Gradient is nan whenever exponent is <1

Questions
3

Thanks! I think I solved the original problem, but another problem occurs where something stranger might be going on. Here is some more code:

def print_value_theano(value, wrt):
    tt.printing.Print('value')(
        value
    )
    tt.printing.Print('grad')(
        tt.jacobian(value.flatten(), wrt)
    )
    print('\n')


with pm.Model() as model_test:
    
    beta = pm.Exponential(
        'beta',
        lam=0.5,
        testval=2.
    )
    
    ap = np.array([1.])+beta 
    bp = np.array([1.])+beta
    
    # This is fine!
    print_value_theano(
        (ap*bp)**0.9,
        beta
    )
        
    zeros = tt.zeros(1)
    a = tt.concatenate((zeros, ap))
    b = tt.concatenate((zeros, bp))
    
    # This is fine!
    print_value_theano(
        (a*b)**0.9, 
        beta
    )
    
    # same result with: 
    # value = a[:,np.newaxis,np.newaxis] * b[:,np.newaxis,np.newaxis,np.newaxis]
    value = tt.shape_padright(a, 2) * tt.shape_padright(b, 4)
    
    # The gradient of this is all NAN!!
    print_value_theano(
        value**0.9, 
        beta
    )

This prints out:

value __str__ = [7.22467406]
grad __str__ = [4.33480443]


value __str__ = [0.         7.22467406]
grad __str__ = [0.         4.33480443]


value __str__ = [[[[[0.        ]]
   [[0.        ]]]]
 [[[[0.        ]]
   [[7.22467406]]]]]
grad __str__ = [nan nan nan nan]

Note that (a*b)**0.9 has a well-defined gradient, but the padding breaks things. Maybe this is still related to the gradient as such, but I don’t see how the padding would make a difference here. Thanks again for the help!