input

input

TorchBinomialLayer

Bases: TorchExpFamilyLayer

The Binomial distribution layer.

This is fully factorized down to univariate Binomial distributions.

Source code in cirkit/backend/torch/layers/input.py

class TorchBinomialLayer(TorchExpFamilyLayer):
    """The Binomial distribution layer.

    This is fully factorized down to univariate Binomial distributions.
    """

    # DISABLE: It's designed to have these arguments.
    # pylint: disable-next=too-many-arguments
    def __init__(
        self,
        scope_idx: Tensor,
        num_output_units: int,
        *,
        num_channels: int = 1,
        total_count: int = 1,
        probs: TorchParameter | None = None,
        logits: TorchParameter | None = None,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initialize a Binomial layer.

        Args:
            scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
                $D$ is the number of variables on which the input layers in each fold are defined on.
                Alternatively, a tensor of shape $(D,)$ can be specified, which will be interpreted
                as a tensor of shape $(1, D)$, i.e., with $F = 1$.
            num_output_units: The number of output units.
            num_channels: The number of channels.
            total_count: The number of trials.
            probs: The probabilities parameter of shape $(F, K, C)$, where $K$ is the number of
                output units, and $C$ is the number of channels.
            logits: The logits parameter of shape $(F, K, C)$, where $K$ is the number of
                output units, and $C$ is the number of channels.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the scope contains more than one variable.
            ValueError: If the total count is not positive.
            ValueError: If both the probs and logits parameters are provided, or none of them.
            ValueError: If the parameter's shape is incorrect.
        """
        num_variables = scope_idx.shape[-1]
        if num_variables != 1:
            raise ValueError("The Binomial layer encodes a univariate distribution")
        if total_count < 0:
            raise ValueError("The number of trials must be non-negative")
        super().__init__(
            scope_idx,
            num_output_units,
            num_channels=num_channels,
            semiring=semiring,
        )
        self.total_count = total_count
        if not ((logits is None) ^ (probs is None)):
            raise ValueError("Exactly one between 'logits' and 'probs' must be specified")
        if logits is None:
            assert probs is not None
            if not self._valid_parameter_shape(probs):
                raise ValueError(
                    f"Expected number of folds {self.num_folds} "
                    f"and shape {self._probs_logits_shape} for 'probs', found"
                    f"{probs.num_folds} and {probs.shape}, respectively"
                )
        else:
            if not self._valid_parameter_shape(logits):
                raise ValueError(
                    f"Expected number of folds {self.num_folds} "
                    f"and shape {self._probs_logits_shape} for 'logits', found"
                    f"{logits.num_folds} and {logits.shape}, respectively"
                )
        self.probs = probs
        self.logits = logits

    def _valid_parameter_shape(self, p: TorchParameter) -> bool:
        if p.num_folds != self.num_folds:
            return False
        return p.shape == self._probs_logits_shape

    @property
    def _probs_logits_shape(self) -> tuple[int, ...]:
        return self.num_output_units, self.num_channels

    @property
    def config(self) -> Mapping[str, Any]:
        return {
            "num_output_units": self.num_output_units,
            "num_channels": self.num_channels,
            "total_count": self.total_count,
        }

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        if self.logits is None:
            return {"probs": self.probs}
        return {"logits": self.logits}

    def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
        if x.is_floating_point():
            x = x.long()  # The input to Binomial should be discrete
        x = x.permute(0, 2, 3, 1)  # (F, C, B, 1) -> (F, B, 1, C)
        if self.logits is not None:
            logits = self.logits().unsqueeze(dim=1)  # (F, 1, K, C)
            dist = distributions.Binomial(self.total_count, logits=logits)
        else:
            probs = self.probs().unsqueeze(dim=1)  # (F, 1, K, C)
            dist = distributions.Binomial(self.total_count, probs=probs)
        x = dist.log_prob(x)  # (F, B, K, C)
        return torch.sum(x, dim=3)

    def log_partition_function(self) -> Tensor:
        device = self.logits.device if self.logits is not None else self.probs.device
        return torch.zeros(size=(self.num_folds, 1, self.num_output_units), device=device)

    def sample(self, num_samples: int = 1) -> Tensor:
        logits = torch.log(self.probs()) if self.logits is None else self.logits()
        dist = distributions.Binomial(self.total_count, logits=logits)
        samples = dist.sample((num_samples,))  # (num_samples, F, K, C)
        samples = samples.permute(1, 3, 2, 0)  # (F, C, K, num_samples)
        return samples

_probs_logits_shape property

config property

logits = logits instance-attribute

params property

probs = probs instance-attribute

total_count = total_count instance-attribute

__init__(scope_idx, num_output_units, *, num_channels=1, total_count=1, probs=None, logits=None, semiring=None)

Initialize a Binomial layer.

Parameters:

Name	Type	Description	Default
scope_idx	Tensor	A tensor of shape \((F, D)\), where \(F\) is the number of folds, and \(D\) is the number of variables on which the input layers in each fold are defined on. Alternatively, a tensor of shape \((D,)\) can be specified, which will be interpreted as a tensor of shape \((1, D)\), i.e., with \(F = 1\).	required
num_output_units	int	The number of output units.	required
num_channels	int	The number of channels.	1
total_count	int	The number of trials.	1
probs	TorchParameter | None	The probabilities parameter of shape \((F, K, C)\), where \(K\) is the number of output units, and \(C\) is the number of channels.	None
logits	TorchParameter | None	The logits parameter of shape \((F, K, C)\), where \(K\) is the number of output units, and \(C\) is the number of channels.	None
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the scope contains more than one variable.
ValueError	If the total count is not positive.
ValueError	If both the probs and logits parameters are provided, or none of them.
ValueError	If the parameter's shape is incorrect.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    scope_idx: Tensor,
    num_output_units: int,
    *,
    num_channels: int = 1,
    total_count: int = 1,
    probs: TorchParameter | None = None,
    logits: TorchParameter | None = None,
    semiring: Semiring | None = None,
) -> None:
    r"""Initialize a Binomial layer.

    Args:
        scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
            $D$ is the number of variables on which the input layers in each fold are defined on.
            Alternatively, a tensor of shape $(D,)$ can be specified, which will be interpreted
            as a tensor of shape $(1, D)$, i.e., with $F = 1$.
        num_output_units: The number of output units.
        num_channels: The number of channels.
        total_count: The number of trials.
        probs: The probabilities parameter of shape $(F, K, C)$, where $K$ is the number of
            output units, and $C$ is the number of channels.
        logits: The logits parameter of shape $(F, K, C)$, where $K$ is the number of
            output units, and $C$ is the number of channels.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the scope contains more than one variable.
        ValueError: If the total count is not positive.
        ValueError: If both the probs and logits parameters are provided, or none of them.
        ValueError: If the parameter's shape is incorrect.
    """
    num_variables = scope_idx.shape[-1]
    if num_variables != 1:
        raise ValueError("The Binomial layer encodes a univariate distribution")
    if total_count < 0:
        raise ValueError("The number of trials must be non-negative")
    super().__init__(
        scope_idx,
        num_output_units,
        num_channels=num_channels,
        semiring=semiring,
    )
    self.total_count = total_count
    if not ((logits is None) ^ (probs is None)):
        raise ValueError("Exactly one between 'logits' and 'probs' must be specified")
    if logits is None:
        assert probs is not None
        if not self._valid_parameter_shape(probs):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._probs_logits_shape} for 'probs', found"
                f"{probs.num_folds} and {probs.shape}, respectively"
            )
    else:
        if not self._valid_parameter_shape(logits):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._probs_logits_shape} for 'logits', found"
                f"{logits.num_folds} and {logits.shape}, respectively"
            )
    self.probs = probs
    self.logits = logits

_valid_parameter_shape(p)

Source code in cirkit/backend/torch/layers/input.py

def _valid_parameter_shape(self, p: TorchParameter) -> bool:
    if p.num_folds != self.num_folds:
        return False
    return p.shape == self._probs_logits_shape

log_partition_function()

Source code in cirkit/backend/torch/layers/input.py

def log_partition_function(self) -> Tensor:
    device = self.logits.device if self.logits is not None else self.probs.device
    return torch.zeros(size=(self.num_folds, 1, self.num_output_units), device=device)

log_unnormalized_likelihood(x)

Source code in cirkit/backend/torch/layers/input.py

def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
    if x.is_floating_point():
        x = x.long()  # The input to Binomial should be discrete
    x = x.permute(0, 2, 3, 1)  # (F, C, B, 1) -> (F, B, 1, C)
    if self.logits is not None:
        logits = self.logits().unsqueeze(dim=1)  # (F, 1, K, C)
        dist = distributions.Binomial(self.total_count, logits=logits)
    else:
        probs = self.probs().unsqueeze(dim=1)  # (F, 1, K, C)
        dist = distributions.Binomial(self.total_count, probs=probs)
    x = dist.log_prob(x)  # (F, B, K, C)
    return torch.sum(x, dim=3)

sample(num_samples=1)

Source code in cirkit/backend/torch/layers/input.py

def sample(self, num_samples: int = 1) -> Tensor:
    logits = torch.log(self.probs()) if self.logits is None else self.logits()
    dist = distributions.Binomial(self.total_count, logits=logits)
    samples = dist.sample((num_samples,))  # (num_samples, F, K, C)
    samples = samples.permute(1, 3, 2, 0)  # (F, C, K, num_samples)
    return samples

TorchCategoricalLayer

Bases: TorchExpFamilyLayer

The Categorical distribution layer, parameterized by either probabilities or logits.

