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Licchavis, the appearance... is rare in the world... a person who explains the teaching and training proclaimed by a Tathagata (AN 5.195).
Tataghata's teach the sankhara of Dependent Origination are threefold; which are defined in MN 44; SN 41.6; etc; namely:
kāyasaṅkhāro (body conditioner - in & out breathing)
vacīsaṅkhāro (verbal conditioner - initial and sustained thinking)
cittasaṅkhāro (mind conditioner - perception & feeling)
Katame ca, bhikkhave, saṅkhārā? Tayome, bhikkhave, saṅkhārā—kāyasaṅkhāro, vacīsaṅkhāro, cittasaṅkhāro. Ime vuccanti, bhikkhave, saṅkhārā.
SN 12.2
Ignorant memories imprinted by ignorance that ignorantly arise are obviously included within these saṅkhāra however it appears obvious none of these saṅkhāra explicitly refer to 'memory' because 'memory' is often praised in the suttas (eg. IN SN 48.10).
Any non-intentional inner thoughts, perceptions, feelings & disturbances of breathing that spontaneously erupt due to ignorance are saṅkhāra. They can be memories or can otherwise not be memories.
For example, imaginings that arise due to fear when entering an unknown place are sankhara not based in memory. Or the first sexual thoughts of a pubescent hormonal teenager are not thoughts based in memory.
Below, are examples of when Thanissaro and Buddhadasa attempted to explain the 'sankhara':
2) Fabrication: the process of intentionally shaping states of body and mind. These processes are of three sorts: a) bodily fabrication: the in-and-out breath, b) verbal fabrication: directed thought and evaluation, and c) mental fabrication: feeling (feeling tones of pleasure, pain, or neither pleasure nor pain) and perception (the mental labels applied to the objects of the senses for the purpose of memory and recognition).
What is mental concocting? The Buddha said: "Monks, there are these three kinds of mental concocting: bodily formation, verbal formation and mental formation." The sayings of the Buddha in the Pali Scriptures explain sankhara as that which brews up or gives rise to the bodily functions, that which brews up verbal functions and that which brews up mental functions.
However, based on AN 5.195, I would follow Dhammadhatu's rare explanation.