def test_basic_relu_multi_input(self) -> None: model = BasicModel2() input1 = torch.tensor([[3.0]]) input2 = torch.tensor([[1.0]], requires_grad=True) baseline1 = torch.tensor([[0.0]]) baseline2 = torch.tensor([[0.0]]) inputs = (input1, input2) baselines = (baseline1, baseline2) gs = GradientShap(model) n_samples = 30000 attributions, delta = cast( Tuple[Tuple[Tensor, ...], Tensor], gs.attribute( inputs, baselines=baselines, n_samples=n_samples, return_convergence_delta=True, ), ) _assert_attribution_delta(self, inputs, attributions, n_samples, delta) ig = IntegratedGradients(model) attributions_ig = ig.attribute(inputs, baselines=baselines) self._assert_shap_ig_comparision(attributions, attributions_ig)
def _assert_compare_with_emb_patching(self, input, baseline, additional_args): model = BasicEmbeddingModel(nested_second_embedding=True) lig = LayerIntegratedGradients(model, model.embedding1) attributions, delta = lig.attribute( input, baselines=baseline, additional_forward_args=additional_args, return_convergence_delta=True, ) # now let's interpret with standard integrated gradients and # the embeddings for monkey patching interpretable_embedding = configure_interpretable_embedding_layer( model, "embedding1" ) input_emb = interpretable_embedding.indices_to_embeddings(input) baseline_emb = interpretable_embedding.indices_to_embeddings(baseline) ig = IntegratedGradients(model) attributions_with_ig, delta_with_ig = ig.attribute( input_emb, baselines=baseline_emb, additional_forward_args=additional_args, target=0, return_convergence_delta=True, ) remove_interpretable_embedding_layer(model, interpretable_embedding) assertArraysAlmostEqual(attributions, attributions_with_ig) assertArraysAlmostEqual(delta, delta_with_ig)
def _assert_attributions( self, model: Module, attributions: Tensor, inputs: Tensor, baselines: Union[Tensor, int, float], delta: Tensor, target: TargetType = None, ) -> None: self.assertEqual(inputs.shape, attributions.shape) delta_condition = all(abs(delta.numpy().flatten()) < 0.003) self.assertTrue( delta_condition, "The sum of attribution values {} is not " "nearly equal to the difference between the endpoint for " "some samples".format(delta), ) # compare with integrated gradients if isinstance(baselines, (int, float)) or inputs.shape == baselines.shape: ig = IntegratedGradients(model) attributions_ig = ig.attribute(inputs, baselines=baselines, target=target) assertAttributionComparision(self, attributions, attributions_ig)
def test_batched_input_smoothgrad_wo_mutliplying_by_inputs(self) -> None: model = BasicModel_MultiLayer() inputs = torch.tensor( [[1.5, 2.0, 1.3], [0.5, 0.1, 2.3], [1.5, 2.0, 1.3]], requires_grad=True ) ig_wo_mutliplying_by_inputs = IntegratedGradients( model, multiply_by_inputs=False ) nt_wo_mutliplying_by_inputs = NoiseTunnel(ig_wo_mutliplying_by_inputs) ig = IntegratedGradients(model) nt = NoiseTunnel(ig) n_samples = 5 target = 0 type = "smoothgrad" attributions_wo_mutliplying_by_inputs = nt_wo_mutliplying_by_inputs.attribute( inputs, nt_type=type, nt_samples=n_samples, stdevs=0.0, target=target, n_steps=500, ) with self.assertWarns(DeprecationWarning): attributions = nt.attribute( inputs, nt_type=type, n_samples=n_samples, stdevs=0.0, target=target, n_steps=500, ) assertTensorAlmostEqual( self, attributions_wo_mutliplying_by_inputs * inputs, attributions )
def __init__( self, forward_func: Callable, layer: Module, device_ids: Optional[List[int]] = None, ) -> None: r""" Args: forward_func (callable): The forward function of the model or any modification of it layer (torch.nn.Module): Layer for which attributions are computed. Output size of attribute matches this layer's input or output dimensions, depending on whether we attribute to the inputs or outputs of the layer, corresponding to the attribution of each neuron in the input or output of this layer. device_ids (list(int)): Device ID list, necessary only if forward_func applies a DataParallel model. This allows reconstruction of intermediate outputs from batched results across devices. If forward_func is given as the DataParallel model itself, then it is not necessary to provide this argument. """ LayerAttribution.__init__(self, forward_func, layer, device_ids=device_ids) GradientAttribution.__init__(self, forward_func) self.ig = IntegratedGradients(forward_func)
def _deeplift_assert(self, model, attr_method, inputs, baselines, custom_attr_func=None): input_bsz = len(inputs[0]) if callable(baselines): baseline_parameters = signature(baselines).parameters if len(baseline_parameters) > 0: baselines = baselines(inputs) else: baselines = baselines() baseline_bsz = (len(baselines[0]) if isinstance( baselines[0], torch.Tensor) else 1) # Run attribution multiple times to make sure that it is # working as expected for _ in range(5): model.zero_grad() attributions, delta = attr_method.attribute( inputs, baselines, return_convergence_delta=True, custom_attribution_func=custom_attr_func, ) attributions_without_delta = attr_method.attribute( inputs, baselines, custom_attribution_func=custom_attr_func) for attribution, attribution_without_delta in zip( attributions, attributions_without_delta): self.assertTrue( torch.all(torch.eq(attribution, attribution_without_delta))) if isinstance(attr_method, DeepLiftShap): self.assertEqual([input_bsz * baseline_bsz], list(delta.shape)) else: self.assertEqual([input_bsz], list(delta.shape)) delta_external = attr_method.compute_convergence_delta( attributions, baselines, inputs) assertArraysAlmostEqual(delta, delta_external, 0.0) delta_condition = all(abs(delta.numpy().flatten()) < 0.00001) self.assertTrue( delta_condition, "The sum of attribution values {} is not " "nearly equal to the difference between the endpoint for " "some samples".format(delta), ) for input, attribution in zip(inputs, attributions): self.assertEqual(input.shape, attribution.shape) if (isinstance(baselines[0], (int, float)) or inputs[0].shape == baselines[0].shape): # Compare with Integrated Gradients ig = IntegratedGradients(model) attributions_ig = ig.attribute(inputs, baselines) assertAttributionComparision(self, attributions, attributions_ig)
def test_multi_target_error(self) -> None: net = BasicModel_MultiLayer() inp = torch.zeros((1, 3)) with self.assertRaises(AssertionError): attr = IntegratedGradients(net) attr.attribute(inp, additional_forward_args=(None, True), target=(1, 0))