Source code in cirkit/backend/torch/layers/input.py

class TorchCategoricalLayer(TorchExpFamilyLayer):
    """The Categorical distribution layer, parameterized by either probabilities or logits."""

    # pylint: disable-next=too-many-arguments
    def __init__(
        self,
        scope_idx: Tensor,
        num_output_units: int,
        num_channels: int = 1,
        *,
        num_categories: int = 2,
        probs: TorchParameter | None = None,
        logits: TorchParameter | None = None,
        semiring: Semiring | None = None,
    ) -> None:
        """Initialize a Categorical layer.

        Args:
            scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
                $D$ is the number of variables on which the input layers in each fold are defined on.
                Alternatively, a tensor of shape $(D,)$ can be specified, which will be interpreted
                as a tensor of shape $(1, D)$, i.e., with $F = 1$.
            num_output_units: The number of output units.
            num_channels: The number of channels.
            num_categories: The number of categories for Categorical distribution.
            probs: The probabilities parameter of shape $(F, K, C, V)$, where $K$ is the number of
                output units, $C$ is the number of channels, and $V$ is the number of categories.
            logits: The logits parameter of shape $(F, K, C, V)$, where $K$ is the number of
                output units, $C$ is the number of channels, and $V$ is the number of categories.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the scope contains more than one variable.
            ValueError: If the number of categories is negative.
            ValueError: If both the probs and logits parameters are provided, or none of them.
            ValueError: If the parameter's shape is incorrect.
        """
        num_variables = scope_idx.shape[-1]
        if num_variables != 1:
            raise ValueError("The Gaussian layer encodes a univariate distribution")
        if num_categories <= 0:
            raise ValueError(
                "The number of categories for Categorical distribution must be positive"
            )
        super().__init__(
            scope_idx,
            num_output_units,
            num_channels=num_channels,
            semiring=semiring,
        )
        self.num_categories = num_categories
        if not ((logits is None) ^ (probs is None)):
            raise ValueError("Exactly one between 'logits' and 'probs' must be specified")
        if logits is None:
            assert probs is not None
            if not self._valid_parameter_shape(probs):
                raise ValueError(
                    f"Expected number of folds {self.num_folds} "
                    f"and shape {self._probs_logits_shape} for 'probs', found"
                    f"{probs.num_folds} and {probs.shape}, respectively"
                )
        elif not self._valid_parameter_shape(logits):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._probs_logits_shape} for 'logits', found"
                f"{logits.num_folds} and {logits.shape}, respectively"
            )
        self.probs = probs
        self.logits = logits

    def _valid_parameter_shape(self, p: TorchParameter) -> bool:
        if p.num_folds != self.num_folds:
            return False
        return p.shape == self._probs_logits_shape

    @property
    def _probs_logits_shape(self) -> tuple[int, ...]:
        return self.num_output_units, self.num_channels, self.num_categories

    @property
    def config(self) -> Mapping[str, Any]:
        return {
            "num_output_units": self.num_output_units,
            "num_channels": self.num_channels,
            "num_categories": self.num_categories,
        }

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        if self.logits is None:
            return {"probs": self.probs}
        return {"logits": self.logits}

    def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
        if x.is_floating_point():
            x = x.long()  # The input to Categorical should be discrete
        # x: (F, C, B, 1) -> (F, C, B)
        x = x.squeeze(dim=3)
        # logits: (F, K, C, N)
        logits = torch.log(self.probs()) if self.logits is None else self.logits()
        if self.num_channels == 1:
            idx_fold = torch.arange(self.num_folds)
            x = logits[:, :, 0][idx_fold[:, None], :, x[:, 0]]
        else:
            idx_fold = torch.arange(self.num_folds)[:, None, None]
            idx_channel = torch.arange(self.num_channels)[None, :, None]
            x = torch.sum(logits[idx_fold, :, idx_channel, x], dim=1)
        return x

    def log_partition_function(self) -> Tensor:
        if self.logits is None:
            return torch.zeros(
                size=(self.num_folds, 1, self.num_output_units), device=self.probs.device
            )
        logits = self.logits()
        return torch.sum(torch.logsumexp(logits, dim=3), dim=2).unsqueeze(dim=1)

    def sample(self, num_samples: int = 1) -> Tensor:
        logits = torch.log(self.probs()) if self.logits is None else self.logits()
        dist = distributions.Categorical(logits=logits)
        samples = dist.sample((num_samples,))  # (N, F, K, C)
        samples = samples.permute(1, 3, 2, 0)  # (F, C, K, N)
        return samples

_probs_logits_shape property

config property

logits = logits instance-attribute

num_categories = num_categories instance-attribute

params property

probs = probs instance-attribute

__init__(scope_idx, num_output_units, num_channels=1, *, num_categories=2, probs=None, logits=None, semiring=None)

Initialize a Categorical layer.

Parameters:

Name	Type	Description	Default
scope_idx	Tensor	A tensor of shape \((F, D)\), where \(F\) is the number of folds, and \(D\) is the number of variables on which the input layers in each fold are defined on. Alternatively, a tensor of shape \((D,)\) can be specified, which will be interpreted as a tensor of shape \((1, D)\), i.e., with \(F = 1\).	required
num_output_units	int	The number of output units.	required
num_channels	int	The number of channels.	1
num_categories	int	The number of categories for Categorical distribution.	2
probs	TorchParameter | None	The probabilities parameter of shape \((F, K, C, V)\), where \(K\) is the number of output units, \(C\) is the number of channels, and \(V\) is the number of categories.	None
logits	TorchParameter | None	The logits parameter of shape \((F, K, C, V)\), where \(K\) is the number of output units, \(C\) is the number of channels, and \(V\) is the number of categories.	None
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the scope contains more than one variable.
ValueError	If the number of categories is negative.
ValueError	If both the probs and logits parameters are provided, or none of them.
ValueError	If the parameter's shape is incorrect.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    scope_idx: Tensor,
    num_output_units: int,
    num_channels: int = 1,
    *,
    num_categories: int = 2,
    probs: TorchParameter | None = None,
    logits: TorchParameter | None = None,
    semiring: Semiring | None = None,
) -> None:
    """Initialize a Categorical layer.

    Args:
        scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
            $D$ is the number of variables on which the input layers in each fold are defined on.
            Alternatively, a tensor of shape $(D,)$ can be specified, which will be interpreted
            as a tensor of shape $(1, D)$, i.e., with $F = 1$.
        num_output_units: The number of output units.
        num_channels: The number of channels.
        num_categories: The number of categories for Categorical distribution.
        probs: The probabilities parameter of shape $(F, K, C, V)$, where $K$ is the number of
            output units, $C$ is the number of channels, and $V$ is the number of categories.
        logits: The logits parameter of shape $(F, K, C, V)$, where $K$ is the number of
            output units, $C$ is the number of channels, and $V$ is the number of categories.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the scope contains more than one variable.
        ValueError: If the number of categories is negative.
        ValueError: If both the probs and logits parameters are provided, or none of them.
        ValueError: If the parameter's shape is incorrect.
    """
    num_variables = scope_idx.shape[-1]
    if num_variables != 1:
        raise ValueError("The Gaussian layer encodes a univariate distribution")
    if num_categories <= 0:
        raise ValueError(
            "The number of categories for Categorical distribution must be positive"
        )
    super().__init__(
        scope_idx,
        num_output_units,
        num_channels=num_channels,
        semiring=semiring,
    )
    self.num_categories = num_categories
    if not ((logits is None) ^ (probs is None)):
        raise ValueError("Exactly one between 'logits' and 'probs' must be specified")
    if logits is None:
        assert probs is not None
        if not self._valid_parameter_shape(probs):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._probs_logits_shape} for 'probs', found"
                f"{probs.num_folds} and {probs.shape}, respectively"
            )
    elif not self._valid_parameter_shape(logits):
        raise ValueError(
            f"Expected number of folds {self.num_folds} "
            f"and shape {self._probs_logits_shape} for 'logits', found"
            f"{logits.num_folds} and {logits.shape}, respectively"
        )
    self.probs = probs
    self.logits = logits

_valid_parameter_shape(p)

Source code in cirkit/backend/torch/layers/input.py

def _valid_parameter_shape(self, p: TorchParameter) -> bool:
    if p.num_folds != self.num_folds:
        return False
    return p.shape == self._probs_logits_shape

log_partition_function()

Source code in cirkit/backend/torch/layers/input.py

def log_partition_function(self) -> Tensor:
    if self.logits is None:
        return torch.zeros(
            size=(self.num_folds, 1, self.num_output_units), device=self.probs.device
        )
    logits = self.logits()
    return torch.sum(torch.logsumexp(logits, dim=3), dim=2).unsqueeze(dim=1)

log_unnormalized_likelihood(x)

