Mipham Rinpoche (19th century) invokes Saraswati in the introduction to The Blazing Lights of the Sun and Moon (Tib. Sherab Raltri:)
Saraswati [or Sarasvati] is essentially an Indian goddess. She appears as a Buddhist yidam in her capacity as an embodiment of virtuous activities of all kinds especially cultural ones such as learning, and also the performing arts, especially music. Her mythology also includes an important purificatory aspect. In many regards, she shares characteristics with White Tara.
In Tibetan, Saraswati is Yang Chenmo, or when her musical aspect is emphasized, she is Piwa Karpo. In Mongolian she is Keleyin ukin Tegri, in Chinese she is called Tapien-ts'ai t'iennu or Miao-yin mu, and in Japan she is equated with Benten. The Tibetan singer Yungchen Lhamo is named for Saraswati.
She is often identifiable by her plain white garment, (though not in this image) her veena which is a stringed musical instrument, and her association with the consonants and vowels of the Sanskrit language. Her own seed syllable is haym.
In the Sadhanamala (162) Maha-Sarasvati's mantra is:
In Hinduism, she is the daughter of Devi and wife of Lord Brahma, and her vehicle is the celestial bird called the hamsha or kinnara, usually portrayed as a swan but sometimes a peacock. She is called Sharda Devi or Sharada (Sarada) and the hymn to her says that her home is Kashmir, once famous for its pandits or learned scholars.
Saraswati means 'the one that flows' and is the name of a Vedic river that once flowed, but has vanished. That is the source of her connection with fluidity of all fertile kinds including speech, writing, song, music and thought. She is also known as Vak [speech.]
In India, grandmothers make a pentagram or Saraswati-sign with honey on the tongue of newborns to invoke the blessing of speech.
In Buddhism, as well as being a yidam or inspirational deity Saraswati is sometimes considered the consort of Manjushri, the knowledge bodhisattva. She was the yidam of the reformer and founder of the lam-rim system, Tsongkhapa.
She is sometimes considered the peaceful form of the protector, Palden Lhamo. That connection may derive from her dark blue colour which is the same as that of Nila Saraswati, who is the dark blue emanation of Durga, the Mahakali of Hindu tantric tradition.
Yangchenma is sometimes equated with White Tara since she is white with one face and, sometimes, three eyes. She can also be depicted with only two hands, knees bent with crossed ankles as she sits playing her instrument. When she is depicted with 4, one hand holds a book of scripture and another a tenwa [mala] that symbolizes the string of letters of the alphabet.
There is also a red Sarasvati -- Yangchen Marmo, and also a vajra, or Dorje Yangchenma, whose mantra in this last form as Arya Vajrasarasvati (sadhanas no.161 & 163) is:
Om, pichu pichu prajna vardhani jvala jvala medhavardhani dhiri dhiri
~ mantra information courtesy M. B., Nepal