EE-559 Deep learning 1.6. Tensor internals
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1 EE-559 Deep learning 1.6. Tensor internals François Fleuret Tue Feb 26 15:45:36 UTC 2019 ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
2 A tensor is a view of a [part of a] storage, which is a low-level 1d vector. = torch.zeros(2, 4).storage() [torch.floatstorage of size 8] >>> q = x.storage() >>> q[4] = 1.0 tensor([[ 0., 0., 0., 0.], [ 1., 0., 0., 0.]]) François Fleuret EE-559 Deep learning / 1.6. Tensor internals 1 / 5
3 Multiple tensors can share the same storage. It happens when using operations such as view(), expand() or transpose(). >>> y = x.view(2, 2, 2) >>> y tensor([[[ 0., 0.], [ 0., 0.]], [[ 1., 0.], [ 0., 0.]]]) >>> y[1, 1, 0] = 7.0 tensor([[ 0., 0., 0., 0.], [ 1., 0., 7., 0.]]) >>> y.narrow(0, 1, 1).fill_(3.0) tensor([[[ 3., 3.], [ 3., 3.]]]) tensor([[ 0., 0., 0., 0.], [ 3., 3., 3., 3.]]) François Fleuret EE-559 Deep learning / 1.6. Tensor internals 2 / 5
4 The first coefficient of a tensor is the one at storage_offset() in storage(). François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
5 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
6 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. >>> q = torch.arange(0, 20).storage() = torch.empty(0).set_(q, storage_offset = 5, size = (3, 2), stride = (4, 1)) tensor([[ 5., 6.], [ 9., 10.], [ 13., 14.]]) François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
7 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. >>> q = torch.arange(0, 20).storage() = torch.empty(0).set_(q, storage_offset = 5, size = (3, 2), stride = (4, 1)) tensor([[ 5., 6.], [ 9., 10.], [ 13., 14.]]) q = François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
8 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. >>> q = torch.arange(0, 20).storage() = torch.empty(0).set_(q, storage_offset = 5, size = (3, 2), stride = (4, 1)) tensor([[ 5., 6.], [ 9., 10.], [ 13., 14.]]) q = x[0,0] x[0,1] x[1,0] x[1,1] x[2,0] x[2,1] François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
9 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. >>> q = torch.arange(0, 20).storage() = torch.empty(0).set_(q, storage_offset = 5, size = (3, 2), stride = (4, 1)) tensor([[ 5., 6.], [ 9., 10.], [ 13., 14.]]) offset q = x[0,0] x[0,1] x[1,0] x[1,1] x[2,0] x[2,1] François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
10 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. >>> q = torch.arange(0, 20).storage() = torch.empty(0).set_(q, storage_offset = 5, size = (3, 2), stride = (4, 1)) tensor([[ 5., 6.], [ 9., 10.], [ 13., 14.]]) offset stride(0) stride(0) q = x[0,0] x[0,1] x[1,0] x[1,1] x[2,0] x[2,1] François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
11 The first coefficient of a tensor is the one at storage_offset() in storage(). Incrementing index k by 1 move by stride(k) elements in the storage. >>> q = torch.arange(0, 20).storage() = torch.empty(0).set_(q, storage_offset = 5, size = (3, 2), stride = (4, 1)) tensor([[ 5., 6.], [ 9., 10.], [ 13., 14.]]) offset stride(0) stride(0) q = x[0,0] x[0,1] x[1,0] x[1,1] x[2,0] x[2,1] stride(1) stride(1) stride(1) François Fleuret EE-559 Deep learning / 1.6. Tensor internals 3 / 5
12 We can explicitly create different views of the same storage >>> n = torch.linspace(1, 4, 4) >>> n tensor([ 1., 2., 3., 4.]) >>> torch.tensor(0.).set_(n.storage(), 1, (3, 3), (0, 1)) tensor([[ 2., 3., 4.], [ 2., 3., 4.], [ 2., 3., 4.]]) >>> torch.tensor(0.).set_(n.storage(), 1, (2, 4), (1, 0)) tensor([[ 2., 2., 2., 2.], [ 3., 3., 3., 3.]]) François Fleuret EE-559 Deep learning / 1.6. Tensor internals 4 / 5
13 We can explicitly create different views of the same storage >>> n = torch.linspace(1, 4, 4) >>> n tensor([ 1., 2., 3., 4.]) >>> torch.tensor(0.).set_(n.storage(), 1, (3, 3), (0, 1)) tensor([[ 2., 3., 4.], [ 2., 3., 4.], [ 2., 3., 4.]]) >>> torch.tensor(0.).set_(n.storage(), 1, (2, 4), (1, 0)) tensor([[ 2., 2., 2., 2.], [ 3., 3., 3., 3.]]) This is in particular how transpositions and broadcasting are implemented. = torch.empty(100, 100).stride() (100, 1) >>> y = x.t() >>> y.stride() (1, 100) François Fleuret EE-559 Deep learning / 1.6. Tensor internals 4 / 5
14 This organization explains the following (maybe surprising) error = torch.empty(100, 100).t().view(-1) Traceback (most recent call last): File "<stdin>", line 1, in <module> RuntimeError: invalid argument 2: view size is not compatible with input tensor s size and stride (at least one dimension spans across two contiguous subspaces). Call.contiguous() before.view() x.t() shares x s storage and cannot be flattened to 1d. François Fleuret EE-559 Deep learning / 1.6. Tensor internals 5 / 5
15 This organization explains the following (maybe surprising) error = torch.empty(100, 100).t().view(-1) Traceback (most recent call last): File "<stdin>", line 1, in <module> RuntimeError: invalid argument 2: view size is not compatible with input tensor s size and stride (at least one dimension spans across two contiguous subspaces). Call.contiguous() before.view() x.t() shares x s storage and cannot be flattened to 1d. This can be fixed with contiguous(), which returns a contiguous version of the tensor, making a copy if needed. The function reshape() combines view() and contiguous(). François Fleuret EE-559 Deep learning / 1.6. Tensor internals 5 / 5
16 The end
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