CODEWITHSUNDEEP
tensorflow
Alex Allen
Alex Allen

Reputation: 39

hessian of a variable returned by tf.concat() is None

Let x and y be vectors of length N, and z is a function z = f(x,y). In Tensorflow v1.0.0, tf.hessians(z,x) and tf.hessians(z,y) both returns an N by N matrix, which is what I expected.

However, when I concatenate the x and y into a vector p of size 2*N using tf.concat, and run tf.hessian(z, p), it returns error "ValueError: None values not supported."

I understand this is because in the computation graph x,y ->z and x,y -> p, so there is no gradient between p and z. To circumvent the problem, I can create p first, slice it into x and y, but I will have to change a ton of my code. Is there a more elegant way?

related question: Slice of a variable returns gradient None

import tensorflow as tf
import numpy as np

N = 2
A = tf.Variable(np.random.rand(N,N).astype(np.float32))
B = tf.Variable(np.random.rand(N,N).astype(np.float32))

x = tf.Variable(tf.random_normal([N]) )
y = tf.Variable(tf.random_normal([N]) )

#reshape to N by 1
x_1 = tf.reshape(x,[N,1])
y_1 = tf.reshape(y,[N,1])

#concat x and y to form a vector with length of 2*N
p = tf.concat([x,y],axis = 0)

#define the function
z = 0.5*tf.matmul(tf.matmul(tf.transpose(x_1), A), x_1) + 0.5*tf.matmul(tf.matmul(tf.transpose(y_1), B), y_1) + 100

#works , hx and hy are both N by N matrix
hx = tf.hessians(z,x)
hy = tf.hessians(z,y)

#this gives error "ValueError: None values not supported."
#expecting a matrix of size 2*N by 2*N
hp = tf.hessians(z,p)

Upvotes: 0

Views: 419

Answers (1)

LI Xuhong
LI Xuhong

Reputation: 2356

Compute the hessian by its definition.

gxy = tf.gradients(z, [x, y])
gp = tf.concat([gxy[0], gxy[1]], axis=0)
hp = []
for i in range(2*N):
    hp.append(tf.gradients(gp[i], [x, y]))

Because tf.gradients computes the sum of (dy/dx), so when computing the second partial derivative, one should slice the vector into scalars and then compute the gradient. Tested on tf1.0 and python2.

Upvotes: 1

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