原文
Easily extensible autograd implemented python with pytorch API. Uses numpy to do the heavy-lifting. Implementation is very similar to pytorch (graph-based reverse-mode autodiff). It wouldn't be too tough to extend the autograd, implement torch.nn, and possibly run on GPU (presumably with CuPy or Numba). It would be an interesting (but useless) endeavor to rewrite mytorch in a low level language using BLAS library calls instead on numpy, just like pytorch.
mytorch supports the computation of arbitrarily high derivatives for both scalars and non-scalars. Both torch.autograd.backward and torch.autograd.grad are supported.
import mytorch as torch
a = torch.tensor(3., dtype=torch.float32, requires_grad=True)
b = torch.tensor(10., dtype=torch.float32, requires_grad=True)
c = 2 + (a + b ** 2) / (a + b + a * b)
print("a =", a)
print("b =", b)
print("c = 2 + (a + b ** 2) / (a + b + a * b) =", c)
# NOTE: You could also use c.backward() to accumulate the gradients in a.grad and b.grad
dc_da, dc_db = torch.autograd.grad(c, [a, b])
# NOTE: To get higher order derivatives like below, pytorch would require ∂c/∂a and
# ∂c/∂b to be calculated with create_graph=True; mytorch does not require it
d2c_da2 = torch.autograd.grad(dc_da, [a])[0]
d2c_db2 = torch.autograd.grad(dc_db, [b])[0]
print(f"∂c/∂a = {dc_da}")
print(f"∂c/∂b = {dc_db}")
print(f"∂²c/∂a² = {d2c_da2}")
print(f"∂²c/∂b² = {d2c_db2}")Output:
a = tensor(3.0, requires_grad=True)
b = tensor(10.0, requires_grad=True)
c = 2 + (a + b ** 2) / (a + b + a * b)
= tensor(4.395348787307739, requires_grad=True)
∂c/∂a = tensor(-0.5895078420767982, requires_grad=True)
∂c/∂b = tensor(0.24229313142239048, requires_grad=True)
∂²c/∂a² = tensor(0.3016086633881293, requires_grad=True)
∂²c/∂b² = tensor(0.0014338360144389717, requires_grad=True)Here is a non-scalar example (with broadcasting):
import mytorch as torch
a = torch.tensor([[1, 2, 3], [4, 5, 6]], dtype=torch.float32, requires_grad=True)
b = torch.tensor([7, 8, 9], dtype=torch.float32, requires_grad=True)
# b is broadcasted
c = a + b
print("a =", a)
print("b =", b)
print("c =", c)
c.backward(torch.ones(2, 3))
print("∂c/∂a =", a.grad)
print("∂c/∂b =", b.grad)Output:
a = tensor([[1. 2. 3.]
[4. 5. 6.]], requires_grad=True)
b = tensor([7. 8. 9.], requires_grad=True)
c = tensor([[ 8. 10. 12.]
[11. 13. 15.]], requires_grad=True)
∂c/∂a = tensor([[1. 1. 1.]
[1. 1. 1.]], requires_grad=False)
∂c/∂b = tensor([2. 2. 2.], requires_grad=False)