def _compute_attribution_batch_helper_evaluate( self, model, inputs, baselines=None, target=None, additional_forward_args=None): ig = IntegratedGradients(model) if not isinstance(inputs, tuple): inputs = (inputs, ) if baselines is not None and not isinstance(baselines, tuple): baselines = (baselines, ) if baselines is None: baselines = _zeros(inputs) for method in [ "riemann_right", "riemann_left", "riemann_middle", "riemann_trapezoid", "gausslegendre", ]: for internal_batch_size in [None, 1, 20]: attributions, delta = ig.attribute( inputs, baselines, additional_forward_args=additional_forward_args, method=method, n_steps=200, target=target, internal_batch_size=internal_batch_size, return_convergence_delta=True, ) total_delta = 0 for i in range(inputs[0].shape[0]): attributions_indiv, delta_indiv = ig.attribute( tuple(input[i:i + 1] for input in inputs), tuple(baseline[i:i + 1] for baseline in baselines), additional_forward_args=additional_forward_args, method=method, n_steps=200, target=target, return_convergence_delta=True, ) total_delta += abs(delta_indiv).sum().item() for j in range(len(attributions)): assertArraysAlmostEqual( attributions[j][i:i + 1].squeeze(0).tolist(), attributions_indiv[j].squeeze(0).tolist(), ) self.assertAlmostEqual(abs(delta).sum().item(), total_delta, delta=0.005)
def _compute_attribution_batch_helper_evaluate( self, model: Module, inputs: TensorOrTupleOfTensorsGeneric, baselines: Union[None, Tensor, Tuple[Tensor, ...]] = None, target: Union[None, int] = None, additional_forward_args: Any = None, approximation_method: str = "gausslegendre", ) -> None: ig = IntegratedGradients(model) if not isinstance(inputs, tuple): inputs = (inputs, ) # type: ignore inputs: Tuple[Tensor, ...] if baselines is not None and not isinstance(baselines, tuple): baselines = (baselines, ) if baselines is None: baselines = _tensorize_baseline(inputs, _zeros(inputs)) for internal_batch_size in [None, 10, 20]: attributions, delta = ig.attribute( inputs, baselines, additional_forward_args=additional_forward_args, method=approximation_method, n_steps=100, target=target, internal_batch_size=internal_batch_size, return_convergence_delta=True, ) total_delta = 0.0 for i in range(inputs[0].shape[0]): attributions_indiv, delta_indiv = ig.attribute( tuple(input[i:i + 1] for input in inputs), tuple(baseline[i:i + 1] for baseline in baselines), additional_forward_args=additional_forward_args, method=approximation_method, n_steps=100, target=target, internal_batch_size=internal_batch_size, return_convergence_delta=True, ) total_delta += abs(delta_indiv).sum().item() for j in range(len(attributions)): assertTensorAlmostEqual( self, attributions[j][i:i + 1].squeeze(0), attributions_indiv[j].squeeze(0), delta=0.05, mode="max", ) self.assertAlmostEqual(abs(delta).sum().item(), total_delta, delta=0.005)
def _validate_completness(self, model, inputs, target, type="vanilla", baseline=None): ig = IntegratedGradients(model.forward) for method in [ "riemann_right", "riemann_left", "riemann_middle", "riemann_trapezoid", "gausslegendre", ]: model.zero_grad() if type == "vanilla": attributions, delta = ig.attribute( inputs, baselines=baseline, target=target, method=method, n_steps=1000, return_convergence_delta=True, ) delta_expected = ig.compute_convergence_delta( attributions, baseline, inputs, target) assertTensorAlmostEqual(self, delta_expected, delta) delta_condition = all(abs(delta.numpy().flatten()) < 0.003) self.assertTrue( delta_condition, "The sum of attribution values {} is not " "nearly equal to the difference between the endpoint for " "some samples".format(delta), ) self.assertEqual([inputs.shape[0]], list(delta.shape)) else: nt = NoiseTunnel(ig) n_samples = 10 attributions, delta = nt.attribute( inputs, baselines=baseline, nt_type=type, n_samples=n_samples, stdevs=0.0002, n_steps=1000, target=target, method=method, return_convergence_delta=True, ) self.assertEqual([inputs.shape[0] * n_samples], list(delta.shape)) self.assertTrue(all(abs(delta.numpy().flatten()) < 0.05)) self.assertEqual(attributions.shape, inputs.shape)
def _validate_completness( self, model: Module, input: Tensor, target: Tensor, type: str = "vanilla", approximation_method: str = "gausslegendre", baseline: Optional[Union[Tensor, int, float, Tuple[Union[Tensor, int, float], ...]]] = None, ) -> None: ig = IntegratedGradients(model.forward) model.zero_grad() if type == "vanilla": attributions, delta = ig.attribute( input, baselines=baseline, target=target, method=approximation_method, n_steps=200, return_convergence_delta=True, ) delta_expected = ig.compute_convergence_delta( attributions, baseline, input, target) assertTensorAlmostEqual(self, delta_expected, delta) delta_condition = all(abs(delta.numpy().flatten()) < 0.005) self.assertTrue( delta_condition, "The sum of attribution values {} is not " "nearly equal to the difference between the endpoint for " "some samples".format(delta), ) self.assertEqual([input.shape[0]], list(delta.shape)) else: nt = NoiseTunnel(ig) n_samples = 10 attributions, delta = nt.attribute( input, baselines=baseline, nt_type=type, n_samples=n_samples, stdevs=0.0002, n_steps=100, target=target, method=approximation_method, return_convergence_delta=True, ) self.assertEqual([input.shape[0] * n_samples], list(delta.shape)) self.assertTrue(all(abs(delta.numpy().flatten()) < 0.05)) self.assertEqual(attributions.shape, input.shape)
def test_basic_multi_input(self): batch_size = 10 x1 = torch.ones(batch_size, 3) x2 = torch.ones(batch_size, 4) inputs = (x1, x2) batch_size_baselines = 20 baselines = ( torch.zeros(batch_size_baselines, 3), torch.zeros(batch_size_baselines, 4), ) class Net(nn.Module): def __init__(self): super().__init__() self.linear = nn.Linear(7, 1) def forward(self, x1, x2): return self.linear(torch.cat((x1, x2), dim=-1)) model = Net() model.eval() model.zero_grad() np.random.seed(0) torch.manual_seed(0) gradient_shap = GradientShap(model) n_samples = 50 attributions, delta = gradient_shap.attribute( (x1, x2), baselines, n_samples=n_samples, return_convergence_delta=True) attributions_without_delta = gradient_shap.attribute((x1, x2), baselines) self._assert_attribution_delta(inputs, attributions, n_samples, delta) # Compare with integrated gradients ig = IntegratedGradients(model) baselines = (torch.zeros(batch_size, 3), torch.zeros(batch_size, 4)) attributions_ig = ig.attribute(inputs, baselines=baselines) self._assert_shap_ig_comparision(attributions, attributions_ig) # compare attributions retrieved with and without # `return_convergence_delta` flag for attribution, attribution_without_delta in zip( attributions, attributions_without_delta): assertTensorAlmostEqual(self, attribution, attribution_without_delta)
