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# lipdp.model module

## `DP_Accountant`

Bases: `keras.callbacks.Callback`

Callback to compute the DP guarantees at the end of each epoch.

Note: wandb is not a strict requirement for this callback to work, logging is also supported.

Attributes:

Name | Type | Description
--- | --- | ---
`log_fn` |  | log function to use. Takes a dictionary of (key, value) pairs as input. if 'wandb', use wandb.log. if 'logging', use logging.info. if 'all', use both wandb.log and logging.info.

Source code in `lipdp/model.py`

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    class DP_Accountant(keras.callbacks.Callback):
        """Callback to compute the DP guarantees at the end of each epoch.

        Note: wandb is not a strict requirement for this callback to work, logging is also supported.

        Attributes:
            log_fn: log function to use. Takes a dictionary of (key, value) pairs as input.
                    if 'wandb', use wandb.log.
                    if 'logging', use logging.info.
                    if 'all', use both wandb.log and logging.info.
        """

        def __init__(self, log_fn="all"):
            super().__init__()
            if log_fn == "wandb":
                import wandb

                log_fn = wandb.log
            elif log_fn == "logging":
                import logging

                log_fn = logging.info
            elif log_fn == "all":
                import wandb
                import logging

                log_fn = lambda x: [wandb.log(x), logging.info(x)]
            self.log_fn = log_fn

        def on_epoch_end(self, epoch, logs=None):
            niter = (epoch + 1) * self.model.dataset_metadata.nb_steps_per_epochs
            epsilon, delta = get_eps_delta(model=self.model, niter=niter)
            print(f"\n {(epsilon,delta)}-DP guarantees for epoch {epoch+1} \n")
            # plot epoch at the same time as epsilon and delta to ease comparison of plots in wandb API.
            self.log_fn({"epsilon": epsilon, "delta": delta, "epoch": epoch + 1})

## `DP_Model`

Bases: `lip.model.Model`

Source code in `lipdp/model.py`

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    class DP_Model(lip.model.Model):
        def __init__(
                self,
                dp_layers,
                *args,
                dp_parameters: DPParameters,
                dataset_metadata: DatasetMetadata,
                debug: bool = False,
                **kwargs,
        ):
            """Model Class based on the deel.lip.Sequential model. Only layer from the lipdp.layers module are allowed since
            the framework assume Lipschitz layers.

            Args:
                dp_layers: the list of layers to use ( as done in sequential ) but here we can leverage
                    the fact that layers may have multiple inputs/outputs.
                dp_parameters (DPParameters): parameters used to set the dp procedure.
                dataset_metadata (DatasetMetadata): information about the dataset. Must contain: the input shape, number
                    of training samples, the input bound, number of batches in the dataset and the batch size.
                debug (bool, optional): when true print additionnal debug informations (must be in eager mode). Defaults to False.

            Note:
                The model is then calibrated to verify (epsilon,delta)-DP guarantees by noisying the values of the gradients during the training step.
                DP accounting is done with the associated Callback.

            Raises:
                TypeError: when the dp_parameters.noisify_strategy is not one of "local" or "global"
            """
            super().__init__(*args, **kwargs)
            self.dp_layers = dp_layers
            self.dp_parameters = dp_parameters
            self.dataset_metadata = dataset_metadata
            self.debug = debug
            if self.dp_parameters.noisify_strategy == "global":
                self.noisify_fun = global_noisify
            elif self.dp_parameters.noisify_strategy == "local":
                self.noisify_fun = local_noisify
            else:
                raise TypeError(
                    "Incorrect noisify_strategy argument during model initialisation."
                )

        def layers_forward_order(self):
            return self.dp_layers

        def layers_backward_order(self):
            return self.dp_layers[::-1]

        def call(self, inputs, *args, **kwarsg):
            x = inputs
            for layer in self.layers_forward_order():
                x = layer(x, *args, **kwarsg)
            return x

        # Define the differentially private training step
        def train_step(self, data):
            # Unpack data
            x, y = data

            with tf.GradientTape() as tape:
                y_pred = self(x, training=True)  # Forward pass
                # tf.cast(y_pred,dtype=y.dtype)
                # Compute the loss value
                # (the loss function is configured in `compile()`)
                loss = self.compiled_loss(y, y_pred, regularization_losses=self.losses)

