Pytorch Logit Logic

A pytorch extension which provides functions and classes for logit-space operators equivalent to probabilistic Boolean logic-gates AND, OR, and XNOR for independent probabilities.

This provides the activation functions used in our paper:

SC Lowe, R Earle, J d'Eon, T Trappenberg, S Oore (2022). Logical Activation Functions: Logit-space equivalents of Probabilistic Boolean Operators. In Advances in Neural Information Processing Systems, volume 36. doi: 10.48550/arxiv.2110.11940.

For your convenience, we provide a copy of this citation in bibtex format.

Example usage:

from pytorch_logit_logic import actfun_name2factory
from torch import nn


class MLP(nn.Module):
    """
    A multi-layer perceptron which supports higher-dimensional activations.

    Parameters
    ----------
    in_channels : int
        Number of input channels.
    out_channels : int
        Number of output channels.
    n_layer : int, default=1
        Number of hidden layers.
    hidden_width : int, optional
        Pre-activation width. Default: same as ``in_channels``.
        Note that the actual pre-act width used may differ by rounding to
        the nearest integer that is divisible by the activation function's
        divisor.
    actfun : str, default="ReLU"
        Name of activation function to use.
    actfun_k : int, optional
        Dimensionality of the activation function. Default is the lowest
        ``k`` that the activation function supports, i.e. ``1`` for regular
        1D activation functions like ReLU, and ``2`` for GLU, MaxOut, and
        NAIL_OR.
    """

    def __init__(
        self,
        in_channels,
        out_channels,
        n_layer=1,
        hidden_width=None,
        actfun="ReLU",
        actfun_k=None,
    ):
        super().__init__()

        # Create a factory that generates objects that perform this activation
        actfun_factory = actfun_name2factory(actfun, k=actfun_k)
        # Get the divisor and space reduction factors for this activation
        # function. The pre-act needs to be divisible by the divisor, and
        # the activation will change the channel dimension by feature_factor.
        _actfun = actfun_factory()
        divisor = getattr(_actfun, "k", 1)
        feature_factor = getattr(_actfun, "feature_factor", 1)

        if hidden_width is None:
            hidden_width = in_channels

        # Ensure the hidden width is divisible by the divisor
        hidden_width = int(int(round(hidden_width / divisor)) * divisor)

        layers = []
        n_current = in_channels
        for i_layer in range(0, n_layer):
            layer = []
            layer.append(nn.Linear(n_current, hidden_width))
            n_current = hidden_width
            layer.append(actfun_factory())
            n_current = int(round(n_current * feature_factor))
            layers.append(nn.Sequential(*layer))
        self.layers = nn.Sequential(*layers)
        self.classifier = nn.Linear(n_current, out_channels)

    def forward(self, x):
        x = self.layers(x)
        x = self.classifier(x)
        return x


model = MLP(
    in_channels=512,
    out_channels=10,
    n_layer=2,
    actfun="nail_or",
)