def _validate_completness(self, model, inputs, target, type="vanilla"): ig = IntegratedGradients(model.forward) for method in [ "riemann_right", "riemann_left", "riemann_middle", "riemann_trapezoid", "gausslegendre", ]: model.zero_grad() if type == "vanilla": attributions, delta = ig.attribute( inputs, target=target, method=method, n_steps=1000, return_convergence_delta=True, ) # attributions are returned as tuples for the integrated_gradients self.assertAlmostEqual( attributions.sum(), model.forward(inputs)[:, target] - model.forward(0 * inputs)[:, target], delta=0.005, ) delta_expected = abs(attributions.sum().item() - ( model.forward(inputs)[:, target].item() - model.forward(0 * inputs)[:, target].item())) self.assertAlmostEqual(abs(delta).sum().item(), delta_expected, delta=0.005) self.assertEqual([inputs.shape[0]], list(delta.shape)) else: nt = NoiseTunnel(ig) n_samples = 10 attributions, delta = nt.attribute( inputs, nt_type=type, n_samples=n_samples, stdevs=0.0002, n_steps=1000, target=target, method=method, return_convergence_delta=True, ) self.assertEqual([inputs.shape[0] * n_samples], list(delta.shape)) self.assertTrue(all(abs(delta.numpy().flatten()) < 0.05)) self.assertEqual(attributions.shape, inputs.shape)
def test_classification(self): num_in = 40 inputs = torch.arange(0.0, num_in * 2.0).reshape(2, num_in) baselines = torch.arange(0.0, num_in * 4.0).reshape(4, num_in) target = torch.tensor(1) # 10-class classification model model = SoftmaxModel(num_in, 20, 10) model.eval() model.zero_grad() gradient_shap = GradientShap(model) n_samples = 10 attributions, delta = gradient_shap.attribute( inputs, baselines=baselines, target=target, n_samples=n_samples, stdevs=0.009, return_convergence_delta=True, ) _assert_attribution_delta(self, (inputs, ), (attributions, ), n_samples, delta) # try to call `compute_convergence_delta` externally with self.assertRaises(AssertionError): gradient_shap.compute_convergence_delta(attributions, inputs, baselines, target=target) # now, let's expand target and choose random baselines from `baselines` tensor rand_indices = np.random.choice(baselines.shape[0], inputs.shape[0]).tolist() chosen_baselines = baselines[rand_indices] target_extendes = torch.tensor([1, 1]) external_delta = gradient_shap.compute_convergence_delta( attributions, chosen_baselines, inputs, target=target_extendes) _assert_delta(self, external_delta) # Compare with integrated gradients ig = IntegratedGradients(model) baselines = torch.arange(0.0, num_in * 2.0).reshape(2, num_in) attributions_ig = ig.attribute(inputs, baselines=baselines, target=target) self._assert_shap_ig_comparision((attributions, ), (attributions_ig, ))
def _assert_attributions( self, model, attributions, inputs, baselines, delta, target=None ): self.assertEqual(inputs.shape, attributions.shape) delta_condition = all(abs(delta.numpy().flatten()) < 0.003) self.assertTrue( delta_condition, "The sum of attribution values {} is not " "nearly equal to the difference between the endpoint for " "some samples".format(delta), ) # compare with integrated gradients if inputs.shape == baselines.shape: ig = IntegratedGradients(model) attributions_ig = ig.attribute(inputs, baselines=baselines, target=target) assertAttributionComparision(self, attributions, attributions_ig)
def test_sigmoid_classification(self): num_in = 20 input = torch.arange(0.0, num_in * 1.0, requires_grad=True).unsqueeze(0) baseline = 0 * input target = torch.tensor(0) # TODO add test cases for multiple different layers model = SigmoidDeepLiftModel(num_in, 5, 1) dl = DeepLift(model) model.zero_grad() attributions, delta = dl.attribute( input, baseline, target=target, return_convergence_delta=True ) self._assert_attributions(model, attributions, input, baseline, delta, target) # compare with integrated gradients ig = IntegratedGradients(model) attributions_ig = ig.attribute(input, baseline, target=target) assertAttributionComparision(self, (attributions,), (attributions_ig,))
def test_basic_multi_input(self) -> None: batch_size = 10 x1 = torch.ones(batch_size, 3) x2 = torch.ones(batch_size, 4) inputs = (x1, x2) batch_size_baselines = 20 baselines = ( torch.zeros(batch_size_baselines, 3), torch.zeros(batch_size_baselines, 4), ) model = BasicLinearModel() model.eval() model.zero_grad() np.random.seed(0) torch.manual_seed(0) gradient_shap = GradientShap(model) n_samples = 50 attributions, delta = cast( Tuple[Tuple[Tensor, ...], Tensor], gradient_shap.attribute(inputs, baselines, n_samples=n_samples, return_convergence_delta=True), ) attributions_without_delta = gradient_shap.attribute((x1, x2), baselines) _assert_attribution_delta(self, inputs, attributions, n_samples, delta) # Compare with integrated gradients ig = IntegratedGradients(model) baselines = (torch.zeros(batch_size, 3), torch.zeros(batch_size, 4)) attributions_ig = ig.attribute(inputs, baselines=baselines) self._assert_shap_ig_comparision(attributions, attributions_ig) # compare attributions retrieved with and without # `return_convergence_delta` flag for attribution, attribution_without_delta in zip( attributions, attributions_without_delta): assertTensorAlmostEqual(self, attribution, attribution_without_delta)
def _ig_matching_test_assert( self, model: Module, output_layer: Module, test_input: Tensor, baseline: Union[None, Tensor] = None, ) -> None: out = model(test_input) input_attrib = IntegratedGradients(model) ig_attrib = NeuronIntegratedGradients(model, output_layer) for i in range(out.shape[1]): ig_vals = input_attrib.attribute(test_input, target=i, baselines=baseline) neuron_ig_vals = ig_attrib.attribute(test_input, (i,), baselines=baseline) assertArraysAlmostEqual( ig_vals.reshape(-1).tolist(), neuron_ig_vals.reshape(-1).tolist(), delta=0.001, ) self.assertEqual(neuron_ig_vals.shape, test_input.shape)
def test_simple_target_nt_tensor(self): net = BasicModel_MultiLayer() inp = torch.randn(4, 3) self._target_batch_test_assert( NoiseTunnel, IntegratedGradients(net), inputs=inp, targets=torch.tensor([0, 1, 1, 0]), stdevs=0.0, test_batches=True, )
