Sigmoid/softmax Transforms

What are Sigmoid/softmax Transforms?

Sigmoid transforms are S-shaped functions that squash an unbounded input into a fixed interval. The logistic function maps any real number into the open interval from 0 to 1; the hyperbolic tangent maps into minus 1 to plus 1; arctangent variants behave similarly. Near zero the mapping is close to linear, and it saturates toward the bounds as inputs grow, so ordinary readings keep their differences while outliers are compressed against the rails.

Softmax is the vector version: it exponentiates a list of scores and divides each result by the sum of the results, producing positive weights that add up to one, which reads like a probability across competing alternatives. In indicator work, sigmoids appear wherever an unbounded series needs a bounded display, most famously the inverse Fisher transform, which pushes a scaled oscillator through the hyperbolic tangent so readings cluster near the extremes. The transform reshapes a series; it adds no new information.

How traders use it

• To bound unbounded oscillators (momentum differences, volume deltas, regression slopes), usually standardized first as a Z-score, so fixed thresholds and cross-instrument comparisons make sense.
• To reshape an oscillator's behavior: tanh-style shaping makes readings spend more time pinned near the extremes, so departures from an extreme zone stand out more clearly.
• To turn raw scores into weights: softmax over several signal or regime scores yields a normalized weighting for ensemble voting, and a logistic squash maps a single score onto a 0-to-1 confidence-style scale.