            # Compute gradients
            trainable_vars = self.trainable_variables
            gradients = tape.gradient(loss, trainable_vars)
            # Get gradient bounds
            gradient_bounds = compute_gradient_bounds(model=self)
            noisy_gradients = self.noisify_fun(
                self, gradient_bounds, trainable_vars, gradients
            )
            # Each optimizer is a postprocessing of the already (epsilon,delta)-DP gradients
            self.optimizer.apply_gradients(zip(noisy_gradients, trainable_vars))
            # self.optimizer.apply_gradients(zip(gradients, trainable_vars))
            # Update Metrics
            self.compiled_metrics.update_state(y, y_pred)
            # Condense to verify |W|_2 = 1
            self.condense()
            return {m.name: m.result() for m in self.metrics}

### `__init__(dp_layers, *args, dp_parameters, dataset_metadata, debug=False, **kwargs)`

Model Class based on the deel.lip.Sequential model. Only layer from the lipdp.layers module are allowed since the framework assume Lipschitz layers.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`dp_layers` |  | the list of layers to use ( as done in sequential ) but here we can leverage the fact that layers may have multiple inputs/outputs. | required
`dp_parameters` | `DPParameters` | parameters used to set the dp procedure. | required
`dataset_metadata` | `DatasetMetadata` | information about the dataset. Must contain: the input shape, number of training samples, the input bound, number of batches in the dataset and the batch size. | required
`debug` | `bool` | when true print additionnal debug informations (must be in eager mode). Defaults to False. | `False`

Note

The model is then calibrated to verify (epsilon,delta)-DP guarantees by noisying the values of the gradients during the training step. DP accounting is done with the associated Callback.

Raises:

Type | Description
--- | ---
`TypeError` | when the dp_parameters.noisify_strategy is not one of "local" or "global"

Source code in `lipdp/model.py`

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    def __init__(
            self,
            dp_layers,
            *args,
            dp_parameters: DPParameters,
            dataset_metadata: DatasetMetadata,
            debug: bool = False,
            **kwargs,
    ):
        """Model Class based on the deel.lip.Sequential model. Only layer from the lipdp.layers module are allowed since
        the framework assume Lipschitz layers.

        Args:
            dp_layers: the list of layers to use ( as done in sequential ) but here we can leverage
                the fact that layers may have multiple inputs/outputs.
            dp_parameters (DPParameters): parameters used to set the dp procedure.
            dataset_metadata (DatasetMetadata): information about the dataset. Must contain: the input shape, number
                of training samples, the input bound, number of batches in the dataset and the batch size.
            debug (bool, optional): when true print additionnal debug informations (must be in eager mode). Defaults to False.

        Note:
            The model is then calibrated to verify (epsilon,delta)-DP guarantees by noisying the values of the gradients during the training step.
            DP accounting is done with the associated Callback.

        Raises:
            TypeError: when the dp_parameters.noisify_strategy is not one of "local" or "global"
        """
        super().__init__(*args, **kwargs)
        self.dp_layers = dp_layers
        self.dp_parameters = dp_parameters
        self.dataset_metadata = dataset_metadata
        self.debug = debug
        if self.dp_parameters.noisify_strategy == "global":
            self.noisify_fun = global_noisify
        elif self.dp_parameters.noisify_strategy == "local":
            self.noisify_fun = local_noisify
        else:
            raise TypeError(
                "Incorrect noisify_strategy argument during model initialisation."
            )

## `DP_Sequential`

Bases: `lip.model.Sequential`

Source code in `lipdp/model.py`

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    class DP_Sequential(lip.model.Sequential):
        def __init__(
                self,
                *args,
                dp_parameters: DPParameters,
                dataset_metadata: DatasetMetadata,
                debug: bool = False,
                **kwargs,
        ):
            """Model Class based on the deel.lip.Sequential model. Only layer from the lipdp.layers module are allowed since
            the framework assume Lipschitz layers.