def _deeplift_helper(self, model, attr_method, inputs, baselines): input_bsz = inputs[0].shape[0] baseline_bsz = baselines[0].shape[0] # Run attribution multiple times to make sure that it is working as # expected for _ in range(5): model.zero_grad() attributions, delta = attr_method.attribute( inputs, baselines, return_convergence_delta=True) attributions_without_delta = attr_method.attribute( inputs, baselines) for attribution, attribution_without_delta in zip( attributions, attributions_without_delta): self.assertTrue( torch.all(torch.eq(attribution, attribution_without_delta))) if isinstance(attr_method, DeepLiftShap): self.assertEqual([input_bsz * baseline_bsz], list(delta.shape)) else: self.assertEqual([input_bsz], list(delta.shape)) delta_external = attr_method.compute_convergence_delta( attributions, baselines, inputs) assertArraysAlmostEqual(delta, delta_external, 0.0) delta_condition = all(abs(delta.numpy().flatten()) < 0.00001) self.assertTrue( delta_condition, "The sum of attribution values {} is not " "nearly equal to the difference between the endpoint for " "some samples".format(delta), ) for input, attribution in zip(inputs, attributions): self.assertEqual(input.shape, attribution.shape) if inputs[0].shape == baselines[0].shape: # Compare with Integrated Gradients ig = IntegratedGradients(model) attributions_ig = ig.attribute(inputs, baselines) assertAttributionComparision(self, attributions, attributions_ig)
def test_multi_target_nt(self): net = BasicModel_MultiLayer() inp = torch.randn(4, 3) self._target_batch_test_assert( NoiseTunnel, IntegratedGradients(net), inputs=inp, additional_forward_args=(None, True), stdevs=0.0, targets=[(1, 0, 0), (0, 1, 1), (1, 1, 1), (0, 0, 0)], test_batches=True, )
def __init__( self, forward_func: Callable, layer: Module, device_ids: Union[None, List[int]] = None, multiply_by_inputs: bool = True, ) -> None: r""" Args: forward_func (callable): The forward function of the model or any modification of it layer (torch.nn.Module): Layer for which attributions are computed. Output size of attribute matches this layer's input or output dimensions, depending on whether we attribute to the inputs or outputs of the layer, corresponding to the attribution of each neuron in the input or output of this layer. device_ids (list(int)): Device ID list, necessary only if forward_func applies a DataParallel model. This allows reconstruction of intermediate outputs from batched results across devices. If forward_func is given as the DataParallel model itself, then it is not necessary to provide this argument. multiply_by_inputs (bool, optional): Indicates whether to factor model inputs' multiplier in the final attribution scores. In the literature this is also known as local vs global attribution. If inputs' multiplier isn't factored in, then this type of attribution method is also called local attribution. If it is, then that type of attribution method is called global. More detailed can be found here: https://arxiv.org/abs/1711.06104 In case of layer integrated gradients, if `multiply_by_inputs` is set to True, final sensitivity scores are being multiplied by layer activations for inputs - layer activations for baselines. """ LayerAttribution.__init__(self, forward_func, layer, device_ids=device_ids) GradientAttribution.__init__(self, forward_func) self.ig = IntegratedGradients(forward_func, multiply_by_inputs)
def test_multiple_layers_multiple_inputs_shared_input(self) -> None: input1 = torch.randn(5, 3) input2 = torch.randn(5, 3) input3 = torch.randn(5, 3) inputs = (input1, input2, input3) baseline = tuple(torch.zeros_like(inp) for inp in inputs) net = BasicModel_MultiLayer_TrueMultiInput() lig = LayerIntegratedGradients(net, layer=[net.m1, net.m234]) ig = IntegratedGradients(net) # test layer inputs attribs_inputs = lig.attribute(inputs, baseline, target=0, attribute_to_layer_input=True) attribs_inputs_regular_ig = ig.attribute(inputs, baseline, target=0) self.assertIsInstance(attribs_inputs, list) self.assertEqual(len(attribs_inputs), 2) self.assertIsInstance(attribs_inputs[0], Tensor) self.assertIsInstance(attribs_inputs[1], tuple) self.assertEqual(len(attribs_inputs[1]), 3) assertTensorTuplesAlmostEqual( self, # last input for second layer is first input => # add the attributions ( attribs_inputs[0] + attribs_inputs[1][-1], ) + attribs_inputs[1][0:-1], attribs_inputs_regular_ig, delta=1e-5, ) # test layer outputs attribs = lig.attribute(inputs, baseline, target=0) ig = IntegratedGradients(lambda x, y: x + y) attribs_ig = ig.attribute( (net.m1(input1), net.m234(input2, input3, input1, 1)), (net.m1(baseline[0]), net.m234(baseline[1], baseline[2], baseline[1], 1)), target=0, ) assertTensorTuplesAlmostEqual(self, attribs, attribs_ig, delta=1e-5)
def test_multiple_layers_multiple_input_outputs(self) -> None: # test with multiple layers, where one layer accepts multiple inputs input1 = torch.randn(5, 3) input2 = torch.randn(5, 3) input3 = torch.randn(5, 3) input4 = torch.randn(5, 3) inputs = (input1, input2, input3, input4) baseline = tuple(torch.zeros_like(inp) for inp in inputs) net = BasicModel_MultiLayer_TrueMultiInput() lig = LayerIntegratedGradients(net, layer=[net.m1, net.m234]) ig = IntegratedGradients(net) # test layer inputs attribs_inputs = lig.attribute(inputs, baseline, target=0, attribute_to_layer_input=True) attribs_inputs_regular_ig = ig.attribute(inputs, baseline, target=0) self.assertIsInstance(attribs_inputs, list) self.assertEqual(len(attribs_inputs), 2) self.assertIsInstance(attribs_inputs[0], Tensor) self.assertIsInstance(attribs_inputs[1], tuple) self.assertEqual(len(attribs_inputs[1]), 3) assertTensorTuplesAlmostEqual( self, (attribs_inputs[0], ) + attribs_inputs[1], attribs_inputs_regular_ig, delta=1e-7, ) # test layer outputs attribs = lig.attribute(inputs, baseline, target=0) ig = IntegratedGradients(lambda x, y: x + y) attribs_ig = ig.attribute( (net.m1(input1), net.m234(input2, input3, input4, 1)), (net.m1(baseline[0]), net.m234(baseline[1], baseline[2], baseline[3], 1)), target=0, ) assertTensorTuplesAlmostEqual(self, attribs, attribs_ig, delta=1e-7)
