Mitigating AI risk has become a topic of intense effort in recent years and months. These well-intentioned efforts grow out of real concern for the uncertain future given the rapid development of AI technologies. In the current form they are unlikely to succeed. The purpose of this document is to make a case that developing a fundamental mathematical theory of deep learning is a prerequisite for managing risk as our society transitions to wide use of AI technology. Theory in this context refers to identifying precise measurable quantities and mathematically describing their patterns, the way it is used in physics and engineering, rather than proving rigorous theorems. Recent progress in the theory of statistical inference and optimization of neural networks provides hope that such a theory may indeed be possible. Admittedly, even a comprehensive theory of deep learning cannot guarantee a successful AI transition. If we

Possible the most well-written and rigorous piece on safety I've read so far, may or may not changed my view on safety research as a whole! We indeed could really use more theories to cut through ambiguities and connect speculations with the empiricals.

> Theory in this context refers to identifying precise measurable quantities and mathematically describing their patterns, the way it is used in physics and engineering, rather than proving rigorous theorems. ~ there are many instances when internal developments in pure math later became very useful in physics and engineering. Maybe, there are already existing pieces of pure math knowledge which could be useful for mathematical descriptions of LLMs? To possible detect them, an interdiscplinary interaction between AI experts and interested pure mathematicians is required.

I am very much in favor of bringing in mathematicians, applied or pure. Still, we need to treat these phenomena as physics -- mathematical theories need to have explanatory/predictive power to be of use.

There is a need for math theories or math vision which provide a kind of structured concentrated understanding and prediction of the central issues of LLM. Of course, in view of the fast pace of LLM developments, producing full rigorous math proofs will have to wait for some decades and hundreds of PhD math theses. What would be 7-10 LLM papers or talks/posts for interested mathematicians to have a look at in order to go fast into the heart of the matter?

Indeed a great motivation for working towards theory :)

Possible the most well-written and rigorous piece on safety I've read so far, may or may not changed my view on safety research as a whole! We indeed could really use more theories to cut through ambiguities and connect speculations with the empiricals.

Although it's necessary, but very difficult.

I am hopeful it might be easier than it seems.

A great piece about security, Can we get in contact to discuss further?

> Theory in this context refers to identifying precise measurable quantities and mathematically describing their patterns, the way it is used in physics and engineering, rather than proving rigorous theorems. ~ there are many instances when internal developments in pure math later became very useful in physics and engineering. Maybe, there are already existing pieces of pure math knowledge which could be useful for mathematical descriptions of LLMs? To possible detect them, an interdiscplinary interaction between AI experts and interested pure mathematicians is required.

I am very much in favor of bringing in mathematicians, applied or pure. Still, we need to treat these phenomena as physics -- mathematical theories need to have explanatory/predictive power to be of use.

There is a need for math theories or math vision which provide a kind of structured concentrated understanding and prediction of the central issues of LLM. Of course, in view of the fast pace of LLM developments, producing full rigorous math proofs will have to wait for some decades and hundreds of PhD math theses. What would be 7-10 LLM papers or talks/posts for interested mathematicians to have a look at in order to go fast into the heart of the matter?