A full understanding of the behavior of a large language model (LLM) requires our grasp of its input token space. If this space differs from our assumptions, our comprehension of and conclusions about the LLM will likely be flawed. We elucidate the structure of the token embeddings both empirically and theoretically. We present a novel statistical test assuming that the neighborhood around each token has a relatively flat and smooth structure as the null hypothesis. Failing to reject the null is uninformative, but rejecting it at a specific token $\psi$ implies an irregularity in the token subspace in a $\psi$-neighborhood, $B(\psi)$. The structure assumed in the null is a generalization of a manifold with boundary called a \emph{smooth fiber bundle} (which can be split into two spatial regimes -- small and large radius), so we denote our new hypothesis test as the ``fiber bundle hypothesis.'' By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the evidence suggests that the token subspace is not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, if one prompt contains a token implicated by our test, the response to that prompt will likely exhibit less stability than the other.

This paper presents LAGOON - an open source platform for understanding the complex ecosystems of Open Source Software (OSS) communities. The platform currently utilizes spatiotemporal graphs to store and investigate the artifacts produced by these communities, and help analysts identify bad actors who might compromise an OSS project's security. LAGOON provides ingest of artifacts from several common sources, including source code repositories, issue trackers, mailing lists and scraping content from project websites. Ingestion utilizes a modular architecture, which supports incremental updates from data sources and provides a generic identity fusion process that can recognize the same community members across disparate accounts. A user interface is provided for visualization and exploration of an OSS project's complete sociotechnical graph. Scripts are provided for applying machine learning to identify patterns within the data. While current focus is on the identification of bad actors in the Python community, the platform's reusability makes it easily extensible with new data and analyses, paving the way for LAGOON to become a comprehensive means of assessing various OSS-based projects and their communities.

We present Deep-n-Cheap – an open-source AutoML framework to search for deep learning models. This search includes both architecture and training hyperparameters, and supports convolutional neural networks and multilayer perceptrons. Our framework is targeted for deployment on both benchmark and custom datasets, and as a result, offers a greater degree of search space customizability as compared to a more limited search over only pre-existing models from literature. We also introduce the technique of ’search transfer’, which demonstrates the generalization capabilities of our models to multiple datasets. Deep-n-Cheap includes a user-customizable complexity penalty which trades off performance with training time or number of parameters. Specifically, our framework results in models offering performance comparable to state-of-the-art while taking 1-2 orders of magnitude less time to train than models from other AutoML and model search frameworks. Additionally, this work investigates and develops various insights regarding the search process. In particular, we show the superiority of a greedy strategy and justify our choice of Bayesian optimization as the primary search methodology over random / grid search.