Parametrization Functionality (pytorch#33344)

Summary:
Provides the implementation for feature request issue pytorch#28937.

Adds the `Parametrization` functionality and implements `Pruning` on top of it.
It adds the `auto` mode, on which the parametrization is just computed once per forwards pass. The previous implementation computed the pruning on every forward, which is not optimal when pruning RNNs for example.

It implements a caching mechanism for parameters. This is implemented through the mechanism proposed at the end of the discussion pytorch#7313. In particular, it assumes that the user will not manually change the updated parameters between the call to `backwards()` and the `optimizer.step()`. If they do so, they would need to manually call the `.invalidate()` function provided in the implementation. This could be made into a function that gets a model and invalidates all the parameters in it. It might be the case that this function has to be called in the `.cuda()` and `.to` and related functions.

As described in pytorch#7313, this could be used, to implement in a cleaner way the `weight_norm` and `spectral_norm` functions. It also allows, as described in pytorch#28937, for the implementation of constrained optimization on manifolds (i.e. orthogonal constraints, positive definite matrices, invertible matrices, weights on the sphere or the hyperbolic space...)

TODO (when implementation is validated):
- More thorough test
- Documentation

Resolves  pytorch#28937

albanD

Pull Request resolved: pytorch#33344

Reviewed By: zhangguanheng66

Differential Revision: D26816708

Pulled By: albanD

fbshipit-source-id: 07c8f0da661f74e919767eae31335a9c60d9e8fe

Author: lezcano

docs/source/nn.rst

@@ -346,11 +346,21 @@ From the ``torch.nn.utils`` module
     parameters_to_vector
     vector_to_parameters
 
+.. autosummary::
+    :toctree: generated
+    :nosignatures:
+
+    parametrize.register_parametrization
+    parametrize.remove_parametrizations
+    parametrize.cached
+    parametrize.is_parametrized
+
 .. autosummary::
     :toctree: generated
     :nosignatures:
     :template: classtemplate.rst
 
+    parametrize.ParametrizationList
     prune.BasePruningMethod
 
 .. autosummary::

test/test_nn.py

@@ -27,6 +27,7 @@
 import torch.nn.init as init
 import torch.nn.utils.rnn as rnn_utils
 from torch.nn.utils import clip_grad_norm_, clip_grad_value_
+import torch.nn.utils.parametrize as parametrize
 import torch.nn.utils.prune as prune
 from torch.nn.utils import parameters_to_vector, vector_to_parameters
 from torch.nn import Parameter
@@ -1939,6 +1940,354 @@ def test_vector_to_parameters(self):
         sample = next(model.parameters())[0, 0, 0]
         self.assertTrue(torch.equal(sample.data, vec.data[:5]))
 
