Circuit Complexity of Hierarchical Knowledge Tracing and Implications for Log-Precision Transformers
Knowledge tracing models mastery over interconnected concepts, often organized by prerequisites. We analyze hierarchical prerequisite propagation through a circuit-complexity lens to clarify what is provable about transformer-style computation on deep concept hierarchies. Using recent results that log-precision transformers lie in logspace-uniform $\mathsf{TC}^0$, we formalize prerequisite-tree tasks including recursive-majority mastery propagation. Unconditionally, recursive-majority propagation lies in $\mathsf{NC}^1$ via $O(\log n)$-depth bounded-fanin circuits, while separating it from uniform $\mathsf{TC}^0$ would require major progress on open lower bounds. Under a monotonicity rest...
| Authors | Naiming Liu, Richard Baraniuk, Shashank Sonkar |
|---|---|
| Primary category | cs.LG |
| Published | 25 March 2026 |
| Last updated at source | 25 March 2026 |
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