Hayagriva - Two stories about His udhbhava (genesis)

 (These two paragraphs are verbatim copy pasted from https://manblunder.com/articlesview/lalitha-sahasranama-purva-bhag. My sincere thanks to the people involved in this excellent resource)

There is a story in Bṛhadāraṇayaka Upaniṣad (II.v) about a learned person with horse head.  There was a sage by name Dadhyac, an exponent in Atharva Veda who taught madhu vidyā to Lord Indra.  Indra asked Dadhyac not to teach this madhu vidyā to anyone else after teaching him.  If Dadhyac taught this anyone else, his head would be chopped off by Indra. Aaśvin deva-s somehow wanted to learn this madhu vidyā.  They told Dadhyac that they would first replace his head with a horse head and that he should teach them madhu vidyā with the horse head (detailed in Bṛhadāraṇayaka Upaniṣad II.v.16).  Once it is taught, Indra would chop of his head and that Dadhyac would lose only the horse head.  The horse head would then be replaced by his original head.  Everything happened according to their plan and Aaśvin-s were taught madhu vidyā by sage Dadhyac. In the said Upaniṣad, V.v.16 ends with pra yadīmuvāca.  In this word kāmakalā bīja īṁ ईं (pronounced as eeṁ.) is secretively placed.  Kāmakalā is discussed in nāma 322 in this Sahasranāma.  This īṁ is considered as the most important aspect of Śrī Vidyā.  However, the riṣi who taught madhu vidyā is not the incarnation of Viṣṇu.  Hayagrīva, the incarnation of Lord Viṣṇu initiated Agastya into Śrī Vidyā worship through Lalitā Sahasranāma.  

The following story is found in Devi Bhāgavata (I.5). Viṣṇu was very tired after waging a war with demons. He sat in padmāsana (well known cross legged or lotus posture) resting his head on one side of the bow after placing the other side of the bow, firmly on the ground.  Indra and other gods wanted to perform a great yajña and came to seek blessings from Viṣṇu as He is the Lord of all yajna-s.  They went to Vaikuṇṭha, the abode of Vishnu.  But He was not there. They found out He was resting elsewhere and reached there.  They decided to wait till He woke up.  Since the yajña was to be urgently performed, they could not wait any longer and they asked termites to bite the bow string of Viṣṇu’s bow.  The string was snapped and in the force it chopped off Viṣṇu’s head.  Gods and goddesses searched for His head, but that was not to be found. They all prayed towards Lalitāmbikā who asked them to bring a horse head and fix it on Viṣṇu.  Viṣṇu was then known as Hayagrīva.  He got Śrī Vidyā initiation from Her and this avatār of Viṣṇu is known for the highest wisdom.  Based upon this story Hayagrīva is worshiped for gaining knowledge.  Hayagrīva in turn initiated Agastya into Śrī Vidyā cult. Please note the contextual difference from what is narrated in the ‘the presentation’ section.