def _compute_attribution_and_evaluate( self, model: Module, inputs: TensorOrTupleOfTensorsGeneric, baselines: BaselineType = None, target: Union[None, int] = None, additional_forward_args: Any = None, type: str = "vanilla", approximation_method: str = "gausslegendre", multiply_by_inputs=True, ) -> Tuple[Tensor, ...]: r""" attrib_type: 'vanilla', 'smoothgrad', 'smoothgrad_sq', 'vargrad' """ ig = IntegratedGradients(model, multiply_by_inputs=multiply_by_inputs) self.assertEquals(ig.multiplies_by_inputs, multiply_by_inputs) if not isinstance(inputs, tuple): inputs = (inputs,) # type: ignore inputs: Tuple[Tensor, ...] if baselines is not None and not isinstance(baselines, tuple): baselines = (baselines,) if baselines is None: baselines = _tensorize_baseline(inputs, _zeros(inputs)) if type == "vanilla": attributions, delta = ig.attribute( inputs, baselines, additional_forward_args=additional_forward_args, method=approximation_method, n_steps=500, target=target, return_convergence_delta=True, ) model.zero_grad() attributions_without_delta, delta = ig.attribute( inputs, baselines, additional_forward_args=additional_forward_args, method=approximation_method, n_steps=500, target=target, return_convergence_delta=True, ) model.zero_grad() self.assertEqual([inputs[0].shape[0]], list(delta.shape)) delta_external = ig.compute_convergence_delta( attributions, baselines, inputs, target=target, additional_forward_args=additional_forward_args, ) assertArraysAlmostEqual(delta, delta_external, 0.0) else: nt = NoiseTunnel(ig) n_samples = 5 attributions, delta = nt.attribute( inputs, nt_type=type, nt_samples=n_samples, stdevs=0.00000002, baselines=baselines, target=target, additional_forward_args=additional_forward_args, method=approximation_method, n_steps=500, return_convergence_delta=True, ) with self.assertWarns(DeprecationWarning): attributions_without_delta = nt.attribute( inputs, nt_type=type, n_samples=n_samples, stdevs=0.00000002, baselines=baselines, target=target, additional_forward_args=additional_forward_args, method=approximation_method, n_steps=500, ) self.assertEquals(nt.multiplies_by_inputs, multiply_by_inputs) self.assertEqual([inputs[0].shape[0] * n_samples], list(delta.shape)) for input, attribution in zip(inputs, attributions): self.assertEqual(attribution.shape, input.shape) if multiply_by_inputs: self.assertTrue(all(abs(delta.numpy().flatten()) < 0.07)) # compare attributions retrieved with and without # `return_convergence_delta` flag for attribution, attribution_without_delta in zip( attributions, attributions_without_delta ): assertTensorAlmostEqual( self, attribution, attribution_without_delta, delta=0.05 ) return cast(Tuple[Tensor, ...], attributions)
class LayerIntegratedGradients(LayerAttribution, GradientAttribution): r""" Layer Integrated Gradients is a variant of Integrated Gradients that assigns an importance score to layer inputs or outputs, depending on whether we attribute to the former or to the latter one. Integrated Gradients is an axiomatic model interpretability algorithm that attributes / assigns an importance score to each input feature by approximating the integral of gradients of the model's output with respect to the inputs along the path (straight line) from given baselines / references to inputs. Baselines can be provided as input arguments to attribute method. To approximate the integral we can choose to use either a variant of Riemann sum or Gauss-Legendre quadrature rule. More details regarding the integrated gradients method can be found in the original paper: https://arxiv.org/abs/1703.01365 """ def __init__( self, forward_func: Callable, layer: Module, device_ids: Optional[List[int]] = None, ) -> None: r""" Args: forward_func (callable): The forward function of the model or any modification of it layer (torch.nn.Module): Layer for which attributions are computed. Output size of attribute matches this layer's input or output dimensions, depending on whether we attribute to the inputs or outputs of the layer, corresponding to the attribution of each neuron in the input or output of this layer. device_ids (list(int)): Device ID list, necessary only if forward_func applies a DataParallel model. This allows reconstruction of intermediate outputs from batched results across devices. If forward_func is given as the DataParallel model itself, then it is not necessary to provide this argument. """ LayerAttribution.__init__(self, forward_func, layer, device_ids=device_ids) GradientAttribution.__init__(self, forward_func) self.ig = IntegratedGradients(forward_func) def attribute( self, inputs: Union[Tensor, Tuple[Tensor, ...]], baselines: Optional[ Union[Tensor, int, float, Tuple[Union[Tensor, int, float], ...]] ] = None, target: Optional[ Union[int, Tuple[int, ...], Tensor, List[Tuple[int, ...]]] ] = None, additional_forward_args: Any = None, n_steps: int = 50, method: str = "gausslegendre", internal_batch_size: Optional[int] = None, return_convergence_delta: bool = False, attribute_to_layer_input: bool = False, ) -> Union[ Tensor, Tuple[Tensor, ...], Tuple[Union[Tensor, Tuple[Tensor, ...]], Tensor] ]: r""" This method attributes the output of the model with given target index (in case it is provided, otherwise it assumes that output is a scalar) to layer inputs or outputs of the model, depending on whether `attribute_to_layer_input` is set to True or False, using the approach described above. In addition to that it also returns, if `return_convergence_delta` is set to True, integral approximation delta based on the completeness property of integrated gradients. Args: inputs (tensor or tuple of tensors): Input for which layer integrated gradients are computed. If forward_func takes a single tensor as input, a single input tensor should be provided. If forward_func takes multiple tensors as input, a tuple of the input tensors should be provided. It is assumed that for all given input tensors, dimension 0 corresponds to the number of examples, and if multiple input tensors are provided, the examples must be aligned appropriately. baselines (scalar, tensor, tuple of scalars or tensors, optional): Baselines define the starting point from which integral is computed and can be provided as: - a single tensor, if inputs is a single tensor, with exactly the same dimensions as inputs or the first dimension is one and the remaining dimensions match with inputs. - a single scalar, if inputs is a single tensor, which will be broadcasted for each input value in input tensor. - a tuple of tensors or scalars, the baseline corresponding to each tensor in the inputs' tuple can be: - either a tensor with matching dimensions to corresponding tensor in the inputs' tuple or the first dimension is one and the remaining dimensions match with the corresponding input tensor. - or a scalar, corresponding to a tensor in the inputs' tuple. This scalar value is broadcasted for corresponding input tensor. In the cases when `baselines` is not