I am trying to replicate a neural net to compute the energy of molecules (image given below). The Energy is the sum of bonded/non-bonded interactions and angle/dihedral strains. I have 4 separate neural networks that find out the energy due to each of these, and the total energy is the sum of energies due to each interaction, there may be 100s of these. In my data-set, I only know the total energy.
If my total energy is computed using multiple (an unknown number, decided by the molecule) forward-pos on different neural networks, how do I get keras to backpropagate through the dynamically constructued sum. A non-keras Tensorflow method would work too. (I would have just summed together the outputs of the neural nets if I knew before hand how many bonds would there be, the issue is having to unfold copies of the neural net at runtime).
This is just an example image given in the paper:
In summary, the question is: "How do I implement dynamic unrolling and feed it to a sum in Keras?".
Keras layers can be given a shape of (None, actual-shape...) if one of the dimensions is not known. Then we can use a TensorFlow layer to sum over the axis indexed 0 using tf.reduce_sum(layer, axis=0). So dynamic layer sizes are not hard to achieve in Keras.
However if the input shapes pose more of a constraint, we can pass in the full matrix with dummy 0 values appended, and a mask matrix, then we can use tf.multiply to reject the dummy values, the backpropagation will automatically work of course.
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I have been trying to conduct a few experiments using TensorFlow Probability (TFP), and I got a few questions.
What is the proper value of the coefficient of the KL loss?
In the paper by Blundell (2015), the coefficient is set to 1/M (where M is the number of mini-batches). In the example given by TFP, the coefficient is given as 1/mnist_data.train.num_examples. Why?
As I go from 2d input to 3d images volumes, the KL loss is still significantly larger (~1k) than the cross-entropy (~1), even after dividing by mnist_data.train.num_examples. Why?
What is the guideline for getting a proper value for this coefficient? Maybe like the two-loss terms should be the same order of magnitude?
The current coefficient only takes care of the number of training samples, but not the network complexity or number of parameters in the network, which I assume the KL loss increase with the complexity of the model.
I am trying to implement a neural network with the KL loss, without using keras.model.losses, as some software production and hardware support limitation. I am trying to train my model with TF 1.10 and TFP 0.3.0., the issue is that for tf<=1.14, tf.keras.model does not support tf.layers inside the Keras model, so I can't use my original model straight away. Is there a way to get the KL loss, not from model.losses, but from layers or weights of the network in a TF construct?
Is batch normalization or group normalization still helpful in Bayesian deep learning?
In the paper by Blundell (2015), the coefficient is set to 1/M (where M is the number of mini-batches). In the example given by TFP, the coefficient is given as 1/mnist_data.train.num_examples. Why?
In the BBB paper eq. 8, they refer to M being the number of mini-batches. To be consistent with the non-stochastic gradient learning, it should be scaled by the number of mini-batches which is what is done by Graves. Another alternative is that done in eq. 9, where they scale it by \pi_i, where the sum of all the values in the set {\pi} sum to one.
In the TFP example, it does look like the num_examples is the total number of independent samples within the training set, which is much larger than the number of batches. This is goes by a few names, such as Safe Bayes or Tempering. Have a look at sec. 8 of this paper for some more discussion about the use of tempering within Bayesian inference and it's suitability.
As I go from 2d input to 3d images volumes, the KL loss is still significantly larger (~1k) than the cross-entropy (~1), even after dividing by mnist_data.train.num_examples. Why?
The ELBO will always be larger than just your cross-entropy (which defines your likelihood). Have a look at how the KL divergence term in the ELBO is found. (and a full mean-field approach where each weight/parameter is assumed to be independent).
Since the assumed posterior is factorised (assume each parameter is independent), can write the joint distribution as a product. This means when you take the log when you are computing the KL between the approx. posterior and the prior, you can write it as a sum of the KL terms between each parameter. Since the KL is >= 0, for each parameter you add to your model you will be adding another positive term to your ELBO. This is likely why your loss is so much more for your 3D model, likely because there is more parameters.
