Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to optimal control, to PDE-constrained optimization. We develop an adaptive inexact Newton method for this problem class. In each iteration, we solve the Lagrangian Newton system inexactly via a randomized iterative sketching solver, and select a suitable stepsize by performing line search on an exact augmented Lagrangian merit function. The randomized solvers have advantages over deterministic linear system solvers by significantly reducing per-iteration flops complexity and storage cost, when equipped with suitable sketching matrices. Our method adaptively controls the accuracy of the randomized solver and the penalty parameters of the exact augmented Lagrangian, to ensure that the inexact Newton direction is a descent direction of the exact augmented Lagrangian. This allows us to establish a global almost sure convergence. We also show that a unit stepsize is admissible locally, so that our method exhibits a local linear convergence. Furthermore, we prove that the linear convergence can be strengthened to superlinear convergence if we gradually sharpen the adaptive accuracy condition on the randomized solver. We demonstrate the superior performance of our method on benchmark nonlinear problems in CUTEst test set, constrained logistic regression with data from LIBSVM, and a PDE-constrained problem.

Who Wrote this Code? Watermarking for Code Generation

Large language models for code have recently shown remarkable performance in generating executable code. However, this rapid advancement has been accompanied by many legal and ethical concerns, such as code licensing issues, code plagiarism, and malware generation, making watermarking machine-generated code a very timely problem. Despite such imminent needs, we discover that existing watermarking and machine-generated text detection methods for LLMs fail to function with code generation tasks properly. Hence, in this work, we propose a new watermarking method, SWEET, that significantly improves upon previous approaches when watermarking machine-generated code. Our proposed method selectively applies watermarking to the tokens with high enough entropy, surpassing a defined threshold. The experiments on code generation benchmarks show that our watermarked code has superior quality compared to code produced by the previous state-of-the-art LLM watermarking method. Furthermore, our watermark method also outperforms DetectGPT for the task of machine-generated code detection.

A Simplified Framework for Contrastive Learning for Node Representations

Contrastive learning has recently established itself as a powerful self-supervised learning framework for extracting rich and versatile data representations. Broadly speaking, contrastive learning relies on a data augmentation scheme to generate two versions of the input data and learns low-dimensional representations by maximizing a normalized temperature-scaled cross entropy loss (NT-Xent) to identify augmented samples corresponding to the same original entity. In this paper, we investigate the potential of deploying contrastive learning in combination with Graph Neural Networks for embedding nodes in a graph. Specifically, we show that the quality of the resulting embeddings and training time can be significantly improved by a simple column-wise postprocessing of the embedding matrix, instead of the row-wise postprocessing via multilayer perceptrons (MLPs) that is adopted by the majority of peer methods. This modification yields improvements in downstream classification tasks of up to 1.5% and even beats existing state-of-the-art approaches on 6 out of 8 different benchmarks. We justify our choices of postprocessing by revisiting the "alignment vs. uniformity paradigm", and show that column-wise post-processing improves both "alignment" and "uniformity" of the embeddings.