6 papers
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
Alan Li, Rahul Saha, Anton Xue +4
AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to…
New Lower and Upper Bounds for the Grothendieck Constant
Rahul Saha, Alan Li, Anton Xue +4
We establish new bounds on the Grothendieck constant : \[ \frac{6π}{11} \le K_G \le \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Methodologically, our lower bound approach differs fr…
The Grothendieck Constant is Less Than
Alan Li, Rahul Saha, Anton Xue +4
We prove that the Grothendieck constant . This improves on the work of Braverman, Makarychev, Makarychev, and Naor (2011), who proved…
The Transformer Cookbook
Andy Yang, Christopher Watson, Anton Xue +6
We present the transformer cookbook: a collection of techniques for directly encoding algorithms into a transformer's parameters. This work addresses the steep learning curve of su…
Logicbreaks: A Framework for Understanding Subversion of Rule-based Inference
Anton Xue, Avishree Khare, Rajeev Alur +2
We study how to subvert large language models (LLMs) from following prompt-specified rules. We first formalize rule-following as inference in propositional Horn logic, a mathematic…
On The Concurrence of Layer-wise Preconditioning Methods and Provable Feature Learning
Thomas T. Zhang, Behrad Moniri, Ansh Nagwekar +4
Layer-wise preconditioning methods are a family of memory-efficient optimization algorithms that introduce preconditioners per axis of each layer's weight tensors. These methods ha…