            Args:
                dp_parameters (DPParameters): parameters used to set the dp procedure.
                dataset_metadata (DatasetMetadata): information about the dataset. Must contain: the input shape, number
                    of training samples, the input bound, number of batches in the dataset and the batch size.
                debug (bool, optional): when true print additionnal debug informations (must be in eager mode). Defaults to False.

            Note:
                The model is then calibrated to verify (epsilon,delta)-DP guarantees by noisying the values of the gradients during the training step.
                DP accounting is done with the associated Callback.

            Raises:
                TypeError: when the dp_parameters.noisify_strategy is not one of "local" or "global"
            """
            super().__init__(*args, **kwargs)
            self.dp_parameters = dp_parameters
            self.dataset_metadata = dataset_metadata
            self.debug = debug
            if self.dp_parameters.noisify_strategy == "global":
                self.noisify_fun = global_noisify
            elif self.dp_parameters.noisify_strategy == "local":
                self.noisify_fun = local_noisify
            else:
                raise TypeError(
                    "Incorrect noisify_strategy argument during model initialisation."
                )

        def layers_forward_order(self):
            return self.layers

        def layers_backward_order(self):
            return self.layers[::-1]

        # Define the differentially private training step
        def train_step(self, data):
            # Unpack data
            x, y = data

            with tf.GradientTape() as tape:
                y_pred = self(x, training=True)  # Forward pass
                # tf.cast(y_pred,dtype=y.dtype)
                # Compute the loss value
                # (the loss function is configured in `compile()`)
                loss = self.compiled_loss(y, y_pred, regularization_losses=self.losses)

            # Compute gradients
            trainable_vars = self.trainable_variables
            gradients = tape.gradient(loss, trainable_vars)
            # Get gradient bounds
            gradient_bounds = compute_gradient_bounds(model=self)
            noisy_gradients = self.noisify_fun(
                self, gradient_bounds, trainable_vars, gradients
            )
            # Each optimizer is a postprocessing of the already (epsilon,delta)-DP gradients
            self.optimizer.apply_gradients(zip(noisy_gradients, trainable_vars))
            # self.optimizer.apply_gradients(zip(gradients, trainable_vars))
            # Update Metrics
            self.compiled_metrics.update_state(y, y_pred)
            # Condense to verify |W|_2 = 1
            self.condense()
            return {m.name: m.result() for m in self.metrics}

### `__init__(*args, dp_parameters, dataset_metadata, debug=False, **kwargs)`

Model Class based on the deel.lip.Sequential model. Only layer from the lipdp.layers module are allowed since the framework assume Lipschitz layers.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`dp_parameters` | `DPParameters` | parameters used to set the dp procedure. | required
`dataset_metadata` | `DatasetMetadata` | information about the dataset. Must contain: the input shape, number of training samples, the input bound, number of batches in the dataset and the batch size. | required
`debug` | `bool` | when true print additionnal debug informations (must be in eager mode). Defaults to False. | `False`

Note

The model is then calibrated to verify (epsilon,delta)-DP guarantees by noisying the values of the gradients during the training step. DP accounting is done with the associated Callback.

Raises:

Type | Description
--- | ---
`TypeError` | when the dp_parameters.noisify_strategy is not one of "local" or "global"

Source code in `lipdp/model.py`

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    def __init__(
            self,
            *args,
            dp_parameters: DPParameters,
            dataset_metadata: DatasetMetadata,
            debug: bool = False,
            **kwargs,
    ):
        """Model Class based on the deel.lip.Sequential model. Only layer from the lipdp.layers module are allowed since
        the framework assume Lipschitz layers.

        Args:
            dp_parameters (DPParameters): parameters used to set the dp procedure.
            dataset_metadata (DatasetMetadata): information about the dataset. Must contain: the input shape, number
                of training samples, the input bound, number of batches in the dataset and the batch size.
            debug (bool, optional): when true print additionnal debug informations (must be in eager mode). Defaults to False.

        Note:
            The model is then calibrated to verify (epsilon,delta)-DP guarantees by noisying the values of the gradients during the training step.
            DP accounting is done with the associated Callback.