Another reason this could occur is if you have less data (your M is smaller, than the KL term is weighted less).
What is the guideline for getting a proper value for this coefficient? Maybe like the two-loss terms should be the same order of magnitude?
I am unsure of any specific guideline, for training you are interested primarily in the gradients. A large loss does not mean a large gradient. Have a look at the gradients contributed by the negative log likelihood and the KL term in your ELBO. If the KL term is too large, you probably need a more informative prior or more data (you could simply scale the KL term but this feels a bit yucky for the Bayesian in me).
The current coefficient only takes care of the number of training samples, but not the network complexity or the number of parameters in the network, which I assume the KL loss increase with the complexity of the model.
Yes, as stated before, in general, more parameters == greater ELBO (for a mean-field approach as used in Bayes by Backprop).
I am trying to implement a neural network with the KL loss, without using keras.model.losses, as some software production and hardware support limitation. I am trying to train my model with TF 1.10 and TFP 0.3.0., the issue is that for tf<=1.14, tf.keras.model does not support tf.layers inside the Keras model, so I can't use my original model straight away. Is there a way to get the KL loss, not from model.losses, but from layers or weights of the network in a TF construct?
I am unsure about the best way to tackle this part of it. I would be cautious about going to older versions where it isn't explicitly supported. They put those warnings/exceptions in for a reason.
Is batch normalization or group normalization still helpful in Bayesian deep learning?
For variational inference (as done in Bayes by Backprop) Batchnorm is fine. For sampling methods such as MCMC, Batch normalization is no longer suitable. Have a look at https://arxiv.org/pdf/1908.03491v1.pdf for info on suitability for batch norm with sampling methods for approx. Bayesian inference.
As we know, a DNN is comprised of many layers which consist of many neurons applying the same function to different parts of the input. Meanwhile, if we use Tensorflow to execute a DNN task, we will get a dataflow graph generated by Tensorflow automatically and we can use Tensorboard to visualize the dataflow graph as blow. But there is no neuron in the layer. So I wonder what is the relationship between Tensorflow dataflow graph and a DNN? When a neuron of DNN's layer map into dataflow graph, how is it represented?What is the relationship of neuron in DNN and node in tensorflow(representing an operation)? I just started to learn DNN and Tensorflow, please help me arrange thoughts in order. Thanks:) enter image description here
You have to differentiate between the metaphoric representation of a DNN and it's mathematic description. The math behind a classic neuron is the sum of the weighted inputs + a bias (usually calling a activation function on this result)
So in this case you have an input vector mutplied by a weight vector (containing trainable variables) and then summed up with a bias scalar (also trainable)
If you now consider a layer of neurons instead of one, the weights will become a matrix and the bias a vector. So calculating a feed forward layer is nothing more then a matrix multiplication follow by a sum of vectors.
This is the operation you can see in your tensorflow graph.
You can actually build your Neural Network this way without any use of the so called High Level API which use the Layer abstraction. (Many have done this in the early days of tensorflow)
The actual "magic", which tensorflow does for you is calculating and executing the derivatives of this foreword pass in order to calculate the updates for the weights.
I am trying to create a script that is able to evaluate a model on lfw dataset. As a process, I am reading pair of images (using the LFW annotation list), track and crop the face, align it and pass it through a pre-trained facenet model (.pb using tensorflow) and extract the features. The feature vector size = (1,128) and the input image is (160,160).
To evaluate for the verification task, I am using a Siamese architecture. That is, I am passing a pair of images (same or different person) from two identical models ([2 x facenet] , this is equivalent like passing a batch of images with size 2 from a single network) and calculating the euclidean distance of the embeddings. Finally, I am training a linear SVM classifier to extract 0 when the embedding distance is small and 1 otherwise using pair labels. This way I am trying to learn a threshold to be used while testing.