Source code in cirkit/backend/torch/layers/input.py

def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
    if x.is_floating_point():
        x = x.long()  # The input to Categorical should be discrete
    # x: (F, C, B, 1) -> (F, C, B)
    x = x.squeeze(dim=3)
    # logits: (F, K, C, N)
    logits = torch.log(self.probs()) if self.logits is None else self.logits()
    if self.num_channels == 1:
        idx_fold = torch.arange(self.num_folds)
        x = logits[:, :, 0][idx_fold[:, None], :, x[:, 0]]
    else:
        idx_fold = torch.arange(self.num_folds)[:, None, None]
        idx_channel = torch.arange(self.num_channels)[None, :, None]
        x = torch.sum(logits[idx_fold, :, idx_channel, x], dim=1)
    return x

sample(num_samples=1)

Source code in cirkit/backend/torch/layers/input.py

def sample(self, num_samples: int = 1) -> Tensor:
    logits = torch.log(self.probs()) if self.logits is None else self.logits()
    dist = distributions.Categorical(logits=logits)
    samples = dist.sample((num_samples,))  # (N, F, K, C)
    samples = samples.permute(1, 3, 2, 0)  # (F, C, K, N)
    return samples

TorchConstantLayer

Bases: TorchInputLayer, ABC

An input layer encoding a constant vector or, equivalently, a vector of functions defined over empty variable scopes.

Source code in cirkit/backend/torch/layers/input.py

class TorchConstantLayer(TorchInputLayer, ABC):
    """An input layer encoding a constant vector or, equivalently, a vector of functions
    defined over empty variable scopes.
    """

    def __init__(
        self,
        num_output_units: int,
        num_folds: int,
        *,
        semiring: Semiring | None = None,
    ) -> None:
        """Initializes a constant layer.

        Args:
            num_output_units: The number of output units.
            num_folds: The number of folds.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].
        """
        super().__init__(
            torch.empty(size=(num_folds, 0), dtype=torch.int64), num_output_units, semiring=semiring
        )

    def __call__(self, batch_size: int) -> Tensor:
        # IGNORE: Idiom for nn.Module.__call__.
        return super().__call__(batch_size)  # type: ignore[no-any-return,misc]

    @abstractmethod
    def forward(self, batch_size: int) -> Tensor:
        r"""Invoke the forward function.

        Args:
            batch_size: The batch size $B$ of the output tensor.

        Returns:
            Tensor: The tensor output of this layer, having shape $(F, B, K)$, where $K$
                is the number of output units, and $B$ is the batch size given as input.
        """

__call__(batch_size)

Source code in cirkit/backend/torch/layers/input.py

def __call__(self, batch_size: int) -> Tensor:
    # IGNORE: Idiom for nn.Module.__call__.
    return super().__call__(batch_size)  # type: ignore[no-any-return,misc]

__init__(num_output_units, num_folds, *, semiring=None)

Initializes a constant layer.

Parameters:

Name	Type	Description	Default
num_output_units	int	The number of output units.	required
num_folds	int	The number of folds.	required
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    num_output_units: int,
    num_folds: int,
    *,
    semiring: Semiring | None = None,
) -> None:
    """Initializes a constant layer.

    Args:
        num_output_units: The number of output units.
        num_folds: The number of folds.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].
    """
    super().__init__(
        torch.empty(size=(num_folds, 0), dtype=torch.int64), num_output_units, semiring=semiring
    )

forward(batch_size) abstractmethod

Invoke the forward function.

Parameters:

Name	Type	Description	Default
batch_size	int	The batch size \(B\) of the output tensor.	required

Returns:

Name	Type	Description
Tensor	Tensor	The tensor output of this layer, having shape \((F, B, K)\), where \(K\) is the number of output units, and \(B\) is the batch size given as input.

Source code in cirkit/backend/torch/layers/input.py

@abstractmethod
def forward(self, batch_size: int) -> Tensor:
    r"""Invoke the forward function.

    Args:
        batch_size: The batch size $B$ of the output tensor.

    Returns:
        Tensor: The tensor output of this layer, having shape $(F, B, K)$, where $K$
            is the number of output units, and $B$ is the batch size given as input.
    """

TorchConstantValueLayer

Bases: TorchConstantLayer

An input layer having empty scope and computing a constant value.

Source code in cirkit/backend/torch/layers/input.py

class TorchConstantValueLayer(TorchConstantLayer):
    """An input layer having empty scope and computing a constant value."""

    def __init__(
        self,
        num_output_units: int,
        *,
        log_space: bool = False,
        value: TorchParameter,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initialize a constant value input layer.

        Args:
            num_output_units: The number of output units.
            log_space: Whether the given value is in the log-space, i.e., this constant
                layer should encode functions $\exp(x)$ rather than just x.
            value: The tensor value encoded by the layer, given by a parameter of shape $(F, K)$,
                where $F$ is the number of folds and $K$ is the numer of output units.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the number of folds of the shape of the given value is incorrect.
        """
        super().__init__(
            num_output_units,
            value.num_folds,
            semiring=semiring,
        )
        if value.num_folds != self.num_folds:
            raise ValueError(
                f"The value must have number of folds {self.num_folds}, "
                f"but found {value.num_folds}"
            )
        if value.shape != (num_output_units,):
            raise ValueError(
                f"The shape of the value must be ({num_output_units},), " f"but found {value.shape}"
            )
        self.value = value
        self.log_space = log_space
        self._source_semiring = LSESumSemiring if log_space else SumProductSemiring

    @property
    def config(self) -> Mapping[str, Any]:
        return {"num_output_units": self.num_output_units, "log_space": self.log_space}

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        return {"value": self.value}

    def forward(self, batch_size: int) -> Tensor:
        value = self.value()  # (F, Ko)
        # value: (F, B, Ko)
        value = value.unsqueeze(dim=1).expand(value.shape[0], batch_size, value.shape[1])
        return self.semiring.map_from(value, self._source_semiring)

_source_semiring = LSESumSemiring if log_space else SumProductSemiring instance-attribute

config property

log_space = log_space instance-attribute

params property

value = value instance-attribute

__init__(num_output_units, *, log_space=False, value, semiring=None)

Initialize a constant value input layer.

Parameters:

Name	Type	Description	Default
num_output_units	int	The number of output units.	required
log_space	bool	Whether the given value is in the log-space, i.e., this constant layer should encode functions \(\exp(x)\) rather than just x.	False
value	TorchParameter	The tensor value encoded by the layer, given by a parameter of shape \((F, K)\), where \(F\) is the number of folds and \(K\) is the numer of output units.	required
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the number of folds of the shape of the given value is incorrect.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    num_output_units: int,
    *,
    log_space: bool = False,
    value: TorchParameter,
    semiring: Semiring | None = None,
) -> None:
    r"""Initialize a constant value input layer.

    Args:
        num_output_units: The number of output units.
        log_space: Whether the given value is in the log-space, i.e., this constant
            layer should encode functions $\exp(x)$ rather than just x.
        value: The tensor value encoded by the layer, given by a parameter of shape $(F, K)$,
            where $F$ is the number of folds and $K$ is the numer of output units.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the number of folds of the shape of the given value is incorrect.
    """
    super().__init__(
        num_output_units,
        value.num_folds,
        semiring=semiring,
    )
    if value.num_folds != self.num_folds:
        raise ValueError(
            f"The value must have number of folds {self.num_folds}, "
            f"but found {value.num_folds}"
        )
    if value.shape != (num_output_units,):
        raise ValueError(
            f"The shape of the value must be ({num_output_units},), " f"but found {value.shape}"
        )
    self.value = value
    self.log_space = log_space
    self._source_semiring = LSESumSemiring if log_space else SumProductSemiring

forward(batch_size)

Source code in cirkit/backend/torch/layers/input.py

def forward(self, batch_size: int) -> Tensor:
    value = self.value()  # (F, Ko)
    # value: (F, B, Ko)
    value = value.unsqueeze(dim=1).expand(value.shape[0], batch_size, value.shape[1])
    return self.semiring.map_from(value, self._source_semiring)

TorchEmbeddingLayer

Bases: TorchInputFunctionLayer

The embedding input layer, where each input function maps a discrete variable having finite support \(\{0,\ldots,V-1\}\) to the corresponding entry of a \(V\)-th dimensional vector.

Source code in cirkit/backend/torch/layers/input.py

class TorchEmbeddingLayer(TorchInputFunctionLayer):
    r"""The embedding input layer, where each input function maps a discrete variable having
    finite support $\{0,\ldots,V-1\}$ to the corresponding entry of a $V$-th dimensional vector.
    """

    def __init__(
        self,
        scope_idx: Tensor,
        num_output_units: int,
        num_channels: int = 1,
        *,
        num_states: int = 2,
        weight: TorchParameter,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initialize an embedding input layer.

