  Cognitive diagnosis assessment is a fundamental and crucial task for student
learning. It models the student-exercise interaction, and discovers the
students' proficiency levels on each knowledge attribute. In real-world
intelligent education systems, generalization and interpretability of cognitive
diagnosis methods are of equal importance. However, most existing methods can
hardly make the best of both worlds due to the complicated student-exercise
interaction. To this end, this paper proposes a symbolic cognitive
diagnosis~(SCD) framework to simultaneously enhance generalization and
interpretability. The SCD framework incorporates the symbolic tree to
explicably represent the complicated student-exercise interaction function, and
utilizes gradient-based optimization methods to effectively learn the student
and exercise parameters. Meanwhile, the accompanying challenge is that we need
to tunnel the discrete symbolic representation and continuous parameter
optimization. To address this challenge, we propose to hybridly optimize the
representation and parameters in an alternating manner. To fulfill SCD, it
alternately learns the symbolic tree by derivative-free genetic programming and
learns the student and exercise parameters via gradient-based Adam. The
extensive experimental results on various real-world datasets show the
superiority of SCD on both generalization and interpretability. The ablation
study verifies the efficacy of each ingredient in SCD, and the case study
explicitly showcases how the interpretable ability of SCD works.