+    # torch/nn/utils/parametrize
+    def test_register_and_remove_parametrization(self):
+        r"""Test that it is possible to add a few parametrizations
+        on a parameter or a buffer and that removing them restores the initial state
+        It also tests that backpropagating through them works as expected
+        """
+        # Define a couple matrix parametrizations
+        class Skew(nn.Module):
+            def forward(self, X):
+                X = X.tril(-1)
+                return X - X.T
+
+        class Orthogonal(nn.Module):
+            def forward(self, X):
+                # Cayley map
+                # If X is skew-symmetric it returns an orthogonal matrix
+                Id = torch.eye(X.size(0), device=X.device)
+                return torch.solve(Id - X, Id + X).solution
+
+        # Define a couple vector parametrizations
+        class FirstZero(nn.Module):
+            def forward(self, x):
+                return torch.cat([x.new_zeros(1), x[1:]])
+
+        class LastZero(nn.Module):
+            def forward(self, x):
+                return torch.cat([x[:-1], x.new_zeros(1)])
+
+        model = nn.Linear(8, 8)
+        initial_weight_id = id(model.weight)
+        initial_bias_id = id(model.bias)
+        initial_model = deepcopy(model)
+
+        # Test one parametrization
+        parametrize.register_parametrization(model, "weight", Skew())
+        self.assertTrue(hasattr(model, "parametrizations"))
+        self.assertTrue(parametrize.is_parametrized(model))
+        self.assertTrue(parametrize.is_parametrized(model, "weight"))
+        self.assertFalse(parametrize.is_parametrized(model, "bias"))
+        self.assertNotIn("weight", model._parameters)
+        # Result should be skew-symmetric
+        A = model.weight
+        self.assertTrue(torch.allclose(A, -A.T))
+        # Remove and check consistency
+        parametrize.remove_parametrizations(model, "weight", leave_parametrized=False)
+        self.assertFalse(hasattr(model, "parametrizations"))
+        self.assertEqual(model.weight, initial_model.weight)
+        self.assertEqual(id(model.weight), initial_weight_id)
+        self.assertEqual(model.__class__, nn.Linear)
+
+        # Test two parametrizations at the same time and removing them
+        parametrize.register_parametrization(model, "weight", Skew())
+        parametrize.register_parametrization(model, "weight", Orthogonal())
+        # Result should be orthogonal
+        X = model.weight
+        Id = torch.eye(X.size(0), device=X.device)
+        self.assertTrue(torch.allclose(X.T @ X, Id))
+        # Structure tests
+        self.assertTrue(hasattr(model, "parametrizations"))
+        self.assertTrue(parametrize.is_parametrized(model))
+        self.assertTrue(parametrize.is_parametrized(model, "weight"))
+        self.assertFalse(parametrize.is_parametrized(model, "bias"))
+        self.assertIn("weight", model.parametrizations)
+        self.assertNotIn("weight", model._parameters)
+        # Remove
+        parametrize.remove_parametrizations(model, "weight", leave_parametrized=False)
+        self.assertEqual(model.weight, initial_model.weight)
+        self.assertEqual(id(model.weight), initial_weight_id)
+        self.assertFalse(hasattr(model, "parametrizations"))
+        self.assertEqual(model.__class__, nn.Linear)
+
+        # Add everything
+        parametrize.register_parametrization(model, "weight", Skew())
+        parametrize.register_parametrization(model, "weight", Orthogonal())
+        parametrize.register_parametrization(model, "bias", FirstZero())
+        parametrize.register_parametrization(model, "bias", LastZero())
+
+        # Basic tests
+        self.assertTrue(parametrize.is_parametrized(model))
+        self.assertTrue(parametrize.is_parametrized(model, "weight"))
+        self.assertTrue(parametrize.is_parametrized(model, "bias"))
+        self.assertEqual(model.bias[0].item(), 0.)
+        self.assertEqual(model.bias[-1].item(), 0.)
+        self.assertEqual(len(list(model.parameters())), 2)  # Nothing weird has happpened
+        # Should not throw
+        (model.weight.T @ model.bias).sum().backward()
+        with torch.no_grad():
+            for p in model.parameters():
+                p.add_(- p.grad, alpha=0.01)
+
+        # Remove first parametrization.
+        # Check that the model is still parametrized and so is the second parameter
+        parametrize.remove_parametrizations(model, "weight", leave_parametrized=False)
+        self.assertTrue(parametrize.is_parametrized(model))  # Still parametrized
+        self.assertFalse(parametrize.is_parametrized(model, "weight"))  # Parametrization removed
+        self.assertTrue(parametrize.is_parametrized(model, "bias"))  # Still parametrized
+        self.assertEqual(model.bias[0].item(), 0.)   # Still parametrized
+        self.assertEqual(model.bias[-1].item(), 0.)  # Still parametrized
+        self.assertNotEqual(model.weight, initial_model.weight)  # Has been updated
+        self.assertEqual(id(model.weight), initial_weight_id)  # Keeps the same id
+        self.assertEqual(len(list(model.parameters())), 2)  # Nothing weird has happened
+        # Should not throw
+        (model.weight.T @ model.bias).sum().backward()
+        with torch.no_grad():
+            for p in model.parameters():
+                p.add_(- p.grad, alpha=0.01)
+
