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#math

117 posts80 participants14 posts today
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José A. Alonso

LeanAgent: Lifelong learning for formal theorem proving. ~ Adarsh Kumarappan, Mo Tiwari, Peiyang Song, Robert Joseph George, Chaowei Xiao, Anima Anandkumar. arxiv.org/abs/2410.06209 #LLMs #ITP #LeanProver #Math

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arXiv.orgLeanAgent: Lifelong Learning for Formal Theorem ProvingLarge Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a specific dataset to perform well on particular domains, such as undergraduate-level mathematics. These methods struggle with generalizability to advanced mathematics. A fundamental limitation is that these approaches operate on static domains, failing to capture how mathematicians often work across multiple domains and projects simultaneously or cyclically. We present LeanAgent, a novel lifelong learning framework for formal theorem proving that continuously generalizes to and improves on ever-expanding mathematical knowledge without forgetting previously learned knowledge. LeanAgent introduces several key innovations, including a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity. LeanAgent successfully generates formal proofs for 155 theorems across 23 diverse Lean repositories where formal proofs were previously missing, many from advanced mathematics. It performs significantly better than the static LLM baseline, proving challenging theorems in domains like abstract algebra and algebraic topology while showcasing a clear progression of learning from basic concepts to advanced topics. In addition, we analyze LeanAgent's superior performance on key lifelong learning metrics. LeanAgent achieves exceptional scores in stability and backward transfer, where learning new tasks improves performance on previously learned tasks. This emphasizes LeanAgent's continuous generalizability and improvement, explaining its superior theorem-proving performance.
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Bhavani Shankar 💭

This simple math puzzle has lingered in my mind over a decade because it has such a surprising answer. How would you solve it and explain the result?

In a class of 500 students, 99% are right-handed. How many right-handers should leave the class to make it 98%?

You can check my blog for the solution and an intuitive explanation.

Just BeingEasy math puzzle with an unbelievable answer | Just BeingThe answer to this problem is so surprising that it has lingered in my mind for decades. Try to solve it before looking at the answer. How would you explain the solution intuitively?
#math#puzzle#brainteaser
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Neurofrontiers

When I transitioned from cognitive to computational neuroscience, I found myself in a bit of a bind. I had learned calculus, but I had progressed little beyond pattern recognition: I knew which rules to apply to find solutions to which equations, but the equations themselves lacked any sort of real meaning for me.

So I struggled with understanding how formulas could be implemented in code and why the code I was reading could be described by those formulas. Resources explaining math “for neuroscientists” were unfortunately quite useless for me, because they usually presented the necessary equations for describing various neural systems, assuming the presence of that basic understanding/intuition I lacked.

Of course, I figured things out eventually (otherwise I wouldn’t be writing about it), but I’m 85% sure I’m not the only one who’s ever struggled with this, and so I wrote the tutorial I wish I could’ve had. If you’re in a similar position, I hope you’ll find it useful. And if not, maybe it helps you get a glimpse into the struggles of the non-math people in your life. Either way, it has cats.

neurofrontiers.blog/building-a

Neurofrontiers · Building a virtual neuron - part 1 - Neurofrontiers
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#neuroscience#math#ComputationalNeuroscience
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