        Raises:
            TypeError: when the dp_parameters.noisify_strategy is not one of "local" or "global"
        """
        super().__init__(*args, **kwargs)
        self.dp_parameters = dp_parameters
        self.dataset_metadata = dataset_metadata
        self.debug = debug
        if self.dp_parameters.noisify_strategy == "global":
            self.noisify_fun = global_noisify
        elif self.dp_parameters.noisify_strategy == "local":
            self.noisify_fun = local_noisify
        else:
            raise TypeError(
                "Incorrect noisify_strategy argument during model initialisation."
            )

## `compute_gradient_bounds(model)`

Compute the gradient norm bounds of the model.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`model` |  | model to train. | required

Returns:

Name | Type | Description
--- | --- | ---
`gradient_bounds` |  | dictionary of gradient norm bounds with (key, value) pairs (layer_name, gradient_bound). The order of the bounds is the same as the order of the layers returned by model.layers_backward_order().

Source code in `lipdp/model.py`

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    def compute_gradient_bounds(model):
        """Compute the gradient norm bounds of the model.

        Args:
            model: model to train.

        Returns:
            gradient_bounds: dictionary of gradient norm bounds with (key, value) pairs (layer_name, gradient_bound).
                             The order of the bounds is the same as
                             the order of the layers returned by model.layers_backward_order().
        """
        # Initialisation, get lipschitz constant of loss
        input_bounds = {}
        gradient_bounds = {}
        input_bound = None  # Unknown at the start.

        # Forward pass to assess maximum activation norms
        for layer in model.layers_forward_order():
            assert isinstance(layer, DPLayer)
            if model.debug:
                print(f"Layer {layer.name} input bound: {input_bound}")
            input_bounds[layer.name] = input_bound
            input_bound = layer.propagate_inputs(input_bound)

        if model.debug:
            print(f"Layer {layer.name} input bound: {input_bound}")

        # since we aggregate using SUM_OVER_BATCH
        gradient_bound = model.loss.get_L() / model.dataset_metadata.batch_size

        # Backward pass to compute gradient norm bounds and accumulate Lip constant
        for layer in model.layers_backward_order():
            assert isinstance(layer, DPLayer)
            layer_input_bound = input_bounds[layer.name]
            if layer.has_parameters():
                assert len(layer.trainable_variables) == 1
                var_name = layer.trainable_variables[0].name
                gradient_bounds[var_name] = layer.backpropagate_params(
                    layer_input_bound, gradient_bound
                )
            gradient_bound = layer.backpropagate_inputs(layer_input_bound, gradient_bound)

        # Return gradient bounds
        return gradient_bounds

## `get_noise_multiplier_coefs(model)`

Get the noise multiplier coefficients of the model.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`model` |  | model to train. | required

Returns:

Name | Type | Description
--- | --- | ---
`dict_coefs` |  | dictionary of noise multiplier coefficients. The order of the coefficients is the same as the order of the layers returned by model.layers_forward_order().

Source code in `lipdp/model.py`

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    def get_noise_multiplier_coefs(model):
        """Get the noise multiplier coefficients of the model.

        Args:
            model: model to train.

        Returns:
            dict_coefs: dictionary of noise multiplier coefficients.
                        The order of the coefficients is the same as
                        the order of the layers returned by model.layers_forward_order().
        """
        dict_coefs = {}
        for (
            layer
        ) in (
            model.layers_forward_order()
        ):  # remark: insertion order is preserved in Python 3.7+
            assert isinstance(layer, DPLayer)
            if layer.has_parameters():
                assert len(layer.trainable_variables) == 1
                dict_coefs[layer.trainable_variables[0].name] = layer.nm_coef
        return dict_coefs

## `global_noisify(model, gradient_bounds, trainable_vars, gradients)`

Add noise to gradients.

a single global noise is added to all gradients, based on the global sensitivity.

