A hard threshold is when we have a discontinuous change when the output exceeds a fixed threshold value, for example changing from 0 to 1 when an input temperature exceeds 373.2. Hard thresholds are easy to implement, but may lead to fragile models and can be hard to learn. For this reason many algorithms, notably backpropagation use a soft threshold function such as a sigmoid.
Used in Chap. 9: page 127
Used in glossary entries: backpropagation, sigmoid function, threshold, threshold function

Step threshold function – a hard threshold