provided, we internally use zero scalar corresponding to each input tensor. Default: None target (int, tuple, tensor or list, optional): Output indices for which gradients are computed (for classification cases, this is usually the target class). If the network returns a scalar value per example, no target index is necessary. For general 2D outputs, targets can be either: - a single integer or a tensor containing a single integer, which is applied to all input examples - a list of integers or a 1D tensor, with length matching the number of examples in inputs (dim 0). Each integer is applied as the target for the corresponding example. For outputs with > 2 dimensions, targets can be either: - A single tuple, which contains #output_dims - 1 elements. This target index is applied to all examples. - A list of tuples with length equal to the number of examples in inputs (dim 0), and each tuple containing #output_dims - 1 elements. Each tuple is applied as the target for the corresponding example. Default: None additional_forward_args (any, optional): If the forward function requires additional arguments other than the inputs for which attributions should not be computed, this argument can be provided. It must be either a single additional argument of a Tensor or arbitrary (non-tuple) type or a tuple containing multiple additional arguments including tensors or any arbitrary python types. These arguments are provided to forward_func in order following the arguments in inputs. For a tensor, the first dimension of the tensor must correspond to the number of examples. It will be repeated for each of `n_steps` along the integrated path. For all other types, the given argument is used for all forward evaluations. Note that attributions are not computed with respect to these arguments. Default: None n_steps (int, optional): The number of steps used by the approximation method. Default: 50. method (string, optional): Method for approximating the integral, one of `riemann_right`, `riemann_left`, `riemann_middle`, `riemann_trapezoid` or `gausslegendre`. Default: `gausslegendre` if no method is provided. internal_batch_size (int, optional): Divides total #steps * #examples data points into chunks of size internal_batch_size, which are computed (forward / backward passes) sequentially. For DataParallel models, each batch is split among the available devices, so evaluations on each available device contain internal_batch_size / num_devices examples. If internal_batch_size is None, then all evaluations are processed in one batch. Default: None return_convergence_delta (bool, optional): Indicates whether to return convergence delta or not. If `return_convergence_delta` is set to True convergence delta will be returned in a tuple following attributions. Default: False attribute_to_layer_input (bool, optional): Indicates whether to compute the attribution with respect to the layer input or output. If `attribute_to_layer_input` is set to True then the attributions will be computed with respect to layer input, otherwise it will be computed with respect to layer output. Note that currently it is assumed that either the input or the output of internal layer, depending on whether we attribute to the input or output, is a single tensor. Support for multiple tensors will be added later. Default: False Returns: **attributions** or 2-element tuple of **attributions**, **delta**: - **attributions** (*tensor* or tuple of *tensors*): Integrated gradients with respect to `layer`'s inputs or outputs. Attributions will always be the same size and dimensionality as the input or output of the given layer, depending on whether we attribute to the inputs or outputs of the layer which is decided by the input flag `attribute_to_layer_input`. - **delta** (*tensor*, returned if return_convergence_delta=True): The difference between the total approximated and true integrated gradients. This is computed using the property that the total sum of forward_func(inputs) - forward_func(baselines) must equal the total sum of the integrated gradient. Delta is calculated per example, meaning that the number of elements in returned delta tensor is equal to the number of of examples in inputs. Examples:: >>> # ImageClassifier takes a single input tensor of images Nx3x32x32, >>> # and returns an Nx10 tensor of class probabilities. >>> # It contains an attribute conv1, which is an instance of nn.conv2d, >>> # and the output of this layer has dimensions Nx12x32x32. >>> net = ImageClassifier() >>> lig = LayerIntegratedGradients(net, net.conv1) >>> input = torch.randn(2, 3, 32, 32, requires_grad=True) >>> # Computes layer integrated gradients for class 3. >>> # attribution size matches layer output, Nx12x32x32 >>> attribution = lig.attribute(input, target=3) """ inps, baselines = _format_input_baseline(inputs, baselines) _validate_input(inps, baselines, n_steps, method) baselines = _tensorize_baseline(inps, baselines) additional_forward_args = _format_additional_forward_args( additional_forward_args ) if self.device_ids is None: self.device_ids = getattr(self.forward_func, "device_ids", None) inputs_layer, is_layer_tuple = _forward_layer_eval( self.forward_func, inps, self.layer, device_ids=self.device_ids, additional_forward_args=additional_forward_args, attribute_to_layer_input=attribute_to_layer_input, ) baselines_layer, _ = _forward_layer_eval( self.forward_func, baselines, self.layer, device_ids=self.device_ids, additional_forward_args=additional_forward_args, attribute_to_layer_input=attribute_to_layer_input, ) # inputs -> these inputs are scaled def gradient_func( forward_fn: Callable, inputs: Union[Tensor, Tuple[Tensor, ...]], target_ind: Optional[ Union[int, Tuple[int, ...], Tensor, List[Tuple[int, ...]]] ] = None, additional_forward_args: Any = None, ) -> Tuple[Tensor, ...]: if self.device_ids is None: scattered_inputs = (inputs,) else: # scatter method does not have a precise enough return type in its # stub, so suppress the type warning. scattered_inputs = scatter( # type:ignore inputs, target_gpus=self.device_ids ) scattered_inputs_dict = { scattered_input[0].device: scattered_input for scattered_input in scattered_inputs } with torch.autograd.set_grad_enabled(True): def layer_forward_hook(module, hook_inputs, hook_outputs=None): device = _extract_device(module, hook_inputs, hook_outputs) if is_layer_tuple: return scattered_inputs_dict[device] return scattered_inputs_dict[device][0] if