This is the default behaviour of the original DPGD algorithm. This may yield looser privacy bounds than local noisify.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`model` |  | model to train. | required
`gradient_bounds` |  | dictionary of gradient norm upper bounds. The keys are the names of the trainable variables. | required
`trainable_vars` |  | list of trainable variables. The list is in the same order as gradients. | required
`gradients` |  | list of gradients to add noise to. The list is in the same order as trainable_vars. | required

Returns:

Name | Type | Description
--- | --- | ---
`noisy_grads` |  | list of noisy gradients. The list is in the same order as trainable_vars.

Source code in `lipdp/model.py`

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    def global_noisify(model, gradient_bounds, trainable_vars, gradients):
        """Add noise to gradients.

        Remark: a single global noise is added to all gradients, based on the global sensitivity.
                This is the default behaviour of the original DPGD algorithm.
                This may yield looser privacy bounds than local noisify.

        Args:
            model: model to train.
            gradient_bounds: dictionary of gradient norm upper bounds. The keys are the names of the trainable variables.
            trainable_vars: list of trainable variables. The list is in the same order as gradients.
            gradients: list of gradients to add noise to. The list is in the same order as trainable_vars.

        Returns:
            noisy_grads: list of noisy gradients. The list is in the same order as trainable_vars.
        """
        global_sensitivity = np.sqrt(
            sum([bound**2 for bound in gradient_bounds.values()])
        )
        stddev = model.dp_parameters.noise_multiplier * global_sensitivity
        noises = [tf.random.normal(shape=tf.shape(g), stddev=stddev) for g in gradients]
        if model.debug:
            for grad, var in zip(gradients, trainable_vars):
                upperboundgrad = (
                    gradient_bounds[var.name] * model.dataset_metadata.batch_size
                )
                noise_msg = (
                    f"Adding noise of stddev : {stddev}"
                    f" to variable {var.name}"
                    f" of gradient norm upper bound {upperboundgrad}"
                    f" and effective norm {tf.norm(grad)}"
                )
                print(noise_msg)
        noisy_grads = [g + n for g, n in zip(gradients, noises)]
        return noisy_grads

## `local_noisify(model, gradient_bounds, trainable_vars, gradients)`

Add noise to gradients of trainable variables.

Remark: this yields tighter bounds than global_noisify.

Parameters:

Name | Type | Description | Default
--- | --- | --- | ---
`model` |  | model to train. | required
`gradient_bounds` |  | dictionary of gradient norm upper bounds. Keys are trainable variables names. | required
`trainable_vars` |  | list of trainable variables. Same order as gradients. | required
`gradients` |  | list of gradients. Same order as trainable_vars. | required

Returns:

Type | Description
--- | ---
| list of noisy gradients. Same order as trainable_vars.

Source code in `lipdp/model.py`

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    def local_noisify(model, gradient_bounds, trainable_vars, gradients):
        """Add noise to gradients of trainable variables.

        Remark: this yields tighter bounds than global_noisify.

        Args:
            model: model to train.
            gradient_bounds: dictionary of gradient norm upper bounds. Keys are trainable variables names.
            trainable_vars: list of trainable variables. Same order as gradients.
            gradients: list of gradients. Same order as trainable_vars.

        Returns:
            list of noisy gradients. Same order as trainable_vars.
        """
        nm_coefs = get_noise_multiplier_coefs(model)
        noises = []
        for grad, var in zip(gradients, trainable_vars):
            if var.name in gradient_bounds.keys():
                stddev = (
                    model.dp_parameters.noise_multiplier
                    * gradient_bounds[var.name]
                    * nm_coefs[var.name]
                    * 2
                )
                noises.append(tf.random.normal(shape=tf.shape(grad), stddev=stddev))
                if model.debug:
                    upperboundgrad = (
                        gradient_bounds[var.name] * model.dataset_metadata.batch_size
                    )
                    noise_msg = (
                        f"Adding noise of stddev : {stddev}"
                        f" to variable {var.name}"
                        f" of gradient norm upper bound {upperboundgrad}"
                        f" and effective norm {tf.norm(grad)}"
                    )
                    print(noise_msg)
            else:
                raise ValueError(f"Variable {var.name} not in gradient bounds.")

        noisy_grads = [g + n for g, n in zip(gradients, noises)]
        return noisy_grads