        Args:
            scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
                $D$ is the number of variables on which the input layers in each fold are defined
                on. Alternatively, a tensor of shape $(D,)$ can be specified, which will be
                interpreted as a tensor of shape $(1, D)$, i.e., with $F = 1$.
            num_output_units: The number of output units.
            num_channels: The number of channels.
            num_states: The number of states $V$ each variable can assume.
            weight: The weight parameter of shape $(F, K, C, N)$, where $K$ is the number of output
                units, $C$ is the number of channels, and $V$ is the number of states.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the scope contains more than one variable.
            ValueError: If the number of states $V$ is less than 2.
            ValueError: If the parameter's shape is incorrect.
        """
        num_variables = scope_idx.shape[-1]
        if num_variables != 1:
            raise ValueError("The Embedding layer encodes univariate functions")
        if num_states <= 1:
            raise ValueError("The number of states must be at least 2")
        super().__init__(
            scope_idx,
            num_output_units,
            num_channels=num_channels,
            semiring=semiring,
        )
        self.num_states = num_states
        if not self._valid_weight_shape(weight):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._weight_shape} for 'weight', found"
                f"{weight.num_folds} and {weight.shape}, respectively"
            )
        self.weight = weight

    def _valid_weight_shape(self, p: TorchParameter) -> bool:
        if p.num_folds != self.num_folds:
            return False
        return p.shape == self._weight_shape

    @property
    def _weight_shape(self) -> tuple[int, ...]:
        return self.num_output_units, self.num_channels, self.num_states

    @property
    def config(self) -> Mapping[str, Any]:
        return {
            "num_output_units": self.num_output_units,
            "num_channels": self.num_channels,
            "num_states": self.num_states,
        }

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        return {"weight": self.weight}

    def forward(self, x: Tensor) -> Tensor:
        if x.is_floating_point():
            x = x.long()  # The input to Embedding should be discrete
        x = x.squeeze(dim=3)  # (F, C, B)
        weight = self.weight()
        if self.num_channels == 1:
            idx_fold = torch.arange(self.num_folds)
            x = weight[:, :, 0][idx_fold[:, None], :, x[:, 0]]
            x = self.semiring.map_from(x, SumProductSemiring)
        else:
            idx_fold = torch.arange(self.num_folds)[:, None, None]
            idx_channel = torch.arange(self.num_channels)[None, :, None]
            x = weight[idx_fold, :, idx_channel, x]
            x = self.semiring.map_from(x, SumProductSemiring)
            x = self.semiring.prod(x, dim=1)
        return x  # (F, B, K)

_weight_shape property

config property

num_states = num_states instance-attribute

params property

weight = weight instance-attribute

__init__(scope_idx, num_output_units, num_channels=1, *, num_states=2, weight, semiring=None)

Initialize an embedding input layer.

Parameters:

Name	Type	Description	Default
scope_idx	Tensor	A tensor of shape \((F, D)\), where \(F\) is the number of folds, and \(D\) is the number of variables on which the input layers in each fold are defined on. Alternatively, a tensor of shape \((D,)\) can be specified, which will be interpreted as a tensor of shape \((1, D)\), i.e., with \(F = 1\).	required
num_output_units	int	The number of output units.	required
num_channels	int	The number of channels.	1
num_states	int	The number of states \(V\) each variable can assume.	2
weight	TorchParameter	The weight parameter of shape \((F, K, C, N)\), where \(K\) is the number of output units, \(C\) is the number of channels, and \(V\) is the number of states.	required
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the scope contains more than one variable.
ValueError	If the number of states \(V\) is less than 2.
ValueError	If the parameter's shape is incorrect.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    scope_idx: Tensor,
    num_output_units: int,
    num_channels: int = 1,
    *,
    num_states: int = 2,
    weight: TorchParameter,
    semiring: Semiring | None = None,
) -> None:
    r"""Initialize an embedding input layer.

    Args:
        scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
            $D$ is the number of variables on which the input layers in each fold are defined
            on. Alternatively, a tensor of shape $(D,)$ can be specified, which will be
            interpreted as a tensor of shape $(1, D)$, i.e., with $F = 1$.
        num_output_units: The number of output units.
        num_channels: The number of channels.
        num_states: The number of states $V$ each variable can assume.
        weight: The weight parameter of shape $(F, K, C, N)$, where $K$ is the number of output
            units, $C$ is the number of channels, and $V$ is the number of states.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the scope contains more than one variable.
        ValueError: If the number of states $V$ is less than 2.
        ValueError: If the parameter's shape is incorrect.
    """
    num_variables = scope_idx.shape[-1]
    if num_variables != 1:
        raise ValueError("The Embedding layer encodes univariate functions")
    if num_states <= 1:
        raise ValueError("The number of states must be at least 2")
    super().__init__(
        scope_idx,
        num_output_units,
        num_channels=num_channels,
        semiring=semiring,
    )
    self.num_states = num_states
    if not self._valid_weight_shape(weight):
        raise ValueError(
            f"Expected number of folds {self.num_folds} "
            f"and shape {self._weight_shape} for 'weight', found"
            f"{weight.num_folds} and {weight.shape}, respectively"
        )
    self.weight = weight

_valid_weight_shape(p)

Source code in cirkit/backend/torch/layers/input.py

def _valid_weight_shape(self, p: TorchParameter) -> bool:
    if p.num_folds != self.num_folds:
        return False
    return p.shape == self._weight_shape

forward(x)

Source code in cirkit/backend/torch/layers/input.py

def forward(self, x: Tensor) -> Tensor:
    if x.is_floating_point():
        x = x.long()  # The input to Embedding should be discrete
    x = x.squeeze(dim=3)  # (F, C, B)
    weight = self.weight()
    if self.num_channels == 1:
        idx_fold = torch.arange(self.num_folds)
        x = weight[:, :, 0][idx_fold[:, None], :, x[:, 0]]
        x = self.semiring.map_from(x, SumProductSemiring)
    else:
        idx_fold = torch.arange(self.num_folds)[:, None, None]
        idx_channel = torch.arange(self.num_channels)[None, :, None]
        x = weight[idx_fold, :, idx_channel, x]
        x = self.semiring.map_from(x, SumProductSemiring)
        x = self.semiring.prod(x, dim=1)
    return x  # (F, B, K)

TorchEvidenceLayer

Bases: TorchConstantLayer

The input layer computing the output of another input layer on a given observation.

Source code in cirkit/backend/torch/layers/input.py

class TorchEvidenceLayer(TorchConstantLayer):
    """The input layer computing the output of another input layer on a given observation."""

    def __init__(
        self,
        layer: TorchInputLayer,
        *,
        observation: TorchParameter,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initializes an evidence layer.

        Args:
            layer: The input layer on which compute the evidence of.
            observation: The observation, i.e., the input to pass to the given input layer.
                It must be a parameter of shape $(F, C, D)$, where $F$ is the number of folds
                of the given layer, $D$ is the number variables the given layer is defined on,
                and $C$ is the number channels per variable.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the number of folds or the shape of the given observation is incorrect,
                with respect to the expected input shape of the given input layer.
        """
        if observation.num_folds != layer.num_folds:
            raise ValueError(
                f"The number of folds in the observation and in the layer should be the same, "
                f"but found {observation.num_folds} and {layer.num_folds} respectively"
            )
        if len(observation.shape) != 2:
            raise ValueError(
                f"Expected observation of shape (num_channels, num_variables), "
                f"but found {observation.shape}"
            )
        num_channels, num_variables = observation.shape
        if num_channels != layer.num_channels:
            raise ValueError(
                f"Expected an observation with number of channels {layer.num_channels}, "
                f"but found {num_channels}"
            )
        if num_variables != layer.num_variables:
            raise ValueError(
                f"Expected an observation with number of variables {layer.num_variables}, "
                f"but found {num_variables}"
            )
        super().__init__(layer.num_output_units, layer.num_folds, semiring=semiring)
        self.layer = layer
        self.observation = observation

    @property
    def config(self) -> Mapping[str, Any]:
        return {}

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        return {"observation": self.observation}

    @property
    def sub_modules(self) -> Mapping[str, TorchInputLayer]:
        return {"layer": self.layer}

    def forward(self, batch_size: int) -> Tensor:
        obs = self.observation()  # (F, C, D)
        obs = obs.unsqueeze(dim=2)  # (F, C, 1, D)
        x = self.layer(obs)  # (F, 1, K)
        return x.expand(x.shape[0], batch_size, x.shape[2])

    def sample(self, num_samples: int = 1) -> Tensor:
        if self.num_variables != 1:
            raise NotImplementedError("Sampling a multivariate Evidence layer is not implemented")
        # Sampling an evidence layer translates to return the given observation
        obs = self.observation()  # (F, C, D=1)
        obs = obs.unsqueeze(dim=-1)  # (F, C, 1, 1)
        return obs.expand(size=(-1, -1, self.num_output_units, num_samples))

config property

layer = layer instance-attribute

observation = observation instance-attribute

params property

sub_modules property

__init__(layer, *, observation, semiring=None)

Initializes an evidence layer.

