To "embrace" the truth is different from simply understanding the truth. To understand without embracing the truth is not saving faith. To assent to the truth understood IS saving faith. That kind of faith always produces results in one's thinking and behavior. Dead faith is not the same as living faith. A "dead" faith is not genuine faith at all. It is merely understanding without assent.

Assentia/fiducia plus notitia is saving faith.

For "who has known the mind of the LORD that he may instruct Him?" But we have the mind of Christ. (1 Corinthians 2:16 NKJ)