clip_grad_norm (which is actually deprecated in favor of clip_grad_norm_ following the more consistent syntax of a trailing _ when in-place modification is performed) clips the norm of the overall gradient by concatenating all parameters passed to the function, as can be seen from the documentation:

The norm is computed over all gradients together, as if they were concatenated into a single vector. Gradients are modified in-place.

From your example it looks like that you want clip_grad_value_ instead which has a similar syntax and also modifies the gradients in-place:

clip_grad_value_(model.parameters(), clip_value)

Another option is to register a backward hook. This takes the current gradient as an input and may return a tensor which will be used in-place of the previous gradient, i.e. modifying it. This hook is called each time after a gradient has been computed, i.e. there's no need for manually clipping once the hook has been registered:

for p in model.parameters():
    p.register_hook(lambda grad: torch.clamp(grad, -clip_value, clip_value))

For anyone, who is having the same problem like me a few minutes ago:

For about two years it is also possible to have column-dependent bounds in torch.clamp (see PR):

In: x = torch.randn(2, 3)
        print(x)

Out: tensor([[-0.2069, 1.4082, 0.2615],
             [0.6478, 0.0883, -0.7795]])

Setting a lower and upper bound:

lower = torch.Tensor([[-1., 0., 0.]])
upper = torch.Tensor([[0., 1., 1.]])

Now you can simply use torch.clamp as follows:

In: clamped_x = torch.clamp(x, min=lower, max=upper)
    print(clamped_x)

Out: tensor([[-0.2069, 1.0000, 0.2615],
             [0.0000, 0.0883, 0.0000]])

I hope that helps :)