Parameters:

Name	Type	Description	Default
layer	TorchInputLayer	The input layer on which compute the evidence of.	required
observation	TorchParameter	The observation, i.e., the input to pass to the given input layer. It must be a parameter of shape \((F, C, D)\), where \(F\) is the number of folds of the given layer, \(D\) is the number variables the given layer is defined on, and \(C\) is the number channels per variable.	required
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the number of folds or the shape of the given observation is incorrect, with respect to the expected input shape of the given input layer.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    layer: TorchInputLayer,
    *,
    observation: TorchParameter,
    semiring: Semiring | None = None,
) -> None:
    r"""Initializes an evidence layer.

    Args:
        layer: The input layer on which compute the evidence of.
        observation: The observation, i.e., the input to pass to the given input layer.
            It must be a parameter of shape $(F, C, D)$, where $F$ is the number of folds
            of the given layer, $D$ is the number variables the given layer is defined on,
            and $C$ is the number channels per variable.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the number of folds or the shape of the given observation is incorrect,
            with respect to the expected input shape of the given input layer.
    """
    if observation.num_folds != layer.num_folds:
        raise ValueError(
            f"The number of folds in the observation and in the layer should be the same, "
            f"but found {observation.num_folds} and {layer.num_folds} respectively"
        )
    if len(observation.shape) != 2:
        raise ValueError(
            f"Expected observation of shape (num_channels, num_variables), "
            f"but found {observation.shape}"
        )
    num_channels, num_variables = observation.shape
    if num_channels != layer.num_channels:
        raise ValueError(
            f"Expected an observation with number of channels {layer.num_channels}, "
            f"but found {num_channels}"
        )
    if num_variables != layer.num_variables:
        raise ValueError(
            f"Expected an observation with number of variables {layer.num_variables}, "
            f"but found {num_variables}"
        )
    super().__init__(layer.num_output_units, layer.num_folds, semiring=semiring)
    self.layer = layer
    self.observation = observation

forward(batch_size)

Source code in cirkit/backend/torch/layers/input.py

def forward(self, batch_size: int) -> Tensor:
    obs = self.observation()  # (F, C, D)
    obs = obs.unsqueeze(dim=2)  # (F, C, 1, D)
    x = self.layer(obs)  # (F, 1, K)
    return x.expand(x.shape[0], batch_size, x.shape[2])

sample(num_samples=1)

Source code in cirkit/backend/torch/layers/input.py

def sample(self, num_samples: int = 1) -> Tensor:
    if self.num_variables != 1:
        raise NotImplementedError("Sampling a multivariate Evidence layer is not implemented")
    # Sampling an evidence layer translates to return the given observation
    obs = self.observation()  # (F, C, D=1)
    obs = obs.unsqueeze(dim=-1)  # (F, C, 1, 1)
    return obs.expand(size=(-1, -1, self.num_output_units, num_samples))

TorchExpFamilyLayer

Bases: TorchInputFunctionLayer, ABC

The abstract base class for exponential family distribution layers. An input layer that is an exponential family distribution must define two methods. The first one is the log_unnormalized_likelihood, used to compute the possibly-unnormalized log-likelihood. The second one is the log_partition_function, used to compute the logarithm of the partition function.

Source code in cirkit/backend/torch/layers/input.py

class TorchExpFamilyLayer(TorchInputFunctionLayer, ABC):
    """The abstract base class for exponential family distribution layers.
    An input layer that is an exponential family distribution must define two methods.
    The first one is the ```log_unnormalized_likelihood```, used to compute the
    possibly-unnormalized log-likelihood. The second one is the ```log_partition_function```,
    used to compute the logarithm of the partition function."""

    def forward(self, x: Tensor) -> Tensor:
        x = self.log_unnormalized_likelihood(x)
        return self.semiring.map_from(x, LSESumSemiring)

    def integrate(self) -> Tensor:
        log_partition = self.log_partition_function()
        return self.semiring.map_from(log_partition, LSESumSemiring)

    @abstractmethod
    def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
        """Compute the (possibly unnormalized) log-likelihood of the given inputs.

        Args:
            x: The input tensor.

        Returns:
            Tensor: The (possibly unnormalized) log-likelihood as a tensor of shape $(F, K)$,
                where $F$ is the number of folds and $K$ is the number of output units.
        """

    @abstractmethod
    def log_partition_function(self) -> Tensor:
        """Compute the logarithm of the partition function of the layer.

        Returns:
            Tensor: The logarithm of the partition function as a tensor of shape $(F, K)$,
                where $F$ is the number of folds and $K$ is the number of output units.
                Note that it will be a tensor of zeros if the layer encodes already normalized
                exponential family distributions.
        """

forward(x)

Source code in cirkit/backend/torch/layers/input.py

def forward(self, x: Tensor) -> Tensor:
    x = self.log_unnormalized_likelihood(x)
    return self.semiring.map_from(x, LSESumSemiring)

integrate()

Source code in cirkit/backend/torch/layers/input.py

def integrate(self) -> Tensor:
    log_partition = self.log_partition_function()
    return self.semiring.map_from(log_partition, LSESumSemiring)

log_partition_function() abstractmethod

Compute the logarithm of the partition function of the layer.

Returns:

Name	Type	Description
Tensor	Tensor	The logarithm of the partition function as a tensor of shape \((F, K)\), where \(F\) is the number of folds and \(K\) is the number of output units. Note that it will be a tensor of zeros if the layer encodes already normalized exponential family distributions.

Source code in cirkit/backend/torch/layers/input.py

@abstractmethod
def log_partition_function(self) -> Tensor:
    """Compute the logarithm of the partition function of the layer.

    Returns:
        Tensor: The logarithm of the partition function as a tensor of shape $(F, K)$,
            where $F$ is the number of folds and $K$ is the number of output units.
            Note that it will be a tensor of zeros if the layer encodes already normalized
            exponential family distributions.
    """

log_unnormalized_likelihood(x) abstractmethod

Compute the (possibly unnormalized) log-likelihood of the given inputs.

Parameters:

Name	Type	Description	Default
x	Tensor	The input tensor.	required

Returns:

Name	Type	Description
Tensor	Tensor	The (possibly unnormalized) log-likelihood as a tensor of shape \((F, K)\), where \(F\) is the number of folds and \(K\) is the number of output units.

Source code in cirkit/backend/torch/layers/input.py

@abstractmethod
def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
    """Compute the (possibly unnormalized) log-likelihood of the given inputs.

    Args:
        x: The input tensor.

    Returns:
        Tensor: The (possibly unnormalized) log-likelihood as a tensor of shape $(F, K)$,
            where $F$ is the number of folds and $K$ is the number of output units.
    """

TorchGaussianLayer

Bases: TorchExpFamilyLayer

The Gaussian distribution layer. Optionally, this layer can encode unnormalized Gaussian distributions with the spefication of a log-partition function parameter.

Source code in cirkit/backend/torch/layers/input.py

class TorchGaussianLayer(TorchExpFamilyLayer):
    """The Gaussian distribution layer. Optionally, this layer can encode unnormalized Gaussian
    distributions with the spefication of a log-partition function parameter."""

    def __init__(
        self,
        scope_idx: Tensor,
        num_output_units: int,
        num_channels: int = 1,
        *,
        mean: TorchParameter,
        stddev: TorchParameter,
        log_partition: TorchParameter | None = None,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initialize a Gaussian layer.

        Args:
            scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
                $D$ is the number of variables on which the input layers in each fold are defined on.
                Alternatively, a tensor of shape $(D,)$ can be specified, which will be interpreted
                as a tensor of shape $(1, D)$, i.e., with $F = 1$.
            num_output_units: The number of output units.
            num_channels: The number of channels.
            mean: The mean parameter, having shape $(F, K, C)$, where $K$ is the number of
                output units and $C$ is the number of channels.
            stddev: The standard deviation parameter, having shape $(F, K, C)$, where $K$ is the
                number of output units and $C$ is the number of channels.
            log_partition: An optional parameter of shape $(F, K, C)$, encoding the log-partition.
                function. If this is not None, then the Gaussian layer encodes unnormalized
                Gaussian likelihoods, which are then normalized with the given log-partition
                function.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the scope contains more than one variable.
            ValueError: If the mean and standard deviation parameter shapes are incorrect.
            ValueError: If the log-partition function parameter shape is incorrect.
        """
        num_variables = scope_idx.shape[-1]
        if num_variables != 1:
            raise ValueError("The Gaussian layer encodes a univariate distribution")
        super().__init__(
            scope_idx,
            num_output_units,
            num_channels=num_channels,
            semiring=semiring,
        )
        if not self._valid_mean_stddev_shape(mean):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._mean_stddev_shape} for 'mean', found"
                f"{mean.num_folds} and {mean.shape}, respectively"
            )
        if not self._valid_mean_stddev_shape(stddev):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._mean_stddev_shape} for 'stddev', found"
                f"{stddev.num_folds} and {stddev.shape}, respectively"
            )
        if log_partition is not None and not self._valid_log_partition_shape(log_partition):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._log_partition_shape} for 'log_partition', found"
                f"{log_partition.num_folds} and {log_partition.shape}, respectively"
            )
        self.mean = mean
        self.stddev = stddev
        self.log_partition = log_partition

    def _valid_mean_stddev_shape(self, p: TorchParameter) -> bool:
        if p.num_folds != self.num_folds:
            return False
        return p.shape == self._mean_stddev_shape

    def _valid_log_partition_shape(self, log_partition: TorchParameter) -> bool:
        if log_partition.num_folds != self.num_folds:
            return False
        return log_partition.shape == self._log_partition_shape

