So since this is the extent that Memory will be introduced for now, I think I'll drop a tidbit that might hint at who/what Memory actually is. In the previous chapter, Rid found a tiny hole that life force returned to and that's how he found the little space inside his soul.
Early on in the LN, Rid had a dream about OG!Rid based on the butterfly chapter (Chapter 5). At this moment OG!Rid first learned and realized the meaning of death. When Nunnally fell ill, OG!Rid saw the despair on Reiner's face and instinctively realized that death was coming for his mother. From then on he lashed out at everything, particularly Meredy because she kept turning to him asking about their mother. This only fueled his anger even more and he turned physically violent. At this time he was 5 years old and although the servants quickly learned to separate the two, the damage was done. Reiner believed OG!Rid had shown his true colors as a violent tyrant and began to look at him in disgust and disappointment. From then on Reiner rarely visited home and became increasingly distant. This also explains why he has such low specs in the game despite being so talented. Reiner completely neglected Rid's heir training after deeming him completely unsuitable.
For the next year, OG!Rid would keep lashing out at the servants, his sister, property, everything. Then one day, he had a vivid dream. In it, Nunnally passed away. Reiner drowned himself in his work even more. Meredy, unable to cope with the loss of her mother, the neglect of her father, and the abuse of her brother, lost her mind and starved herself to death in her room. She was completely unrecognizable. Reiner attended the funeral but continued to look at OG!Rid with contempt. The years went by and OG!Rid lost all will to live. He decided to seek death by joining the OG villainess's faction where his wish is ultimately granted.
Then OG!Rid woke up and immediately realized it was not a simple dream but a vision of the future. He cursed his powerlessness. He wished for strength to save his loved ones and became aware of a door inside of himself. He became obsessed with opening that door and when he finally did, he lost consciousness and collapsed in the garden.
Then Rid wakes up and realizes this is something OG!Rid wanted to show him. Rid promises to OG!Rid that he will fulfill that wish in his stead. Because OG!Rid is still somewhere inside, now a part of Rid.
To tie it back to Memory, the magic was created by entering a hole inside of his own being/soul. Current Rid is an amalgamation of OG!Rid and the man formerly known as Kanda Hajime, with the latter serving as the foundation for the current personality. Memory's avatar is that of Rid and although it called itself a "personification of Rid's memories" in the previous chapter, later on Memory says it'll always help Rid "because I am you, and you are me". If current Rid is primarily Kanda Hajime, then it seems that Memory is possibly closer to OG!Rid. Another hint from way later on appears when he visits the abandoned Ronamis manor (mother's side of the family) in the capital and experiences deja vu despite having never been there before. I think the implication here (and this is just a super wild guess based on tropes) is that OG!Rid cast space-time magic in his dying moments to send his memories back through time while roping in Kanda from another world for help. And among those memories may have been OG!Rid's time in the capital for the main plot of Tokirella.
I'm actually really disappointed the manga cut this out because it better explains Rid's motivations. The obsession with strength and developing Bardia is not simply about saving his mother. It's also potentially a massive clue to how Kanda was reincarnated into Rid. OG!Rid discovering and opening a door inside himself which leads to Kanda's reincarnation? Then Rid finds an opening inside himself and meets someone that looks just like him? How could these two not be related?
As for the training here, this all feeds into current Rid being extremely strong for his age. He is a Marquis's son so military strength is expected. However, he pushes himself because he has inherited the memories of OG!Rid who experienced the destruction of Bardia through a vision and Kanda who witnessed it through the game. This will pay off very soon.