+        # Remove the second parametrization.
+        # Check that the module is not parametrized
+        parametrize.remove_parametrizations(model, "bias", leave_parametrized=False)
+        self.assertFalse(parametrize.is_parametrized(model))  # Still parametrized
+        self.assertNotEqual(model.bias, initial_model.bias)  # Has been updated
+        self.assertNotEqual(model.bias[0].item(), 0.)   # Still parametrized
+        self.assertNotEqual(model.bias[-1].item(), 0.)  # Still parametrized
+        self.assertEqual(id(model.bias), initial_bias_id)
+        self.assertFalse(hasattr(model, "parametrizations"))
+        self.assertEqual(model.__class__, nn.Linear)
+        self.assertEqual(len(list(model.parameters())), 2)
+        # Should not throw
+        (model.weight.T @ model.bias).sum().backward()
+        with torch.no_grad():
+            for p in model.parameters():
+                p.add_(- p.grad, alpha=0.01)
+
+    def test_register_and_remove_buffer_parametrization(self):
+        r"""Test that it is possible to add and remove parametrizations on buffers"""
+        # Define a couple vector parametrizations
+        class FirstZero(nn.Module):
+            def forward(self, x):
+                return torch.cat([x.new_zeros(1), x[1:]])
+
+        class LastZero(nn.Module):
+            def forward(self, x):
+                return torch.cat([x[:-1], x.new_zeros(1)])
+
+        model = nn.Linear(8, 8)
+
+        # Instantiate parametrizations on buffers. It should work as expected
+        delattr(model, "bias")
+        model.register_buffer("bias", torch.ones(8))
+        parametrize.register_parametrization(model, "bias", FirstZero())
+        parametrize.register_parametrization(model, "bias", LastZero())
+        self.assertTrue(parametrize.is_parametrized(model))
+        self.assertTrue(parametrize.is_parametrized(model, "bias"))
+        self.assertEqual(model.bias[0].item(), 0.)
+        self.assertEqual(model.bias[-1].item(), 0.)
+        self.assertTrue((model.bias[1:-1] == torch.ones(6)).all())
+        self.assertEqual(len(list(model.parameters())), 1)
+
+        # Remove parametrizations on buffers. It should work as expected
+        parametrize.remove_parametrizations(model, "bias", leave_parametrized=True)
+        self.assertFalse(parametrize.is_parametrized(model))
+        self.assertFalse(parametrize.is_parametrized(model, "bias"))
+        self.assertEqual(model.bias[0].item(), 0.)
+        self.assertEqual(model.bias[-1].item(), 0.)
+        self.assertTrue((model.bias[1:-1] == torch.ones(6)).all())
+        self.assertEqual(len(list(model.parameters())), 1)
+
+    def test_serialization_parametrization(self):
+        r"""Test that it is possible to serialize a parametrized model via state_dict"""
+        # A stateful parametrization
+        class Orthogonal(nn.Module):
+            def __init__(self, n):
+                super().__init__()
+                self.register_buffer("id", torch.eye(n))
+                self.register_buffer("B", torch.empty(n, n))
+                init.orthogonal_(self.B)
+
+            def forward(self, X):
+                A = X.triu(1)
+                A = A - A.T
+                return self.B @ torch.solve(self.id - A, self.id + A).solution
+
+        def get_model():
+            model = torch.nn.Sequential(
+                torch.nn.Linear(5, 5),
+                torch.nn.ReLU(),
+                torch.nn.Linear(5, 1),
+            )
+
+            parametrize.register_parametrization(model[0], "weight", Orthogonal(5))
+            return model
+
+        model = get_model()
+
+        prev_weight = model[0].weight
+        prev_B = model[0].parametrizations.weight[0].B
+
+        new_model = get_model()
+        with TemporaryFileName() as fname:
+            torch.save(model.state_dict(), fname)
+            new_model.load_state_dict(torch.load(fname))
+
+        # Integrity tests
+        self.assertTrue(parametrize.is_parametrized(new_model[0], "weight"))
+        self.assertEqual(prev_weight, new_model[0].weight)
+        self.assertEqual(prev_B, new_model[0].parametrizations.weight[0].B)
+
+        # Trying to save the whole parametrized model raises
+        with self.assertRaisesRegex(RuntimeError, "state_dict"):
+            with TemporaryFileName() as fname:
+                torch.save(model, fname)
+
+    def test_initialization_parametrization(self):
+        r"""Test that it is possible to initialize a parametrization when it
+            implements a `right_inverse` method
+        """
+        class Skew(nn.Module):
+            def forward(self, X):
+                A = X.triu(1)
+                return A - A.T
+
+            def is_skew(self, A):
+                return torch.allclose(A, -A.T, atol=1e-6)
+
+            def right_inverse(self, X):
+                if not self.is_skew(X):
+                    raise ValueError("The matrix is not skew-symmetric.")
+                return X.triu(1)
+
+        # Implements a Cayley map where right_inverse is not quite the inverse of forward
+        class Orthogonal(nn.Module):
+            def __init__(self, n):
+                super().__init__()
+                self.register_buffer("B", torch.eye(n))
+
+            def forward(self, A):
+                Id = torch.eye(X.size(0))
+                return self.B @ torch.solve(Id - A, Id + A).solution
+
+            def is_orthogonal(self, X):