Using this architecture I am getting a score of 60% maximum. On the other hand, using the same architecture on other models (e.g vgg-face), where the features are 4096 [fc7:0] (not embeddings) I am getting 90%. I definitely cannot replicate the scores that I see online (99.x%), but using the embeddings the score is very low. Is there something wrong with the pipeline in general ?? How can I evaluate the embeddings for verification?
Nevermind, the approach is correct, facenet model that is available online is poorly trained and that is the reason for the poor score. Since this model is trained on another dataset and not the original one that is described in the paper (obviously), verification score will be less than expected. However, if you set a constant threshold to the desired value you can probably increase true positives but by sacrificing f1 score.
You can use a similarity search engine. Either using approximated kNN search libraries such as Faiss or Nmslib, cloud-ready similarity search open-source tools such as Milvus, or production-ready managed service such as Pinecone.io.
When I first train an LSTM in Keras on sequence data - my training data -
and then use model.predict() to make predictions with my test data as input, is the hidden state of the LSTM still being adjusted?
Basic operation of a neural network is to take an input (vector) which is connected to the output with connections and, sometimes, other layers such as context layers. These connections are modelled as matrices and vary in strength, we call these weight matrices.
This means that the only thing we do when we are feeding data into the network is to put a vector into the network, multiply the values with the weight matrix and call that the output. In special cases, like recurrent networks, we even keep some values stored in other vectors and combine this stored value with the current input.
During training we not only feed data into the network, we also compute an error value that we evaluate in a clever way so that it tells us how we should change the weight matrices we multiply our inputs (and possibly past inputs for recurrent layers) with.
Therefore: yes, of course the basic execution behavior does not change for recurrent layers. We are just not updating weights anymore.
There are layers that do behave differently during execution time because they are treated as regularisers, i.e. methods that make training the network more efficient, which are deemed as unnecessary during execution. Examples for these layers are Noise and BatchNormalization. Almost all neural network layers (including recurrent ones) include drop-out which is another form of regularisation which disables a random percentage of connections in the layer. This is also only done during training.
In the FCN paper, the authors discuss the patch wise training and fully convolutional training. What is the difference between these two?
Please refer to section 4.4 attached in the following.
It seems to me that the training mechanism is as follows,
Assume the original image is M*M, then iterate the M*M pixels to extract N*N patch (where N<M). The iteration stride can some number like N/3 to generate overlapping patches. Moreover, assume each single image corresponds to 20 patches, then we can put these 20 patches or 60 patches(if we want to have 3 images) into a single mini-batch for training. Is this understanding right? It seems to me that this so-called fully convolutional training is the same as patch-wise training.
The term "Fully Convolutional Training" just means replacing fully-connected layer with convolutional layers so that the whole network contains just convolutional layers (and pooling layers).
The term "Patchwise training" is intended to avoid the redundancies of full image training.
In semantic segmentation, given that you are classifying each pixel in the image, by using the whole image, you are adding a lot of redundancy in the input. A standard approach to avoid this during training segmentation networks is to feed the network with batches of random patches (small image regions surrounding the objects of interest) from the training set instead of full images. This "patchwise sampling" ensures that the input has enough variance and is a valid representation of the training dataset (the mini-batch should have the same distribution as the training set). This technique also helps to converge faster and to balance the classes. In this paper, they claim that is it not necessary to use patch-wise training and if you want to balance the classes you can weight or sample the loss.
In a different perspective, the problem with full image training in per-pixel segmentation is that the input image has a lot of spatial correlation. To fix this, you can either sample patches from the training set (patchwise training) or sample the loss from the whole image. That is why the subsection is called "Patchwise training is loss sampling".
So by "restricting the loss to a randomly sampled subset of its spatial terms excludes patches from the gradient computation." They tried this "loss sampling" by randomly ignoring cells from the last layer so the loss is not calculated over the whole image.