Learning knot invariants across dimensions
Learning knot invariants across dimensions
We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial J(q) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> , and the four-dimensional invariants are the Khovanov polynomial \text{Kh}(q,t) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext mathvariant="normal">Kh</mml:mtext><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> …