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Michael Robinson

Publications and source records attributed to Michael Robinson.

At least 19 recordsLinked to original sources
arXiv2026

Doppler Tracking of the Artemis II Mission (and Other Spacecraft)

This report describes an American University (AU) student-faculty project to track the Orion spacecraft ``Integrity'' during the Artemis II mission, along its Earth-to-Moon trajectory. The Orion spacecraft has an S-band communications transmitter used for space-to-Earth messages. The S-band transmitter uses an orthogonal quadrature phase shift keying (OQPSK) digital mode, from which Doppler frequency measurements can be derived. This project successfully galvanized student excitement for experimental science, and for space science in particular. Even though we did not successfully obtain a Doppler estimate for the Orion spacecraft, we now have a fully functional end-to-end satellite tracking system as detailed in this report.

cs.CE↗
arXiv2026

Original Sin of npm: A Study on Vulnerability Propagation in JavaScript Dependency Networks

Understanding vulnerability propagation is essential for assessing how vulnerabilities spread across components of a software package. This supports more accurate impact analysis and enhances threat detection and mitigation. In this paper, we investigate how a small number of vulnerable JavaScript packages contribute to the creation of a disproportionately large number of vulnerable packages. This paper presents insights from 1,515 reported vulnerabilities gathered from a custom-built vulnerability database containing 1,077,946 JavaScript packages sourced from `npm-follower' and their associated dependency networks. Dependency networks were constructed using the deps.dev API, with vulnerabilities identified by parsing package names and version numbers through the Google Open Source Vulnerability API. Our findings reveal that 61.30% (660,748) of packages are reliant on one or more dependency packages, and 21.60% (232,836) of total packages have at least one known vulnerability throughout their dependency networks -- of which most (42%) are of High severity. We also found that it takes, on average, approximately 4 years and 11 months to fix a vulnerable package from when the first vulnerable version is published on npm -- although publication times of vulnerabilities occur approximately 19 days after a fix is available. Finally, we observe a high concentration of frequently present vulnerabilities throughout dependency networks, with the top-7 most frequent vulnerabilities accounting for 25% of vulnerability cases and the top-23 most frequent accounting for 50%. Based on these findings, we propose recommendations for developers and package managers to mitigate the threat and occurrence of vulnerabilities within the npm dependency network and the broader software repository community.

cs.CR↗
arXiv2025

Analyzing the topological structure of composite dynamical systems

This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from DSEMs to sheaves passes through a formal construction borrowed from electronics called a netlist that specifies how data route through a system. A sheaf can be considered a formal hypothesis about how variables interact, that then specifies how observations can be tested for consistency, how missing data can be inferred, and how uncertainty about the observations can be quantified. Sheaf modeling provides a coherent mathematical framework for studying the interaction of various dynamical subsystems that together determine a larger system.

math.AT↗
arXiv2025

Dowker's theorem for higher-order relations

Given a relation $R \subseteq I \times J$ between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker complexes, are isomorphic. In its modern form, the full result asserts a functorial homotopy equivalence between the two Dowker complexes. What can be said about relations defined on three or more sets? We present a simple generalization to multiway relations of the form $R \subseteq I_1 \times I_2 \times \cdots \times I_m$. The theorem asserts functorial homotopy equivalences between $m$ multiway Dowker complexes and a variant of the rectangle complex of Brun and Salbu from their recent short proof of Dowker's Theorem. Our proof uses Smale's homotopy mapping theorem and factors through a cellular Dowker lemma that expresses the main idea in more general form. To make the geometry more transparent, we work with a class of spaces called prod-complexes then transfer the results to simplicial complexes through a simplexification process. We conclude with a detailed study of ternary relations, identifying seven functorially defined homotopy types and twelve natural transformations between them.

math.AT↗
arXiv2025

The Topological Structures of the Orders of Hypergraphs

We provide first a categorical exploration of, and then completion of the mapping of the relationships among, three fundamental perspectives on binary relations: as the incidence matrices of hypergraphs, as the formal contexts of concept lattices, and as specifying topological cosheaves of simplicial (Dowker) complexes on simplicial (Dowker) complexes. We provide an integrative, functorial framework combining previously known with three new results: 1) given a binary relation, there are order isomorphisms among the bounded edge order of the intersection complexes of its dual hypergraphs and its concept lattice; 2) the concept lattice of a context is an isomorphism invariant of the Dowker cosheaf (of abstract simplicial complexes) of that context; and 3) a novel Dowker cosheaf (of chain complexes) of a relation is an isomorphism invariant of the concept lattice of the context that generalizes Dowker's original homological result. We illustrate these concepts throughout with a running example, and demonstrate relationships to past results.

math.CO↗
arXiv2025

Token embeddings violate the manifold hypothesis

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.

cs.CL↗
arXiv2025

Probing the topology of the space of tokens with structured prompts

This article presents a general and flexible method for prompting a large language model (LLM) to reveal its (hidden) token input embedding up to homeomorphism. Moreover, this article provides strong theoretical justification -- a mathematical proof for generic LLMs -- for why this method should be expected to work. With this method in hand, we demonstrate its effectiveness by recovering the token subspace of Llemma-7B. The results of this paper apply not only to LLMs but also to general nonlinear autoregressive processes.

