Your laptop's memory keeps every byte at a numbered place, an address. Ask for place 010 and you get exactly what's there. Ask with a quarter of the picture and it finds nothing. Get one digit of the address wrong (011) and you get a different picture, whole. Von Neumann's team put it this way in 1946: "a twelve-digit binary number suffices to identify a memory location".
In 1982 John Hopfield described a memory "based on aspects of neurobiology": no places, only cells, every pair joined by a connection, each memory spread across all of them. His words: "a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size". We built one with five pictures of our own (576 cells, 165,600 connections). From a quarter of a picture it rebuilt every one of them exactly. With three quarters of its connections cut at random, every picture still came back whole. Erase a tenth of the numbered memory instead, and the picture has holes exactly where the bits were lost.
An AI model is built the brain's way: what it knows is spread across billions of connection strengths (405 billion in Meta's largest Llama 3, 2024). But those numbers sit at addresses in computer memory, and they "remain static during serving": chatting doesn't change them. Your chat is bytes held beside them and freed when the request ends. So if a chatbot remembers you, an app saved notes and showed them to it again.
How we simulated it: two-state cells updated one at a time by Hopfield's rule; the connection strengths are set with the projection rule (Personnaz, Guyon and Dreyfus, 1985), because Hopfield's original 1982 sum can't keep pictures this alike apart. The pictures, the memories and the network are our own drawings of our own simulation.
What's the first thing you remember from three notes of a song?
Sources: Hopfield, PNAS 79, 2554 (1982); Burks, Goldstine and von Neumann, Preliminary discussion of the logical design of an electronic computing instrument (1946); Meta, The Llama 3 Herd of Models (2024); Kwon et al., PagedAttention, SOSP 2023; Anthropic's documentation (2026); our own simulation, 2026.
Sounds and music: made by us.