    @property
    def _mean_stddev_shape(self) -> tuple[int, ...]:
        return self.num_output_units, self.num_channels

    @property
    def _log_partition_shape(self) -> tuple[int, ...]:
        return self.num_output_units, self.num_channels

    @property
    def config(self) -> Mapping[str, Any]:
        return {"num_output_units": self.num_output_units, "num_channels": self.num_channels}

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        params = {"mean": self.mean, "stddev": self.stddev}
        if self.log_partition is not None:
            params["log_partition"] = self.log_partition
        return params

    def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
        mean = self.mean().unsqueeze(dim=1)  # (F, 1, K, C)
        stddev = self.stddev().unsqueeze(dim=1)  # (F, 1, K, C)
        x = x.permute(0, 2, 3, 1)  # (F, C, B, 1) -> (F, B, 1, C)
        x = distributions.Normal(loc=mean, scale=stddev).log_prob(x)  # (F, B, K, C)
        x = torch.sum(x, dim=3)  # (F, B, K)
        if self.log_partition is not None:
            log_partition = self.log_partition()  # (F, K, C)
            x = x + torch.sum(log_partition, dim=2).unsqueeze(dim=1)
        return x

    def log_partition_function(self) -> Tensor:
        if self.log_partition is None:
            return torch.zeros(
                size=(self.num_folds, 1, self.num_output_units), device=self.mean.device
            )
        log_partition = self.log_partition()  # (F, K, C)
        return torch.sum(log_partition, dim=2).unsqueeze(dim=1)

    def sample(self, num_samples: int = 1) -> Tensor:
        dist = distributions.Normal(loc=self.mean(), scale=self.stddev())
        samples = dist.sample((num_samples,))  # (N, F, K, C)
        samples = samples.permute(1, 3, 2, 0)  # (F, C, K, N)
        return samples

_log_partition_shape property

_mean_stddev_shape property

config property

log_partition = log_partition instance-attribute

mean = mean instance-attribute

params property

stddev = stddev instance-attribute

__init__(scope_idx, num_output_units, num_channels=1, *, mean, stddev, log_partition=None, semiring=None)

Initialize a Gaussian layer.

Parameters:

Name	Type	Description	Default
scope_idx	Tensor	A tensor of shape \((F, D)\), where \(F\) is the number of folds, and \(D\) is the number of variables on which the input layers in each fold are defined on. Alternatively, a tensor of shape \((D,)\) can be specified, which will be interpreted as a tensor of shape \((1, D)\), i.e., with \(F = 1\).	required
num_output_units	int	The number of output units.	required
num_channels	int	The number of channels.	1
mean	TorchParameter	The mean parameter, having shape \((F, K, C)\), where \(K\) is the number of output units and \(C\) is the number of channels.	required
stddev	TorchParameter	The standard deviation parameter, having shape \((F, K, C)\), where \(K\) is the number of output units and \(C\) is the number of channels.	required
log_partition	TorchParameter | None	An optional parameter of shape \((F, K, C)\), encoding the log-partition. function. If this is not None, then the Gaussian layer encodes unnormalized Gaussian likelihoods, which are then normalized with the given log-partition function.	None
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the scope contains more than one variable.
ValueError	If the mean and standard deviation parameter shapes are incorrect.
ValueError	If the log-partition function parameter shape is incorrect.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    scope_idx: Tensor,
    num_output_units: int,
    num_channels: int = 1,
    *,
    mean: TorchParameter,
    stddev: TorchParameter,
    log_partition: TorchParameter | None = None,
    semiring: Semiring | None = None,
) -> None:
    r"""Initialize a Gaussian layer.

    Args:
        scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
            $D$ is the number of variables on which the input layers in each fold are defined on.
            Alternatively, a tensor of shape $(D,)$ can be specified, which will be interpreted
            as a tensor of shape $(1, D)$, i.e., with $F = 1$.
        num_output_units: The number of output units.
        num_channels: The number of channels.
        mean: The mean parameter, having shape $(F, K, C)$, where $K$ is the number of
            output units and $C$ is the number of channels.
        stddev: The standard deviation parameter, having shape $(F, K, C)$, where $K$ is the
            number of output units and $C$ is the number of channels.
        log_partition: An optional parameter of shape $(F, K, C)$, encoding the log-partition.
            function. If this is not None, then the Gaussian layer encodes unnormalized
            Gaussian likelihoods, which are then normalized with the given log-partition
            function.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the scope contains more than one variable.
        ValueError: If the mean and standard deviation parameter shapes are incorrect.
        ValueError: If the log-partition function parameter shape is incorrect.
    """
    num_variables = scope_idx.shape[-1]
    if num_variables != 1:
        raise ValueError("The Gaussian layer encodes a univariate distribution")
    super().__init__(
        scope_idx,
        num_output_units,
        num_channels=num_channels,
        semiring=semiring,
    )
    if not self._valid_mean_stddev_shape(mean):
        raise ValueError(
            f"Expected number of folds {self.num_folds} "
            f"and shape {self._mean_stddev_shape} for 'mean', found"
            f"{mean.num_folds} and {mean.shape}, respectively"
        )
    if not self._valid_mean_stddev_shape(stddev):
        raise ValueError(
            f"Expected number of folds {self.num_folds} "
            f"and shape {self._mean_stddev_shape} for 'stddev', found"
            f"{stddev.num_folds} and {stddev.shape}, respectively"
        )
    if log_partition is not None and not self._valid_log_partition_shape(log_partition):
        raise ValueError(
            f"Expected number of folds {self.num_folds} "
            f"and shape {self._log_partition_shape} for 'log_partition', found"
            f"{log_partition.num_folds} and {log_partition.shape}, respectively"
        )
    self.mean = mean
    self.stddev = stddev
    self.log_partition = log_partition

_valid_log_partition_shape(log_partition)

Source code in cirkit/backend/torch/layers/input.py

def _valid_log_partition_shape(self, log_partition: TorchParameter) -> bool:
    if log_partition.num_folds != self.num_folds:
        return False
    return log_partition.shape == self._log_partition_shape

_valid_mean_stddev_shape(p)

Source code in cirkit/backend/torch/layers/input.py

def _valid_mean_stddev_shape(self, p: TorchParameter) -> bool:
    if p.num_folds != self.num_folds:
        return False
    return p.shape == self._mean_stddev_shape

log_partition_function()

Source code in cirkit/backend/torch/layers/input.py

def log_partition_function(self) -> Tensor:
    if self.log_partition is None:
        return torch.zeros(
            size=(self.num_folds, 1, self.num_output_units), device=self.mean.device
        )
    log_partition = self.log_partition()  # (F, K, C)
    return torch.sum(log_partition, dim=2).unsqueeze(dim=1)

log_unnormalized_likelihood(x)

Source code in cirkit/backend/torch/layers/input.py

def log_unnormalized_likelihood(self, x: Tensor) -> Tensor:
    mean = self.mean().unsqueeze(dim=1)  # (F, 1, K, C)
    stddev = self.stddev().unsqueeze(dim=1)  # (F, 1, K, C)
    x = x.permute(0, 2, 3, 1)  # (F, C, B, 1) -> (F, B, 1, C)
    x = distributions.Normal(loc=mean, scale=stddev).log_prob(x)  # (F, B, K, C)
    x = torch.sum(x, dim=3)  # (F, B, K)
    if self.log_partition is not None:
        log_partition = self.log_partition()  # (F, K, C)
        x = x + torch.sum(log_partition, dim=2).unsqueeze(dim=1)
    return x

sample(num_samples=1)

Source code in cirkit/backend/torch/layers/input.py

def sample(self, num_samples: int = 1) -> Tensor:
    dist = distributions.Normal(loc=self.mean(), scale=self.stddev())
    samples = dist.sample((num_samples,))  # (N, F, K, C)
    samples = samples.permute(1, 3, 2, 0)  # (F, C, K, N)
    return samples

TorchInputFunctionLayer

Bases: TorchInputLayer

An input layer encoding functions defined over a non-empty set of variables.

Source code in cirkit/backend/torch/layers/input.py

class TorchInputFunctionLayer(TorchInputLayer):
    """An input layer encoding functions defined over a non-empty set of variables."""

    def __call__(self, x: Tensor) -> Tensor:
        # IGNORE: Idiom for nn.Module.__call__.
        return super().__call__(x)  # type: ignore[no-any-return,misc]

    @abstractmethod
    def forward(self, x: Tensor) -> Tensor:
        r"""Invoke the forward function.

        Args:
            x: The tensor input to this layer, having shape $(F, C, B, D)$, where $F$
                is the number of folds, $C$ is the number of channels,
                $B$ is the batch size, and $D$ is the number of variables.

