7 papers
Fel's Conjecture on Syzygies of Numerical Semigroups
Evan Chen, Chris Cummins, GSM +18
Let be a numerical semigroup and its semigroup ring. The Hilbert numerator of determines normalized alternating syzygy power sums $K_…
ABC implies that Ramanujan's tau function misses almost all primes
David Kurniadi Angdinata, Evan Chen, Chris Cummins +21
Lehmer conjectured that Ramanujan's tau-function never vanishes. In a related direction, a folklore conjecture asserts that infinitely many primes arise as absolute values of Raman…
Dead ends in square-free digit walks
Evan Chen, Chris Cummins, Ben Eltschig +18
We study "dead ends" in square-free digit walks: square-free integers such that, in base , every one-digit extension is non-square-free. In base , the stochastic…
LOOPer: A Learned Automatic Code Optimizer For Polyhedral Compilers
Massinissa Merouani, Afif Boudaoud, Iheb Nassim Aouadj +7
While polyhedral compilers have shown success in implementing advanced code transformations, they still face challenges in selecting the ones that lead to the most profitable speed…
CWM: An Open-Weights LLM for Research on Code Generation with World Models
FAIR CodeGen team, Jade Copet, Quentin Carbonneaux +48
We release Code World Model (CWM), a 32-billion-parameter open-weights LLM, to advance research on code generation with world models. To improve code understanding beyond what can…
What I cannot execute, I do not understand: Training and Evaluating LLMs on Program Execution Traces
Jordi Armengol-Estapé, Quentin Carbonneaux, Tianjun Zhang +8
Code generation and understanding are critical capabilities for large language models (LLMs). Thus, most LLMs are pretrained and fine-tuned on code data. However, these datasets ty…