Introducing Hooks by Marketing Studio.
25+ hook variations for UGC videos, including cold opens, POV setups, pattern interrupts, and story hooks.
Available on the platform and through MCP on Claude for one-off generations or batch jobs. Supercharged by Marketing Skills.
Today, we're introducing Pomelli Catalog.📣✨
Add your products or services, and Pomelli will use them to generate personalized campaigns and high-quality photoshoots, tailored to your brand.
Free of charge. Available everywhere. Try it at: https://t.co/kLyndsPBpw
📢 Attention PEs! Virtual registration for the global Product Experts Summit opens today for eligible Silver+ PEs. Breakout selection will begin later this month. Check your inbox and the KB for more details! 📩 #PESummit25
Just announced! 📣📣 For the first time in nearly a decade, SP will be playing a multi-city tour of Latin and South American this fall!
Artist pre-sales for select shows start tomorrow July 18 @ 10 am local time. Passcode VAMPIRE
🚀 New on LunarTech YouTube: Dive into ML with our Data Science Case Study! Perfect for your portfolio, this mini-course on Californian house prices uses #pandas, #numpy, #scikitlearn, #matplotlib, #seaborn. Boost skills & your career.
Watch now: https://t.co/E3X7m8B9lt
Euclidean geometry problems have been my favorite math puzzles since middle school. The most intriguing part of it is the creation of auxiliary lines, which opens a space for imagination and the freedom to explore various diagrams. Once a proof is found, these auxiliary lines almost seem magic!
In AlphaGeometry, we've devised a way to synthesize data that trains transformers to predict auxiliary lines. The main idea is straightforward:
1. Sample a random diagram.
2. Deduce all the facts about this diagram using a symbolic algorithm.
3. For each fact, we identify the minimal diagram in which the fact remains true.
4. This leads us to a trajectory from the minimal diagram to the full diagram for learning auxiliary line construction.
5. Sample a lot of random diagrams and gather a lot of data to train a big transformer.
Even though this idea seems straightforward, the underlying details are insanely hard to get right.
1. What's the action space to sample a diagram? We need an action space that allows us to sample interesting diagrams easily.
2. What's the symbolic algorithm to deduce all the facts? We built on prior works e.g. Chou et. al. from 2 decades ago, but also greatly empower their algorithm.
3. What's the algorithm to reduce the diagram to its minimal form? Super non-trivial - but Trieu solved it!!
It took Trieu (@thtrieu_) 4 years (almost his entire PhD) to work out these details. I was very fortunate to meet Trieu back in 2022, when we found we were working on exactly the same idea. During our collaboration, there are multiple times Trieu rewrote the entire project from scratch in order to tackle a new technical problem. It took an insane amount of determination and perseverance that eventually led to today's result.
People ask me how general this technique is, and what the implication is for MATHAI. I think it's clear now that solving math boils down to synthesizing high quality data. Geometry happens to have a nice action space to sample interesting problems. But for general math domains, randomly sampling likely is not the way to go. Instead, figuring out how to bootstrap from existing human data and learn the distribution of interesting problems is much more promising.
The other aspect of this work is that we utilize symbolic tools / formal algorithms to verify the correctness of the data. I think that is also fundamental to math, and how to utilize these formal tools to verify the data is one of the major future challenges. Our recent work accepted to ICLR2024, led by Jin Zhou (@jpzhou), took a small step towards this direction for general math domains: https://t.co/2w5FZWSmNt, but there are still many interesting problems yet to be solved.
Lastly, the way we synthesize those 'magic' steps can be seen as some form of reconstruction, and I believe there are ways to do such reconstruction for other kinds of mathematics to learn these "magic" steps.
Thank you Trieu @thtrieu_ and the rest of the AlphaGeometry team (@lmthang, @quocleix, @hhexiy) for this amazing collaboration. We're one step closer to solving math. LFG!!!