einsum not giving overflow error when applied to int arrays

Question

I just had a bug which was based on np.sum and an equivalent (or at least I thought so...) np.einsum command not giving the same result. Here is an example:

import numpy.random
array = np.random.randint(-10000, 10000, size=(4, 100, 200, 600), dtype=np.int16)

sum1 = np.sum(array, axis=(0,1,2))
sum2 = np.einsum('aijt->t', array)

print(np.allclose(sum1, sum2))

plt.figure()
plt.plot(sum1)
plt.plot(sum2)
plt.show()

After some searching, this is due to overflow of the integer data type.

My question:

• Why is np.einsum not giving the same result as np.sum here? I feel the np.sum behaviour is a lot more desirable leading to less errors.
• Why does np.einsum not throw an overflow error or at least a warning? This is super scary in terms of getting hidden bugs when using it. Should I be checking for those by hand every time I use the command?
• Would this considered be a bug in numpy?