We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting line-by-line embedding of the official ECMAScript specification of JavaScript regular expressions. We demonstrate its practicality by presenting two real-world applications. First, a new notion of contextual equivalence for modern regular expressions, which we use to prove or disprove rewrites drawn from previous work. Second, the first formal proof of the PikeVM algorithm used in many real-world engines. In contrast with the specification and other formalization work, our semantics captures not only the top-priority match, but a full backtracking tree recording all possible matches and their respective priority. All our definitions and results have been mechanized in the Rocq proof assistant.

In recent years, foundation models have significantly advanced data-driven systems across various domains. Yet, their underlying properties, especially when functioning as feature extractors, remain under-explored. In this paper, we investigate the sensitivity to audio effects of audio embeddings extracted from widely-used foundation models, including OpenL3, PANNs, and CLAP. We focus on audio effects as the source of sensitivity due to their prevalent presence in large audio datasets. By applying parameterized audio effects (gain, low-pass filtering, reverberation, and bitcrushing), we analyze the correlation between the deformation trajectories and the effect strength in the embedding space. We propose to quantify the dimensionality and linearizability of the deformation trajectories induced by audio effects using canonical correlation analysis. We find that there exists a direction along which the embeddings move monotonically as the audio effect strength increases, but that the subspace containing the displacements is generally high-dimensional. This shows that pre-trained audio embeddings do not globally linearize the effects. Our empirical results on instrument classification downstream tasks confirm that projecting out the estimated deformation directions cannot generally improve the robustness of pre-trained embeddings to audio effects.