Correction: Positive–negative prototypes fusion framework for open set recognition

Correction to: Scientific Reports 10.1038/s41598-025-09625-4, published online 3 July 2025

The original version of this Article contained errors in Eqs. 4, 5, 6, 11, 13, 14, 15, 16, 17, 21, 22 and 23, where these were partially not rendered correctly. As a result,

Equation 4,

now reads:

Equation 5,

now reads:

Equation 6,

now reads:

Equation 11,

now reads:

Equation 13,

now reads:

Equation 14,

now reads:

Equation 15,

now reads:

Equation 16,

now reads:

Equation 17,

now reads:

Equation 21,

now reads:

Equation 22,

now reads:

Equation 23,

now reads:

The original Article has been corrected.