        Returns:
            Tensor: The tensor output of this layer, having shape $(F, B, K)$, where $K$
                is the number of output units.
        """

__call__(x)

Source code in cirkit/backend/torch/layers/input.py

def __call__(self, x: Tensor) -> Tensor:
    # IGNORE: Idiom for nn.Module.__call__.
    return super().__call__(x)  # type: ignore[no-any-return,misc]

forward(x) abstractmethod

Invoke the forward function.

Parameters:

Name	Type	Description	Default
x	Tensor	The tensor input to this layer, having shape \((F, C, B, D)\), where \(F\) is the number of folds, \(C\) is the number of channels, \(B\) is the batch size, and \(D\) is the number of variables.	required

Returns:

Name	Type	Description
Tensor	Tensor	The tensor output of this layer, having shape \((F, B, K)\), where \(K\) is the number of output units.

Source code in cirkit/backend/torch/layers/input.py

@abstractmethod
def forward(self, x: Tensor) -> Tensor:
    r"""Invoke the forward function.

    Args:
        x: The tensor input to this layer, having shape $(F, C, B, D)$, where $F$
            is the number of folds, $C$ is the number of channels,
            $B$ is the batch size, and $D$ is the number of variables.

    Returns:
        Tensor: The tensor output of this layer, having shape $(F, B, K)$, where $K$
            is the number of output units.
    """

TorchInputLayer

Bases: TorchLayer, ABC

The abstract base class for torch input layers.

Source code in cirkit/backend/torch/layers/input.py

class TorchInputLayer(TorchLayer, ABC):
    """The abstract base class for torch input layers."""

    def __init__(
        self,
        scope_idx: Tensor,
        num_output_units: int,
        *,
        num_channels: int = 1,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initialize a torch input layer.

        Args:
            scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
                $D$ is the number of variables on which the input layers in each fold are defined
                on. Alternatively, a tensor of shape $(D,)$ can be specified, which will be
                interpreted as a tensor of shape $(1, D)$, i.e., with $F = 1$.
            num_output_units: The number of output units.
            num_channels: The number of channels.
            semiring: The evaluation semiring.
                Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

        Raises:
            ValueError: If the scope index is not a vector or a matrix.
        """
        if len(scope_idx.shape) == 1:
            scope_idx = scope_idx.unsqueeze(dim=0)
        elif len(scope_idx.shape) > 2:
            raise ValueError(f"The scope index must be a matrix, but found shape {scope_idx.shape}")
        num_folds, num_variables = scope_idx.shape
        super().__init__(
            num_variables,
            num_output_units,
            arity=num_channels,
            num_folds=num_folds,
            semiring=semiring,
        )
        self.register_buffer("_scope_idx", scope_idx)

    @property
    def scope_idx(self) -> Tensor:
        """Retrieve the scope index tensor.

        Returns:
            The scope index tensor.
        """
        return self._scope_idx

    @property
    def num_variables(self) -> int:
        """The number of variables the input layer is defined on.

        Returns:
            The number of variables.
        """
        return self.num_input_units

    @property
    def num_channels(self) -> int:
        """The number of channels per variable.

        Returns:
            The number of channels.
        """
        return self.arity

    @property
    @abstractmethod
    def config(self) -> Mapping[str, Any]:
        ...

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        return {}

    @property
    def fold_settings(self) -> tuple[Any, ...]:
        pshapes = [(n, p.shape) for n, p in self.params.items()]
        return self.num_variables, *self.config.items(), *pshapes

    def integrate(self) -> Tensor:
        r"""Integrate an input layer over all its variables' domain.

        Returns:
            Tensor: The tensor result of the integration, having shape $(F, K)$, where
                $F$ is the number of folds and $K$ is the number of output units.

        Raises:
            TypeError: If integration is not supported by the layer.
        """
        raise TypeError(f"Integration is not supported for layers of type {type(self)}")

    def sample(self, num_samples: int = 1) -> Tensor:
        r"""If the input layer encodes a probability distribution, then sample from it.

        Args:
            num_samples: The number of data points to sample.

        Returns:
            Tensor: The tensorized sample, having shape $(F, C, K, N)$, where
                $F$ is the number of folds, $K$ is the number of output units,
                $C$ is the number of channels, and $N$ is the number of samples.

        Raises:
            TypeError: If sampling is not supported by the layer.
        """
        raise TypeError(f"Sampling is not supported for layers of type {type(self)}")

    def extra_repr(self) -> str:
        return (
            "  ".join(
                [
                    f"folds: {self.num_folds}",
                    f"channels: {self.num_channels}",
                    f"variables: {self.num_variables}",
                    f"output-units: {self.num_output_units}",
                ]
            )
            + "\n"
            + f"input-shape: {(self.num_folds, self.arity, -1, self.num_input_units)}"
            + "\n"
            + f"output-shape: {(self.num_folds, -1, self.num_output_units)}"
        )

config abstractmethod property

fold_settings property

num_channels property

The number of channels per variable.

Returns:

Type	Description
int	The number of channels.

num_variables property

The number of variables the input layer is defined on.

Returns:

Type	Description
int	The number of variables.

params property

scope_idx property

Retrieve the scope index tensor.

Returns:

Type	Description
Tensor	The scope index tensor.

__init__(scope_idx, num_output_units, *, num_channels=1, semiring=None)

Initialize a torch input layer.

Parameters:

Name	Type	Description	Default
scope_idx	Tensor	A tensor of shape \((F, D)\), where \(F\) is the number of folds, and \(D\) is the number of variables on which the input layers in each fold are defined on. Alternatively, a tensor of shape \((D,)\) can be specified, which will be interpreted as a tensor of shape \((1, D)\), i.e., with \(F = 1\).	required
num_output_units	int	The number of output units.	required
num_channels	int	The number of channels.	1
semiring	Semiring | None	The evaluation semiring. Defaults to SumProductSemiring.	None

Raises:

Type	Description
ValueError	If the scope index is not a vector or a matrix.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    scope_idx: Tensor,
    num_output_units: int,
    *,
    num_channels: int = 1,
    semiring: Semiring | None = None,
) -> None:
    r"""Initialize a torch input layer.

    Args:
        scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
            $D$ is the number of variables on which the input layers in each fold are defined
            on. Alternatively, a tensor of shape $(D,)$ can be specified, which will be
            interpreted as a tensor of shape $(1, D)$, i.e., with $F = 1$.
        num_output_units: The number of output units.
        num_channels: The number of channels.
        semiring: The evaluation semiring.
            Defaults to [SumProductSemiring][cirkit.backend.torch.semiring.SumProductSemiring].

    Raises:
        ValueError: If the scope index is not a vector or a matrix.
    """
    if len(scope_idx.shape) == 1:
        scope_idx = scope_idx.unsqueeze(dim=0)
    elif len(scope_idx.shape) > 2:
        raise ValueError(f"The scope index must be a matrix, but found shape {scope_idx.shape}")
    num_folds, num_variables = scope_idx.shape
    super().__init__(
        num_variables,
        num_output_units,
        arity=num_channels,
        num_folds=num_folds,
        semiring=semiring,
    )
    self.register_buffer("_scope_idx", scope_idx)

extra_repr()

Source code in cirkit/backend/torch/layers/input.py

def extra_repr(self) -> str:
    return (
        "  ".join(
            [
                f"folds: {self.num_folds}",
                f"channels: {self.num_channels}",
                f"variables: {self.num_variables}",
                f"output-units: {self.num_output_units}",
            ]
        )
        + "\n"
        + f"input-shape: {(self.num_folds, self.arity, -1, self.num_input_units)}"
        + "\n"
        + f"output-shape: {(self.num_folds, -1, self.num_output_units)}"
    )

integrate()

Integrate an input layer over all its variables' domain.

Returns:

Name	Type	Description
Tensor	Tensor	The tensor result of the integration, having shape \((F, K)\), where \(F\) is the number of folds and \(K\) is the number of output units.

Raises:

Type	Description
TypeError	If integration is not supported by the layer.

Source code in cirkit/backend/torch/layers/input.py

def integrate(self) -> Tensor:
    r"""Integrate an input layer over all its variables' domain.

    Returns:
        Tensor: The tensor result of the integration, having shape $(F, K)$, where
            $F$ is the number of folds and $K$ is the number of output units.

    Raises:
        TypeError: If integration is not supported by the layer.
    """
    raise TypeError(f"Integration is not supported for layers of type {type(self)}")

sample(num_samples=1)

If the input layer encodes a probability distribution, then sample from it.

Parameters:

Name	Type	Description	Default
num_samples	int	The number of data points to sample.	1

Returns:

Name	Type	Description
Tensor	Tensor	The tensorized sample, having shape \((F, C, K, N)\), where \(F\) is the number of folds, \(K\) is the number of output units, \(C\) is the number of channels, and \(N\) is the number of samples.

Raises:

Type	Description
TypeError	If sampling is not supported by the layer.

Source code in cirkit/backend/torch/layers/input.py

def sample(self, num_samples: int = 1) -> Tensor:
    r"""If the input layer encodes a probability distribution, then sample from it.

    Args:
        num_samples: The number of data points to sample.

