Tensorflow custom layer: Creating a sparse matrix with trainable parameters

Question

A model that I am working on should be predicting quite a lot of variables simultaneously (>1000). Therefore I would like to have a small neural network at the end of the network for each output.

In order to do this compactly, I would like to find a way to create a sparse trainable connection between two layers in the neural network within the Tensorflow framework.

Only a small portion of the connection matrix should be trainable: It is only the parameters that are part of the block-diagonal.

---

For example:

The connection matrix is the following:

The trainable parameters should be in the place of the 1's.

Answer 1

edit so the comment was Is this a trainable object though?

The answer: No. You cannot use sparse matrix currently and make it trainable. Instead you can use a mask matrix (see at the end)

But if you need to use sparse matrix, you just have to use tf.sparse.sparse_dense_matmul() or tf.sparse_tensor_to_dense() where your sparse interacts with a dense matrix. I have taken a simple XOR example from here and replaced dense with a sparse matrix:

#Declaring necessary modules
import tensorflow as tf
import numpy as np
"""
A simple numpy implementation of a XOR gate to understand the backpropagation
algorithm
"""

x = tf.placeholder(tf.float32,shape = [4,2],name = "x")
#declaring a place holder for input x
y = tf.placeholder(tf.float32,shape = [4,1],name = "y")
#declaring a place holder for desired output y

m = np.shape(x)[0]#number of training examples
n = np.shape(x)[1]#number of features
hidden_s = 2 #number of nodes in the hidden layer
l_r = 1#learning rate initialization

theta1 = tf.SparseTensor(indices=[[0, 0],[0, 1], [1, 1]], values=[0.1, 0.2, 0.1], dense_shape=[3, 2])
#theta1 = tf.cast(tf.Variable(tf.random_normal([3,hidden_s]),name = "theta1"),tf.float64)
theta2 = tf.cast(tf.Variable(tf.random_normal([hidden_s+1,1]),name = "theta2"),tf.float32)

#conducting forward propagation
a1 = tf.concat([np.c_[np.ones(x.shape[0])],x],1)
#the weights of the first layer are multiplied by the input of the first layer

#z1 = tf.sparse_tensor_dense_matmul(theta1, a1)

z1 = tf.matmul(a1,tf.sparse_tensor_to_dense(theta1))
#the input of the second layer is the output of the first layer, passed through the 

a2 = tf.concat([np.c_[np.ones(x.shape[0])],tf.sigmoid(z1)],1)
#the input of the second layer is multiplied by the weights

z3 = tf.matmul(a2,theta2)
#the output is passed through the activation function to obtain the final probability

h3 = tf.sigmoid(z3)
cost_func = -tf.reduce_sum(y*tf.log(h3)+(1-y)*tf.log(1-h3),axis = 1)

#built in tensorflow optimizer that conducts gradient descent using specified 

optimiser = tf.train.GradientDescentOptimizer(learning_rate = l_r).minimize(cost_func)

#setting required X and Y values to perform XOR operation
X = [[0,0],[0,1],[1,0],[1,1]]
Y = [[0],[1],[1],[0]]

#initializing all variables, creating a session and running a tensorflow session
init = tf.global_variables_initializer()
sess = tf.Session()
sess.run(init)

#running gradient descent for each iterati
for i in range(200):
   sess.run(optimiser, feed_dict = {x:X,y:Y})#setting place holder values using feed_dict
   if i%100==0:
      print("Epoch:",i)
      print(sess.run(theta1))

and the output is:

Epoch: 0
SparseTensorValue(indices=array([[0, 0],
       [0, 1],
       [1, 1]]), values=array([0.1, 0.2, 0.1], dtype=float32), dense_shape=array([3, 2]))
Epoch: 100
SparseTensorValue(indices=array([[0, 0],
       [0, 1],
       [1, 1]]), values=array([0.1, 0.2, 0.1], dtype=float32), dense_shape=array([3, 2]))

So the only way is to use a mask matrix. You can use it by multiplication or tf.where

1) Multiplication: You can create mask matrix of the desired shape and multiply it with your weight matrix:

mask = tf.Variable([[1,0,0],[0,1,0],[0,0,1]],name ='mask', trainable=False)
weight = tf.cast(tf.Variable(tf.random_normal([3,3])),tf.float32)
desired_tensor = tf.matmul(weight, mask)

2) tf.where

mask = tf.Variable([[1,0,0],[0,1,0],[0,0,1]],name ='mask', trainable=False)
weight = tf.cast(tf.Variable(tf.random_normal([3,3])),tf.float32)
desired_tensor = tf.where(mask > 0, tf.ones_like(weight), weight)

Hope it helps

---

You can do that by using sparse tensors like so:

SparseTensor(indices=[[0, 0], [1, 2]], values=[1, 2], dense_shape=[3, 4])

and the output is:

[[1, 0, 0, 0]
 [0, 0, 2, 0]
 [0, 0, 0, 0]]

you can look up more on the documentation of sparse tensor here:

https://www.tensorflow.org/api_docs/python/tf/sparse/SparseTensor

Hope it helps!

Answer 2

I have written exactly such a layer:

https://github.com/ArnovanHilten/GenNet/blob/master/GenNet_utils/LocallyDirectedConnected_tf2.py

It takes a sparse matrix as an input and lets you decide how to connect between layers. The layer uses sparse tensors and matrix multiplications.