attribute_to_layer_input: hook = self.layer.register_forward_pre_hook(layer_forward_hook) else: hook = self.layer.register_forward_hook(layer_forward_hook) output = _run_forward( self.forward_func, additional_forward_args, target_ind, ) hook.remove() assert output[0].numel() == 1, ( "Target not provided when necessary, cannot" " take gradient with respect to multiple outputs." ) # torch.unbind(forward_out) is a list of scalar tensor tuples and # contains batch_size * #steps elements grads = torch.autograd.grad(torch.unbind(output), inputs) return grads self.ig.gradient_func = gradient_func all_inputs = ( (inps + additional_forward_args) if additional_forward_args is not None else inps ) attributions = self.ig.attribute( inputs_layer, baselines=baselines_layer, target=target, additional_forward_args=all_inputs, n_steps=n_steps, method=method, internal_batch_size=internal_batch_size, return_convergence_delta=False, ) if return_convergence_delta: start_point, end_point = baselines, inps # computes approximation error based on the completeness axiom delta = self.compute_convergence_delta( attributions, start_point, end_point, additional_forward_args=additional_forward_args, target=target, ) return _format_attributions(is_layer_tuple, attributions), delta return _format_attributions(is_layer_tuple, attributions) def has_convergence_delta(self) -> bool: return True
def test_simple_target_missing_error(self) -> None: net = BasicModel_MultiLayer() inp = torch.zeros((1, 3)) with self.assertRaises(AssertionError): attr = IntegratedGradients(net) attr.attribute(inp)
def _assert_compare_with_emb_patching( self, input: Union[Tensor, Tuple[Tensor, ...]], baseline: Union[Tensor, Tuple[Tensor, ...]], additional_args: Union[None, Tuple[Tensor, ...]], multiply_by_inputs: bool = True, multiple_emb: bool = False, ): model = BasicEmbeddingModel(nested_second_embedding=True) if multiple_emb: module_list: List[Module] = [model.embedding1, model.embedding2] lig = LayerIntegratedGradients( model, module_list, multiply_by_inputs=multiply_by_inputs, ) else: lig = LayerIntegratedGradients( model, model.embedding1, multiply_by_inputs=multiply_by_inputs) attributions, delta = lig.attribute( input, baselines=baseline, additional_forward_args=additional_args, return_convergence_delta=True, ) # now let's interpret with standard integrated gradients and # the embeddings for monkey patching e1 = configure_interpretable_embedding_layer(model, "embedding1") e1_input_emb = e1.indices_to_embeddings( input[0] if multiple_emb else input) e1_baseline_emb = e1.indices_to_embeddings( baseline[0] if multiple_emb else baseline) input_emb = e1_input_emb baseline_emb = e1_baseline_emb e2 = None if multiple_emb: e2 = configure_interpretable_embedding_layer(model, "embedding2") e2_input_emb = e2.indices_to_embeddings(*input[1:]) e2_baseline_emb = e2.indices_to_embeddings(*baseline[1:]) input_emb = (e1_input_emb, e2_input_emb) baseline_emb = (e1_baseline_emb, e2_baseline_emb) ig = IntegratedGradients(model, multiply_by_inputs=multiply_by_inputs) attributions_with_ig, delta_with_ig = ig.attribute( input_emb, baselines=baseline_emb, additional_forward_args=additional_args, target=0, return_convergence_delta=True, ) remove_interpretable_embedding_layer(model, e1) if e2 is not None: remove_interpretable_embedding_layer(model, e2) self.assertEqual(isinstance(attributions_with_ig, tuple), isinstance(attributions, list)) self.assertTrue( isinstance(attributions_with_ig, tuple) if multiple_emb else not isinstance(attributions_with_ig, tuple)) # convert to tuple for comparison if not isinstance(attributions_with_ig, tuple): attributions = (attributions, ) attributions_with_ig = (attributions_with_ig, ) else: # convert list to tuple self.assertIsInstance(attributions, list) attributions = tuple(attributions) for attr_lig, attr_ig in zip(attributions, attributions_with_ig): self.assertEqual(attr_lig.shape, attr_ig.shape) assertArraysAlmostEqual(attributions, attributions_with_ig) if multiply_by_inputs: assertArraysAlmostEqual(delta, delta_with_ig)
def __init__( self, forward_func: Callable, layer: ModuleOrModuleList, device_ids: Union[None, List[int]] = None, multiply_by_inputs: bool = True, ) -> None: r""" Args: forward_func (callable): The forward function of the model or any modification of it layer (ModuleOrModuleList): Layer or list of layers for which attributions are computed. For each layer the output size of the attribute matches this layer's input or output dimensions, depending on whether we attribute to the inputs or outputs of the layer, corresponding to the attribution of each neuron in the input or output of this layer. Please note that layers to attribute on cannot be dependent on each other. That is, a subset of layers in `layer` cannot produce the inputs for another layer. For example, if your model is of a simple linked-list based graph structure (think nn.Sequence), e.g. x -> l1 -> l2 -> l3 -> output. If you pass in any one of those layers, you cannot pass in another due to the dependence, e.g. if you pass in l2 you cannot pass in l1 or l3. device_ids (list(int)): Device ID list, necessary only if forward_func applies a DataParallel model. This allows reconstruction of intermediate outputs from batched results across devices. If forward_func is given as the DataParallel model itself, then it is not necessary to provide this argument. multiply_by_inputs (bool, optional): Indicates whether to factor model inputs' multiplier in the final attribution scores. In the literature this is also known as local vs global attribution. If inputs' multiplier isn't factored in, then this type of attribution method is also called local attribution. If it is, then that type of attribution method is called global. More detailed can be found here: https://arxiv.org/abs/1711.06104 In case of layer integrated gradients, if `multiply_by_inputs` is set to True, final sensitivity scores are being multiplied by layer activations for inputs - layer activations for baselines. """ LayerAttribution.__init__(self, forward_func, layer, device_ids=device_ids) GradientAttribution.__init__(self, forward_func) self.ig = IntegratedGradients(forward_func, multiply_by_inputs) if isinstance(layer, list) and len(layer) > 1: warnings.warn( "Multiple layers provided. Please ensure that each layer is" "**not** solely solely dependent on the outputs of" "another layer. Please refer to the documentation for more" "detail.")
