arXiv subjects

Eric Lu

Publications and source records attributed to Eric Lu.

4 recordsLinked to original sources

arXiv2025

First and Second Order Approximations to Stochastic Gradient Descent Methods with Momentum Terms

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due to empirical information rather than rigorous proof. While the dynamics of gradient descent methods can be studied through continuous approximations, existing works only cover scenarios with constant learning rates or SGD without momentum terms. We present approximation results under weak assumptions for SGD that allow learning rates and momentum parameters to vary with respect to time.

cs.LG↗

arXiv2023

Are Graph Neural Networks Optimal Approximation Algorithms?

In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP). Concretely, we prove that polynomial-sized message-passing algorithms can represent the most powerful polynomial time algorithms for Max Constraint Satisfaction Problems assuming the Unique Games Conjecture. We leverage this result to construct efficient graph neural network architectures, OptGNN, that obtain high-quality approximate solutions on landmark combinatorial optimization problems such as Max-Cut, Min-Vertex-Cover, and Max-3-SAT. Our approach achieves strong empirical results across a wide range of real-world and synthetic datasets against solvers and neural baselines. Finally, we take advantage of OptGNN's ability to capture convex relaxations to design an algorithm for producing bounds on the optimal solution from the learned embeddings of OptGNN.

cs.LG↗

arXiv2022

Towards Porting Operating Systems with Program Synthesis

The end of Moore's Law has ushered in a diversity of hardware not seen in decades. Operating system (and system software) portability is accordingly becoming increasingly critical. Simultaneously, there has been tremendous progress in program synthesis. We set out to explore the feasibility of using modern program synthesis to generate the machine-dependent parts of an operating system. Our ultimate goal is to generate new ports automatically from descriptions of new machines. One of the issues involved is writing specifications, both for machine-dependent operating system functionality and for instruction set architectures. We designed two domain-specific languages: Alewife for machine-independent specifications of machine-dependent operating system functionality and Cassiopea for describing instruction set architecture semantics. Automated porting also requires an implementation. We developed a toolchain that, given an Alewife specification and a Cassiopea machine description, specializes the machine-independent specification to the target instruction set architecture and synthesizes an implementation in assembly language with a customized symbolic execution engine. Using this approach, we demonstrate successful synthesis of a total of 140 OS components from two pre-existing OSes for four real hardware platforms. We also developed several optimization methods for OS-related assembly synthesis to improve scalability. The effectiveness of our languages and ability to synthesize code for all 140 specifications is evidence of the feasibility of program synthesis for machine-dependent OS code. However, many research challenges remain; we also discuss the benefits and limitations of our synthesis-based approach to automated OS porting.

cs.PL↗

arXiv2019

Aquarium: Cassiopea and Alewife Languages

This technical report describes two of the domain specific languages used in the Aquarium kernel code synthesis project. It presents the language cores in terms of abstract syntax. Cassiopea is a machine description language for describing the semantics of processor instruction sets. Alewife is a specification language that can be used to write machine-independent specifications for assembly-level instruction blocks. An Alewife specification can be used to verify and synthesize code for any machine described in Cassiopea, given a machine-specific translation for abstractions used in the specification. This article does not include an introduction to either the Aquarium system or the use of the languages. In addition to this version of the article being a draft, the Aquarium project and the languages are works in progress. This article cannot currently be considered either final or complete.

cs.PL↗