Boolean Aggregators

To emulate Boolean operators such as AND and OR, BACON uses a bool.min_max aggregator defined as:

\[\alpha \cdot \min(x_1, x_2) + (1 - \alpha) \cdot \max(x_1, x_2)\]

Here, the andness parameter \(\alpha\) is normalized to the range \([0,1]\) using a sharpened sigmoid function. This encourages \(\alpha\) to converge toward binary extremes (0 or 1), more closely mimicking the behavior of true Boolean operations. Note that when the bool.min_max aggregator is in use, the model’s normalize_andness option should be disabled, since \(\alpha\) is already normalized by the aggregator itself.

• Min-Max Aggregator