<p>Designing materials with targeted lattice thermal conductivity (LTC) demands electronic-level insight into chemical bonding. We introduce two bonding descriptors, namely normalized negative integrated COHP (-ICOHP) and normalized integrated COBI, that correlate strongly with LTC and rattling (mean-squared displacement), surpassing empirical rules and the unnormalized −ICOHP across &gt;4500 inorganic crystals by first-principles. We train a crystal attention graph neural network (CATGNN) to predict these descriptors and screen ~200,000 database structures for extreme LTCs. From 367 (533) candidates with low (high) normalized -ICOHP and normalized ICOBI, first-principles validation identifies 106 dynamically stable compounds with LTC &lt; 5 W m⁻¹ K⁻¹ (68% &lt;2 W m⁻¹ K⁻¹) and 13 stable compounds with LTC &gt; 100 W m⁻¹ K⁻¹. The descriptors’ low cost and clear physical meaning provide a rapid, reliable route to high-throughput discovery and inverse design of crystalline materials with ultralow or ultrahigh LTC for applications in thermal insulation, thermoelectrics, and electronics cooling.</p>