QM and GR can be written as matrix algebra, atoms and electrons are QM, chemistry is atoms and electrons, biology is chemistry, brains are biology.
An LLM could be implemented with a Markov chain, but the naïve matrix is ((vocab size)^(context length))^2, which is far too big to fit in this universe.
Like, the Bekenstein bound means writing the transition matrix for an LLM with just 4k context (and 50k vocabulary) at just one bit resolution, the first row (out of a bit more than 10^18795 rows) ends up with a black hole >10^9800 times larger than the observable universe.
alt Hacker News
QM and GR can be written as matrix algebra, atoms and electrons are QM, chemistry is atoms and electrons, biology is chemistry, brains are biology.
An LLM could be implemented with a Markov chain, but the naïve matrix is ((vocab size)^(context length))^2, which is far too big to fit in this universe.
Like, the Bekenstein bound means writing the transition matrix for an LLM with just 4k context (and 50k vocabulary) at just one bit resolution, the first row (out of a bit more than 10^18795 rows) ends up with a black hole >10^9800 times larger than the observable universe.