+                Id = torch.eye(X.size(0))
+                return torch.allclose(X.T @ X, Id, atol=1e-4)
+
+            def right_inverse(self, X):
+                if not self.is_orthogonal(X):
+                    raise ValueError("The input is not orthogonal.")
+                # cayley(0) == Id, so B @ cayley(0) == B
+                self.B = X
+                return torch.zeros_like(X)
+
+        N = 5
+        model = nn.Linear(N, N)
+        # Register the skew-symmetric onstraint. The result is now skew-symmetric
+        parametrize.register_parametrization(model, "weight", Skew())
+        X = torch.rand(N, N)
+        # X is not skew-symmetric, so it throws an error
+        with self.assertRaises(ValueError):
+            model.weight = X
+        # Make X skew-symmetric
+        X = X - X.T
+        model.weight = X
+        self.assertEqual(model.parametrizations.weight.original, X.triu(1))
+        self.assertEqual(model.weight, X)
+
+        # Having several parametrizations registered should work in the same way
+        parametrize.register_parametrization(model, "weight", Orthogonal(N))
+        # Register now the Cayley map. The result is now orthogonal
+        X = torch.rand(N, N)
+        # X is not orthogonal, so it throws an error
+        with self.assertRaises(ValueError):
+            model.weight = X
+        init.orthogonal_(X)
+        model.weight = X
+        self.assertEqual(model.weight, X)
+        self.assertEqual(model.parametrizations.weight.original, torch.zeros_like(X))
+
+    def test_errors_parametrization(self):
+        # A parametrization shall not change the size of the parameter
+        class ChangeSize(nn.Module):
+            def forward(self, x):
+                return x[:-1]
+
+        # A simple parametrization that does not implement a right_inverse
+        class Double(nn.Module):
+            def forward(self, x):
+                return 2 * x
+
+        module = nn.Linear(3, 4)
+        # This should not throw when registering
+        parametrize.register_parametrization(module, "weight", ChangeSize())
+        # It throws in the forward
+        with self.assertRaisesRegex(RuntimeError, "may not change the size"):
+            module(torch.rand(2))
+        # Undo
+        parametrize.remove_parametrizations(module, "weight", leave_parametrized=False)
+        self.assertFalse(parametrize.is_parametrized(module))
+
+        # Removing a parametrization from an unparametrized tensor throws
+        with self.assertRaisesRegex(ValueError, "does not have a parametrization"):
+            parametrize.remove_parametrizations(module, "bias")
+        # Nothing odd happens
+        self.assertFalse(parametrize.is_parametrized(module))
+
+        # Register a parametrization on a non-existing parameter breaks
+        with self.assertRaisesRegex(ValueError, "does not have a parameter"):
+            parametrize.register_parametrization(module, "foo", ChangeSize())
+        self.assertFalse(parametrize.is_parametrized(module))
+
+        # Try to assign to a parametrization that does not implement `right_inverse`
+        parametrize.register_parametrization(module, "weight", Double())
+        with self.assertRaisesRegex(RuntimeError, "right_inverse"):
+            module.weight = torch.rand(4, 3)
+        # Undo
+        parametrize.remove_parametrizations(module, "weight", leave_parametrized=False)
+        self.assertFalse(parametrize.is_parametrized(module))
+
+    def test_caching_parametrization(self):
+        r"""Test the caching system of a parametrization"""
+        # Define a couple matrix parametrizations
+        class Skew(nn.Module):
+            def forward(self, X):
+                X = X.tril(-1)
+                return X - X.T
+
+        class Orthogonal(nn.Module):
+            def forward(self, X):
+                Id = torch.eye(X.size(0), device=X.device)
+                return torch.solve(Id - X, Id + X).solution
+
+        model = nn.Linear(5, 5)
+        parametrize.register_parametrization(model, "weight", Skew())
+        parametrize.register_parametrization(model, "weight", Orthogonal())
+
+        # Test that the caching system works
+        with parametrize.cached():
+            X = model.weight
+            Y = model.weight
+            self.assertEqual(id(X), id(Y))
+
+    def test_dtype_parametrization(self):
+        r"""Test a case that is not allowed when removing a parametrization"""
+        class ChangeType(nn.Module):
+            def forward(self, X):
+                return X.double()
+
+        module = nn.Linear(4, 4).float()
+        input_ = torch.rand(4).double()
+        # It is allowed to register a parametrization that changes the dtype
+        parametrize.register_parametrization(module, "weight", ChangeType())
+        module(input_)
+        # We can remove it leaving the original tensor
+        parametrize.remove_parametrizations(module, "weight", leave_parametrized=False)
+        # But leaving it parametrized breaks
+        parametrize.register_parametrization(module, "weight", ChangeType())
+        with self.assertRaisesRegex(ValueError, "changes the dtype"):
+            parametrize.remove_parametrizations(module, "weight", leave_parametrized=True)
+
     # torch/nn/utils/prune.py
     @unittest.skipIf(not TEST_NUMPY, "numpy not found")
     def test_validate_pruning_amount_init(self):