    Returns:
        Tensor: The tensorized sample, having shape $(F, C, K, N)$, where
            $F$ is the number of folds, $K$ is the number of output units,
            $C$ is the number of channels, and $N$ is the number of samples.

    Raises:
        TypeError: If sampling is not supported by the layer.
    """
    raise TypeError(f"Sampling is not supported for layers of type {type(self)}")

TorchPolynomialLayer

Bases: TorchInputFunctionLayer

The polynomial input layer, evaluating a vector of parameterized polynomials.

Source code in cirkit/backend/torch/layers/input.py

class TorchPolynomialLayer(TorchInputFunctionLayer):
    """The polynomial input layer, evaluating a vector of parameterized polynomials."""

    def __init__(
        self,
        scope_idx: Tensor,
        num_output_units: int,
        num_channels: int = 1,
        *,
        degree: int,
        coeff: TorchParameter,
        semiring: Semiring | None = None,
    ) -> None:
        r"""Initialize a polynomial layer.

        Args:
            scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
                $D$ is the number of variables on which the input layers in each fold are defined
                on. Alternatively, a tensor of shape $(D,)$ can be specified, which will be
                interpreted as a tensor of shape $(1, D)$, i.e., with $F = 1$.
            num_output_units: The number of output units.
            num_channels: The number of channels.
            degree: The degree of polynomial.
            coeff: The coefficient parameter, having shape $(F, K, \mathsf{degree} + 1)$, where $K$ is the number
                of output units.

        Raises:
            ValueError: If the scope contains more than one variable.
            ValueError: If the coefficients is not correct.
        """
        num_variables = scope_idx.shape[-1]
        if num_variables != 1:
            raise ValueError("The Polynomial layer encodes a univariate distribution")
        if num_channels != 1:
            raise ValueError("The Polynomial layer encodes a univariate distribution")
        super().__init__(
            scope_idx,
            num_output_units,
            num_channels=num_channels,
            semiring=semiring,
        )
        self.degree = degree
        if not self._valid_parameters_shape(coeff):
            raise ValueError(
                f"Expected number of folds {self.num_folds} "
                f"and shape {self._coeff_shape} for 'coeff', found"
                f"{coeff.num_folds} and {coeff.shape}, respectively"
            )
        self.coeff = coeff

    def _valid_parameters_shape(self, p: TorchParameter) -> bool:
        if p.num_folds != self.num_folds:
            return False
        return p.shape == self._coeff_shape

    @property
    def _coeff_shape(self) -> tuple[int, ...]:
        return self.num_output_units, self.degree + 1

    @staticmethod
    def _polyval(coeff: Tensor, x: Tensor) -> Tensor:
        r"""Evaluate polynomial given coefficients and point, with the shape for PolynomialLayer.

        Args:
            coeff: The coefficients of the polynomial, shape $(F, K_o, \mathsf{degree} + 1)$.
            x: The point of the variable, shape $(F, H, B, K_i)$, where $H=K_i=1$.

        Returns:
            Tensor: The value of the polymonial, shape $(F, B, K_o)$.
        """
        x = x.squeeze(dim=1)  # shape (F, H=1, B, Ki=1) -> (F, B, 1).
        y = x.new_zeros(*x.shape[:-1], coeff.shape[-2])  # shape (F, B, Ko).

        # TODO: iterating over dim=2 is inefficient
        for a_n in reversed(
            coeff.unbind(dim=2)
        ):  # Reverse iterator of the degree axis, shape (F, Ko).
            # a_n shape (F, Ko) -> (F, 1, Ko).
            y = torch.addcmul(a_n.unsqueeze(dim=1), x, y)  # y = a_n + x * y, by Horner's method.
        return y  # shape (F, B, Ko).

    @property
    def config(self) -> Mapping[str, Any]:
        return {
            "num_output_units": self.num_output_units,
            "num_channels": self.num_channels,
            "degree": self.degree,
        }

    @property
    def params(self) -> Mapping[str, TorchParameter]:
        return {"coeff": self.coeff}

    def forward(self, x: Tensor) -> Tensor:
        coeff = self.coeff()  # shape (F, Ko, dp1)
        return self.semiring.map_from(TorchPolynomialLayer._polyval(coeff, x), SumProductSemiring)

_coeff_shape property

coeff = coeff instance-attribute

config property

degree = degree instance-attribute

params property

__init__(scope_idx, num_output_units, num_channels=1, *, degree, coeff, semiring=None)

Initialize a polynomial layer.

Parameters:

Name	Type	Description	Default
scope_idx	Tensor	A tensor of shape \((F, D)\), where \(F\) is the number of folds, and \(D\) is the number of variables on which the input layers in each fold are defined on. Alternatively, a tensor of shape \((D,)\) can be specified, which will be interpreted as a tensor of shape \((1, D)\), i.e., with \(F = 1\).	required
num_output_units	int	The number of output units.	required
num_channels	int	The number of channels.	1
degree	int	The degree of polynomial.	required
coeff	TorchParameter	The coefficient parameter, having shape \((F, K, \mathsf{degree} + 1)\), where \(K\) is the number of output units.	required

Raises:

Type	Description
ValueError	If the scope contains more than one variable.
ValueError	If the coefficients is not correct.

Source code in cirkit/backend/torch/layers/input.py

def __init__(
    self,
    scope_idx: Tensor,
    num_output_units: int,
    num_channels: int = 1,
    *,
    degree: int,
    coeff: TorchParameter,
    semiring: Semiring | None = None,
) -> None:
    r"""Initialize a polynomial layer.

    Args:
        scope_idx: A tensor of shape $(F, D)$, where $F$ is the number of folds, and
            $D$ is the number of variables on which the input layers in each fold are defined
            on. Alternatively, a tensor of shape $(D,)$ can be specified, which will be
            interpreted as a tensor of shape $(1, D)$, i.e., with $F = 1$.
        num_output_units: The number of output units.
        num_channels: The number of channels.
        degree: The degree of polynomial.
        coeff: The coefficient parameter, having shape $(F, K, \mathsf{degree} + 1)$, where $K$ is the number
            of output units.

    Raises:
        ValueError: If the scope contains more than one variable.
        ValueError: If the coefficients is not correct.
    """
    num_variables = scope_idx.shape[-1]
    if num_variables != 1:
        raise ValueError("The Polynomial layer encodes a univariate distribution")
    if num_channels != 1:
        raise ValueError("The Polynomial layer encodes a univariate distribution")
    super().__init__(
        scope_idx,
        num_output_units,
        num_channels=num_channels,
        semiring=semiring,
    )
    self.degree = degree
    if not self._valid_parameters_shape(coeff):
        raise ValueError(
            f"Expected number of folds {self.num_folds} "
            f"and shape {self._coeff_shape} for 'coeff', found"
            f"{coeff.num_folds} and {coeff.shape}, respectively"
        )
    self.coeff = coeff

_polyval(coeff, x) staticmethod

Evaluate polynomial given coefficients and point, with the shape for PolynomialLayer.

Parameters:

Name	Type	Description	Default
coeff	Tensor	The coefficients of the polynomial, shape \((F, K_o, \mathsf{degree} + 1)\).	required
x	Tensor	The point of the variable, shape \((F, H, B, K_i)\), where \(H=K_i=1\).	required

Returns:

Name	Type	Description
Tensor	Tensor	The value of the polymonial, shape \((F, B, K_o)\).

Source code in cirkit/backend/torch/layers/input.py

@staticmethod
def _polyval(coeff: Tensor, x: Tensor) -> Tensor:
    r"""Evaluate polynomial given coefficients and point, with the shape for PolynomialLayer.

    Args:
        coeff: The coefficients of the polynomial, shape $(F, K_o, \mathsf{degree} + 1)$.
        x: The point of the variable, shape $(F, H, B, K_i)$, where $H=K_i=1$.

    Returns:
        Tensor: The value of the polymonial, shape $(F, B, K_o)$.
    """
    x = x.squeeze(dim=1)  # shape (F, H=1, B, Ki=1) -> (F, B, 1).
    y = x.new_zeros(*x.shape[:-1], coeff.shape[-2])  # shape (F, B, Ko).

    # TODO: iterating over dim=2 is inefficient
    for a_n in reversed(
        coeff.unbind(dim=2)
    ):  # Reverse iterator of the degree axis, shape (F, Ko).
        # a_n shape (F, Ko) -> (F, 1, Ko).
        y = torch.addcmul(a_n.unsqueeze(dim=1), x, y)  # y = a_n + x * y, by Horner's method.
    return y  # shape (F, B, Ko).

_valid_parameters_shape(p)

Source code in cirkit/backend/torch/layers/input.py

def _valid_parameters_shape(self, p: TorchParameter) -> bool:
    if p.num_folds != self.num_folds:
        return False
    return p.shape == self._coeff_shape

forward(x)

Source code in cirkit/backend/torch/layers/input.py

def forward(self, x: Tensor) -> Tensor:
    coeff = self.coeff()  # shape (F, Ko, dp1)
    return self.semiring.map_from(TorchPolynomialLayer._polyval(coeff, x), SumProductSemiring)