I reported this in #8133, but I think it got lost in my confusion about scalar values in mxnet. But I think this deserves a separate issue.

Unlike numpy, mxnet doesn't support rank 0 arrays, but uses an empty tuple to represent unknown shapes. mx.nd still allows the creation of rank 0 arrays however. This leads to confusion during shape inference and allows out of bounds memory reads and writes:

a = mx.sym.var('a')
b = mx.sym.var('b')
c = a + b

a_ = mx.nd.ones(()) # Has size 1, but bind assumes it has shape (5,)
b_ = mx.nd.ones(5)
func = c.bind(mx.cpu(), {'a': a_, 'b': b_})
func.forward()
func.outputs[0].asnumpy()
array([  2.00000000e+00,   2.52435490e-29,   8.84247875e+05,
         1.08446609e-19,  -1.92860745e-26], dtype=float32)

We can write to invalid memory (and crash the process or potentially get arbitrary code execution) by providing a gradient buffer with the wrong shape

a = mx.sym.var('a')
c = mx.sym.MakeLoss(a)

grad = mx.nd.ones(())
a_ = mx.nd.ones(500)
func = c.bind(mx.cpu(), {'a': a_}, args_grad={'a': grad})
func.forward()
func.backward()