EDIT: With a minimal hint, Gemini, as well as other models like Grok, solve it in one try. There is maybe something interesting to be said here, but much less than expected.

Includes a link to the full Gemini conversation, but setting the stage first:

There is a puzzle. If you are still on Tumblr,  or live in Berkeley where I can and have inflicted it on you in person^[1], you may have seen it. There's a series of arcane runes, composed entirely of []- in some combination, and the runes - the strings of characters - are all assigned to numbers; mostly integers, but some fractions and integer roots. You are promised that this is a notation, and it's a genuine promise.

1 = []
2 = [[]]
3 = [][[]]
4

TL;DR: In a neural network with $d$ parameters, the (local) learning coefficient $\lambda$ can be upper and lower bounded by the rank of the network's Hessian $d_1$:

$\frac{d_1}{2}\le \lambda \le \frac{d_1}{2}+\frac{d-d_1}{4}$.

The lower bound is a known result. The upper bound is a claim by me, and this post contains the proof for it.^[1] If you find any problems, do point them out. 

Edit 16.08.2024: The original version of this post had a three in the denominator of the upper bound. Dmitry Vaintrob spotted an improvement to make it a four.

Introduction

The learning coefficient $\lambda$ is a measure of loss basin volume and model complexity. You can think of it sort of like an effective parameter count of the neural network. Simpler models that do less stuff have smaller $\lambda$.

Calculating $\lambda$ for real networks people actually use is a pain. My hope is that these...

PDF version. berkeleygenomics.org. X.com. Bluesky.

William Thurston was a world-renowned mathematician. His ideas revolutionized many areas of geometry and topology^[1]; the proof of his geometrization conjecture was eventually completed by Grigori Perelman, thus settling the Poincaré conjecture (making it the only solved Millennium Prize problem). After his death, his students wrote reminiscences, describing among other things his exceptional vision.^[2] Here's Jeff Weeks:

Bill’s gift, of course, was his vision, both in the direct sense of seeing geometrical structures that nobody had seen before and in the extended sense of seeing new ways to understand things. While many excellent mathematicians might understand a complicated situation, Bill could look at the same complicated situation and find simplicity.

Thurston emphasized clear vision over algebra, even to a fault. Yair Minksy:

Most inspiring was his

Read the full article here. 

The journalist is an AI skeptic, but does solid financial investigations. Details below:

• 2024 Revenue: According to reporting by The Information, OpenAI's revenue was likely somewhere in the region of $4 billion.
• Burn Rate: The Information also reports that OpenAI lost $5 billion after revenue in 2024, excluding stock-based compensation, which OpenAI, like other startups, uses as a means of compensation on top of cash. Nevertheless, the more it gives away, the less it has for capital raises. To put this in blunt terms, based on reporting by The Information, running OpenAI cost $9 billion dollars in 2024. The cost of the compute to train models alone ($3 billion) obliterates the entirety of its subscription revenue, and the compute from running models ($2 billion) takes

tl;dr:

From my current understanding, one of the following two things should be happening and I would like to understand why it doesn’t:

Either

1. Everyone in AI Safety who thinks slowing down AI is currently broadly a good idea should publicly support PauseAI.

   Or

2. If pausing AI is much more popular than the organization PauseAI, that is a problem that should be addressed in some way.

Pausing AI

There does not seem to be a legible path to prevent possible existential risks from AI without slowing down its current progress.

I am aware that many people interested in AI Safety do not want to prevent AGI from being built EVER, mostly based on transhumanist or longtermist reasoning.

Many people in AI Safety seem to be on board with the goal of “pausing AI”, including, for example,...

We may be on the direct path to AGI and then ASI - the singularity could happen within the next 5-20 years. If you survive to reach it, the potential upside is immense, daily life could become paradise.

With such high stakes, ensuring personal survival until the singularity should be a top priority for yourself and those you care about.

I've created V1 of the Singularity Survival Guide, an evidence-based resource focused on:

1. Identifying the highest-probability preventable causes of death/injury in the near term
2. Providing the highest-ROI risk mitigation strategies
3. Outlining preparations for potential societal instability
4. Presenting information in a shareable, memetic format

Top Risks to Mitigate

🚗 Car & Pedestrian Accidents

The #1 daily threat most people underestimate. Key mitigations include driving less when possible, choosing vehicles with top safety ratings, avoiding high-risk driving times,...

Suppose you’re an AI researcher trying to make AIs which are conscious and reliably moral, so they’re trustworthy and safe for release into the real world, in whatever capacity you intend.

You can’t, or don’t want to manually create them; it’s more economical, and the only way to ensure they’re conscious, if you procedurally generate them along with a world to inhabit. Developing from nothing to maturity within a simulated world, with simulated bodies, enables them to accumulate experiences. 

These experiences, in humans, form the basis of our personalities. A brain grown in sensory deprivation in a lab would never have any experiences, would never learn language, would never think of itself as a person, and wouldn’t ever become a person as we think of people. It needs a...