def attribute( self, inputs: TensorOrTupleOfTensorsGeneric, neuron_selector: Union[int, Tuple[Union[int, slice], ...], Callable], baselines: Union[None, Tensor, Tuple[Tensor, ...]] = None, additional_forward_args: Any = None, n_steps: int = 50, method: str = "gausslegendre", internal_batch_size: Union[None, int] = None, attribute_to_neuron_input: bool = False, ) -> TensorOrTupleOfTensorsGeneric: r""" Args: inputs (tensor or tuple of tensors): Input for which neuron integrated gradients are computed. If forward_func takes a single tensor as input, a single input tensor should be provided. If forward_func takes multiple tensors as input, a tuple of the input tensors should be provided. It is assumed that for all given input tensors, dimension 0 corresponds to the number of examples, and if multiple input tensors are provided, the examples must be aligned appropriately. neuron_selector (int, callable, or tuple of ints or slices): Selector for neuron in given layer for which attribution is desired. Neuron selector can be provided as: - a single integer, if the layer output is 2D. This integer selects the appropriate neuron column in the layer input or output - a tuple of integers or slice objects. Length of this tuple must be one less than the number of dimensions in the input / output of the given layer (since dimension 0 corresponds to number of examples). The elements of the tuple can be either integers or slice objects (slice object allows indexing a range of neurons rather individual ones). If any of the tuple elements is a slice object, the indexed output tensor is used for attribution. Note that specifying a slice of a tensor would amount to computing the attribution of the sum of the specified neurons, and not the individual neurons independantly. - a callable, which should take the target layer as input (single tensor or tuple if multiple tensors are in layer) and return a neuron or aggregate of the layer's neurons for attribution. For example, this function could return the sum of the neurons in the layer or sum of neurons with activations in a particular range. It is expected that this function returns either a tensor with one element or a 1D tensor with length equal to batch_size (one scalar per input example) baselines (scalar, tensor, tuple of scalars or tensors, optional): Baselines define the starting point from which integral is computed. Baselines can be provided as: - a single tensor, if inputs is a single tensor, with exactly the same dimensions as inputs or the first dimension is one and the remaining dimensions match with inputs. - a single scalar, if inputs is a single tensor, which will be broadcasted for each input value in input tensor. - a tuple of tensors or scalars, the baseline corresponding to each tensor in the inputs' tuple can be: - either a tensor with matching dimensions to corresponding tensor in the inputs' tuple or the first dimension is one and the remaining dimensions match with the corresponding input tensor. - or a scalar, corresponding to a tensor in the inputs' tuple. This scalar value is broadcasted for corresponding input tensor. In the cases when `baselines` is not provided, we internally use zero scalar corresponding to each input tensor. Default: None additional_forward_args (any, optional): If the forward function requires additional arguments other than the inputs for which attributions should not be computed, this argument can be provided. It must be either a single additional argument of a Tensor or arbitrary (non-tuple) type or a tuple containing multiple additional arguments including tensors or any arbitrary python types. These arguments are provided to forward_func in order following the arguments in inputs. For a tensor, the first dimension of the tensor must correspond to the number of examples. It will be repeated for each of `n_steps` along the integrated path. For all other types, the given argument is used for all forward evaluations. Note that attributions are not computed with respect to these arguments. Default: None n_steps (int, optional): The number of steps used by the approximation method. Default: 50. method (string, optional): Method for approximating the integral, one of `riemann_right`, `riemann_left`, `riemann_middle`, `riemann_trapezoid` or `gausslegendre`. Default: `gausslegendre` if no method is provided. internal_batch_size (int, optional): Divides total #steps * #examples data points into chunks of size at most internal_batch_size, which are computed (forward / backward passes) sequentially. internal_batch_size must be at least equal to #examples. For DataParallel models, each batch is split among the available devices, so evaluations on each available device contain internal_batch_size / num_devices examples. If internal_batch_size is None, then all evaluations are processed in one batch. Default: None attribute_to_neuron_input (bool, optional): Indicates whether to compute the attributions with respect to the neuron input or output. If `attribute_to_neuron_input` is set to True then the attributions will be computed with respect to neuron's inputs, otherwise it will be computed with respect to neuron's outputs. Note that currently it is assumed that either the input or the output of internal neuron, depending on whether we attribute to the input or output, is a single tensor. Support for multiple tensors will be added later. Default: False Returns: *tensor* or tuple of *tensors* of **attributions**: - **attributions** (*tensor* or tuple of *tensors*): Integrated gradients for particular neuron with respect to each input feature. Attributions will always be the same size as the provided inputs, with each value providing the attribution of the corresponding input index. If a single tensor is provided as inputs, a single tensor is returned. If a tuple is provided for inputs, a tuple of corresponding sized tensors is returned. Examples:: >>> # ImageClassifier takes a single input tensor of images Nx3x32x32, >>> # and returns an Nx10 tensor of class probabilities. >>> # It contains an attribute conv1, which is an instance of nn.conv2d, >>> # and the output of this layer has dimensions Nx12x32x32. >>> net = ImageClassifier() >>> neuron_ig = NeuronIntegratedGradients(net, net.conv1) >>> input = torch.randn(2, 3, 32, 32, requires_grad=True) >>> # To compute neuron attribution, we need to provide the neuron >>> # index for which attribution is desired. Since the layer output >>> # is Nx12x32x32, we need a tuple in the form (0..11,0..31,0..31) >>> # which indexes a particular neuron in the layer output. >>> # For this example, we choose the index (4,1,2). >>> # Computes neuron integrated gradients for neuron with >>> # index (4,1,2). >>> attribution = neuron_ig.attribute(input, (4,1,2)) """ ig = IntegratedGradients(self.forward_func, self.multiplies_by_inputs) ig.gradient_func = construct_neuron_grad_fn(self.layer, neuron_selector, self.device_ids, attribute_to_neuron_input) # NOTE: using __wrapped__ to not log # Return only attributions and not delta return ig.attribute.__wrapped__( # type: ignore ig, # self inputs, baselines, additional_forward_args=additional_forward_args, n_steps=n_steps, method=method, internal_batch_size=internal_batch_size, )