To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. 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 token subspace is provably 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, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

The set of tokens T, when embedded within the latent space X of a large language model (LLM) can be thought of as a finite sample drawn from a distribution supported on a topological subspace of X. One can ask what the smallest (in the sense of inclusion) subspace and simplest (in terms of fewest free parameters) distribution can account for such a sample. Previous work[1] suggests that the smallest topological subspace from which tokens can be drawn is not manifold, but has structure consistent with a stratified manifold. That paper relied upon knowing the token input embedding function T X, which given each token t T, ascribes a representation in X. Because embeddings preserve topological structure, in this paper, we will study T by equating it with the image of the token input embedding function, thereby treating T both as the set of tokens and as a subspace of X. This subspace is called the token subspace of X. Usually X is taken to be Euclidean space R

Large language models encode the correlational structure present in natural language by fitting segments of utterances (tokens) into a high dimensional ambient latent space upon which the models then operate. We assert that in order to develop a foundational, first-principles understanding of the behavior and limitations of large language models, it is crucial to understand the topological and geometric structure of this token subspace. In this article, we present estimators for the dimension and Ricci scalar curvature of the token subspace, and apply it to three open source large language models of moderate size: GPT2, LLEMMA7B, and MISTRAL7B. In all three models, using these measurements, we find that the token subspace is not a manifold, but is instead a stratified manifold, where on each of the individual strata, the Ricci curvature is significantly negative. We additionally find that the dimension and curvature correlate with generative fluency of the models, which suggest that these findings have implications for model behavior.

U.S. Cyber Command wants to expand the use of artificial intelligence and machine learning, and to do so, it's kicked off a broader survey of machine learning requirements across the Defense Department. It's working with the Defense Innovation Unit, the new Chief Digital and Artificial Intelligence Office and the Defense Advanced Research Project Agency to do that. The idea is to determine priorities for greater investment in the near future. U.S. Cyber Command wants to expand the use of artificial intelligence and machine learning, and to do so, it's kicked off a broader survey of machine learning requirements across the Defense Department. It's working with the Defense Innovation Unit, the new Chief Digital and Artificial Intelligence Office and the Defense Advanced Research Project Agency to do that.

General Atomics Aeronautical Systems (GA-ASI), a firm that provides drones and radar solutions for the US military, has released the first concept image for a missile-carrying air-to-air combat drone that can drop bombs in a war zone, engage in aerial threats or escort piloted plans into the battlefield. Part of the Defense Advanced Research Projects Agency's (DARPA) LongShot program, the system includes a manned craft that carries the unmanned aerial vehicle close to a warzone and then drops it mid-air to travel the rest of the way. GA-ASI notes that when carried by a bomber, the combat drone can clear the way for the piloted plane to carry out other missions without being attacked by enemy aerial vehicles. The new concept image shows a manned aircraft in the distance and a close look at the stealthy combat drone with a cockpit similar to a B-52 stealth bomber - but without the windows and a fraction of the size. There is a prominent V-shaped tail and a weapons bay on the side of the rear fuselage with two doors, The Drive reports.

While work in fields of CSCW (Computer Supported Collaborative Work), Psychology and Social Sciences have progressed our understanding of team processes and their effect performance and effectiveness, current methods rely on observations or self-report, with little work directed towards studying team processes with quantifiable measures based on behavioral data. In this report we discuss work tackling this open problem with a focus on understanding individual differences and its effect on team adaptation, and further explore the effect of these factors on team performance as both an outcome and a process. We specifically discuss our contribution in terms of methods that augment survey data and behavioral data that allow us to gain more insight on team performance as well as develop a method to evaluate adaptation and performance across and within a group. To make this problem more tractable we chose to focus on specific types of environments, Alternate Reality Games (ARGs), and for several reasons. First, these types of games involve setups that are similar to a real-world setup, e.g., communication through slack or email. Second, they are more controllable than real environments allowing us to embed stimuli if needed. Lastly, they allow us to collect data needed to understand decisions and communications made through the entire duration of the experience, which makes team processes more transparent than otherwise possible. In this report we discuss the work we did so far and demonstrate the efficacy of the approach.