  A good theory of mathematical beauty is more practical than any current
observation, as new predictions of physical reality can be verified
self-consistently. This belief applies to the current status of understanding
deep neural networks including large language models and even the biological
intelligence. Toy models provide a metaphor of physical reality, allowing
mathematically formulating that reality (i.e., the so-called theory), which can
be updated as more conjectures are justified or refuted. One does not need to
pack all details into a model, but rather, more abstract models are
constructed, as complex systems like brains or deep networks have many sloppy
dimensions but much less stiff dimensions that strongly impact macroscopic
observables. This kind of bottom-up mechanistic modeling is still promising in
the modern era of understanding the natural or artificial intelligence. Here,
we shed light on eight challenges in developing theory of intelligence
following this theoretical paradigm. Theses challenges are representation
learning, generalization, adversarial robustness, continual learning, causal
learning, internal model of the brain, next-token prediction, and finally the
mechanics of subjective experience.
