SearcharxivSearch

arXiv subjects

Bryan Lu

Publications and source records attributed to Bryan Lu.

3 recordsLinked to original sources

Agentic Code Optimization via Compiler-LLM Cooperation

Generating performant executables from high level languages is critical to software performance across a wide range of domains. Modern compilers perform this task by passing code through a series of well-studied optimizations at progressively lower levels of abstraction, but may miss optimization opportunities that require high-level reasoning about a program's purpose. Recent work has proposed using LLMs to fill this gap. While LLMs can achieve large speedups on some programs, they frequently generate code that is incorrect. In this work, we propose a method to balance the correctness of conventional compiler optimizations with the ``creativity'' of LLM-based code generation: compiler-LLM cooperation. Our approach integrates existing compiler optimization passes with LLM-based code generation at multiple levels of abstraction, retaining the best features of both types of code optimization. We realize our approach with a multi-agent system that includes (1) LLM-based optimization agents for each level of abstraction, (2) individual compiler constituents as tools, (3) an LLM-based test generation agent that probes the correctness and performance of generated code, and (4) a guiding LLM that orchestrates the other components. The strategy enables LLM-based optimization of input programs at multiple levels of abstraction and introduces a method for distributing computational budget between levels. Our extensive evaluation shows that compiler-LLM cooperation outperforms both existing compiler optimizations and level-specific LLM-based baselines, producing speedups up to 1.25x.

cs.PL

Ribbon complexes for the 0-Hecke algebra

We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting the basic ribbon product rule in NSym via concatenation and near-concatenation. Iterating these maps yields cochain complexes indexed by generalized ribbons; we prove these complexes are acyclic in positive degrees and that their zeroth cohomology is the projective module indexed by full concatenation. We apply these complexes, together with VandeBogert's ribbon Schur module criterion, to prove Koszulness for a naturally defined internally graded algebra object built from the 0-Hecke tower. Finally, we define skew projective modules whose noncommutative Frobenius characteristics realize skewing by fundamental quasisymmetric functions on NSym.

math.CO

On the Nature and Complexity of an Impartial Two-Player Variant of the Game Lights-Out

In this paper we study a variant of the solitaire game Lights-Out, where the player's goal is to turn off a grid of lights. This variant is a two-player impartial game where the goal is to make the final valid move. This version is playable on any simple graph where each node is given an assignment of either a 0 (representing a light that is off) or 1 (representing a light that is on). We focus on finding the Nimbers of this game on grid graphs and generalized Petersen graphs. We utilize a recursive algorithm to compute the Nimbers for 2 x n grid graphs and for some generalized Petersen graphs.

math.CO