 <p>Okay, I think my issue was forgetting how multinomial regression works. The prediction formula for multinomial regression is</p> <p><a href="https://i.stack.imgur.com/IX4xO.gif" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/IX4xO.gif" alt="enter image description here"></a></p> <p>So you need a set of coefficients for every class.</p>