While there are numerous synonyms for the phrase "crossing the mind," such as thinking, considering, pondering, and contemplating, there are also a few antonyms that convey the opposite meaning. One such antonym is forgetting, which indicates that the thought or idea did not register in the person's memory at all. Another antonym could be dismissing, which implies that the thought was considered but then rejected or ignored altogether. Similarly, ignoring and neglecting also convey a lack of attention and consideration towards the thought. Overall, these antonyms highlight the different ways in which a thought or idea can be processed or ignored by the mind.