Past Lives & Karl Popper's Empiricism Ignoring the math bit... (I hope you'll forgive me I was never any good at that),
Strictly from the I'm going to assume typical method of assessing past memories (you question a healthy, mentally sound adult or adolescent or even pre-teen).... the things we've seen/read/otherwise been informed about in life, especially today with movies and TV vividly reside in our brain. It wouldn't be atypical to "recall" or otherwise see something presented to one in a dramatic fashion at an early age ie. a riveting novel or dramatic TV or movie especially when under an altered state of mind say hypnotism.
From the philosophical angle, in regards to empiricism (I had to look that up), the previous paragraph kind of seems to be supported by that.
As far as empiricism in general it simply seems to be a description of what is mandated by the human experience. If you can't hear or see let alone being deprived of all five senses from birth... obviously your mind would not be able to grow and develop. Not quite sure what the antithesis of empiricism is but am curious.
Edit: Also the theory(?) of genetic memory may have some relevance here. From what I remember supposedly if say you were from a mountainous region and lived there for thousands of years, you may find mountains oddly familiar or even non-mountainous regions "odd" or something. Though from a religious/metaphysical perspective, which is completely different, it's a common concept. Afterlife, "life after death", "shall not die", etc.