training one network, not k, since the 256 random samples are not of any particular type.
Disclaimer: I only started learning about CNNs a month ago, so I may not understand what I think I understand.