A Sharper Picture of Generalization in Transformers

We study transformers' generalization behavior on boolean domains from the perspective of the Fourier Spectra of their target functions. In contrast to prior work (Edelman et al., 2022; Trauger and Tewari, 2024), which derived generalization bounds from Rademacher complexity, we investigate the feasibility of obtaining generalization bounds via PAC-Bayes theory. We show that sparse spectra concentrated on low-degree components enable low-sharpness constructions with good generalization properties. Our idea is to show the existence of flat minima implementing any boolean function of sparsity no greater than the context length, and then apply a PAC-Bayes bound to an idealized low-sharpness learner, resulting in a non-vacuous generalization bound. We evaluate predictions empirically and conduct a mechanistic interpretability study to support the realism of our theoretical construction in real transformers.

TEL'M: Test and Evaluation of Language Models

Language Models have demonstrated remarkable capabilities on some tasks while failing dramatically on others. The situation has generated considerable interest in understanding and comparing the capabilities of various Language Models (LMs) but those efforts have been largely ad hoc with results that are often little more than anecdotal. This is in stark contrast with testing and evaluation processes used in healthcare, radar signal processing, and other defense areas. In this paper, we describe Test and Evaluation of Language Models (TEL'M) as a principled approach for assessing the value of current and future LMs focused on high-value commercial, government and national security applications. We believe that this methodology could be applied to other Artificial Intelligence (AI) technologies as part of the larger goal of "industrializing" AI.