Hello, I’m trying to understand why the gradient returned by autograd does not change w.r.t. the input in a Gaussian kernel. More specifically, suppose we have the following naive implementation of the RBF kernel:

```
def naive_rbf(X, Y, h):
batch, _ = X.shape
Kxy = torch.empty(batch, batch)
dx_Kxy = torch.zeros_like(X)
dy_Kxy = torch.zeros_like(X)
for i in range(batch):
for j in range(batch):
# using row vectors
diff = X[i] - Y[j]
norm = diff @ diff.T
Kxy[i, j] = (-0.5 / h ** 2 * norm).exp()
dx_Kxy[i] += -diff * Kxy[i, j] / h ** 2
dy_Kxy[j] += diff * Kxy[i, j] / h ** 2
return Kxy, dx_Kxy, dy_Kxy
```

So, given that:

I’d expect the gradients w.r.t. different inputs to have opposite signs.

However, if I run:

```
BATCH, DIM = [20, 5]
X = torch.randn(BATCH, DIM)
h = torch.tensor(1.0)
Xg = X.clone().requires_grad_()
K = naive(Xg, X, h)[0]
dx_K = grad(K.sum(), Xg, h)[0]
Xg = X.clone().requires_grad_()
K = naive(X, Xg, h)[0]
dy_K = grad(K.sum(), Xg, h)[0]
torch.allclose(dx_K, dy_K) # True
```

Can anyone shed some light on why this happens?