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For the first time, the victim's name was read in open court. She was identified as UCLA student Katherine Rosen.
Thompson was silent and held his head down for most of the proceeding.
Thompson is believed to have been Rosen's lab partner. He was arrested inside UCLA's Young Hall minutes after the attack.
His bail was increased from $1 million to $3 million.
According to the Los Angeles Times, there may have been some sort of verbal confrontation between the two students before the attack, but police said a motive for the stabbing is unclear.
Her family says she's in critical condition but is expected to recover.
Thompson is due back in court Oct. 27.