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Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic
Eshika Saxena, Alberto Alfarano, François Charton +3
Recent work showed that ML-based attacks on Learning with Errors (LWE), a hard problem used in post-quantum cryptography, outperform classical algebraic attacks in certain settings…
Physics of Language Models: Part 2.2, How to Learn From Mistakes on Grade-School Math Problems
Tian Ye, Zicheng Xu, Yuanzhi Li +1
Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there…
Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process
Tian Ye, Zicheng Xu, Yuanzhi Li +1
Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmark…
Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Laws
Zeyuan Allen-Zhu, Yuanzhi Li
Scaling laws describe the relationship between the size of language models and their capabilities. Unlike prior studies that evaluate a model's capability via loss or benchmarks, w…
Reverse Training to Nurse the Reversal Curse
Olga Golovneva, Zeyuan Allen-Zhu, Jason Weston +1
Large language models (LLMs) have a surprising failure: when trained on "A has a feature B", they do not generalize to "B is a feature of A", which is termed the Reversal Curse. Ev…