math.DG↗
arXiv2024

The structure of the token space for large language models

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.

math.DG↗
arXiv2024

Topological and geometric characterization of synthetic aperture sonar collections

This article explores the theoretical underpinnings of -- and practical results for -- topological and geometric features of data collected by synthetic aperture sonar systems. We prove a strong theoretical guarantee about the structure of the space of echos (the signature space) that is relevant for classification, and that this structure is measurable in laboratory conditions. The guarantee makes minimal assumptions about the sonar platform's trajectory, and establishes that the signature space divides neatly into topological features based upon the number of prominent echos and their placement, and geometric features that capture their corresponding sonar cross section.

cs.CE↗
arXiv2024

Understanding High-Order Network Structure using Permissible Walks on Attributed Hypergraphs

Hypergraphs have been a recent focus of study in mathematical data science as a tool to understand complex networks with high-order connections. One question of particular relevance is how to leverage information carried in hypergraph attributions when doing walk-based techniques. In this work, we focus on a new generalization of a walk in a network that recovers previous approaches and allows for a description of permissible walks in hypergraphs. Permissible walk graphs are constructed by intersecting the attributed $s$-line graph of a hypergraph with a relation respecting graph. The attribution of the hypergraph's line graph commonly carries over information from categorical and temporal attributions of the original hypergraph. To demonstrate this approach on a temporally attributed example, we apply our framework to a Reddit data set composed of hyperedges as threads and authors as nodes where post times are tracked.

cs.SI↗
arXiv2024

Prospects for inconsistency detection using large language models and sheaves

We demonstrate that large language models can produce reasonable numerical ratings of the logical consistency of claims. We also outline a mathematical approach based on sheaf theory for lifting such ratings to hypertexts such as laws, jurisprudence, and social media and evaluating their consistency globally. This approach is a promising avenue to increasing consistency in and of government, as well as to combating mis- and disinformation and related ills.

cs.CY↗
arXiv2024

Tracking before detection using partial orders and optimization

This article addresses the problem of multi-object tracking by using a non-deterministic model of target behaviors with hard constraints. To capture the evolution of target features as well as their locations, we permit objects to lie in a general topological target configuration space, rather than a Euclidean space. We obtain tracker performance bounds based on sample rates, and derive a flexible, agnostic tracking algorithm. We demonstrate our algorithm on two scenarios involving laboratory and field data.

math.DS↗
arXiv2023

Formal Concept Lattice Representations and Algorithms for Hypergraphs

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only in the intersection relationships of the hyperedges, and so forming the "intersection complex" of a hypergraph is quite valuable. This identifies a valuable isomorphism between the intersection complex and the "concept lattice" formed from taking the hypergraph's incidence matrix as a "formal context": hypergraphs also generalize graphs in that their incidence matrices are arbitrary Boolean matrices. This isomorphism allows connecting discrete algorithms for lattices and hypergraphs, in particular s-walks or s-paths on hypergraphs can be mapped to order theoretical operations on the concept lattice. We give new algorithms for formal concept lattices and hypergraph s-walks on concept lattices. We apply this to a large real-world dataset and find deep lattices implying high interconnectivity and complex geometry of hyperedges.

cs.DS↗
arXiv2023

Vulnerability Detection Through an Adversarial Fuzzing Algorithm

Fuzzing is a popular vulnerability automated testing method utilized by professionals and broader community alike. However, despite its abilities, fuzzing is a time-consuming, computationally expensive process. This is problematic for the open source community and smaller developers, as most people will not have dedicated security professionals and/or knowledge to perform extensive testing on their own. The goal of this project is to increase the efficiency of existing fuzzers by allowing fuzzers to explore more paths and find more bugs in shorter amounts of time, while still remaining operable on a personal device. To accomplish this, adversarial methods are built on top of current evolutionary algorithms to generate test cases for further and more efficient fuzzing. The results of this show that adversarial attacks do in fact increase outpaces existing fuzzers significantly and, consequently, crashes found.

cs.SE↗
arXiv2023

Unsupervised clustering of file dialects according to monotonic decompositions of mixtures

This paper proposes an unsupervised classification method that partitions a set of files into non-overlapping dialects based upon their behaviors, determined by messages produced by a collection of programs that consume them. The pattern of messages can be used as the signature of a particular kind of behavior, with the understanding that some messages are likely to co-occur, while others are not. Patterns of messages can be used to classify files into dialects. A dialect is defined by a subset of messages, called the required messages. Once files are conditioned upon dialect and its required messages, the remaining messages are statistically independent. With this definition of dialect in hand, we present a greedy algorithm that deduces candidate dialects from a dataset consisting of a matrix of file-message data, demonstrate its performance on several file formats, and prove conditions under which it is optimal. We show that an analyst needs to consider fewer dialects than distinct message patterns, which reduces their cognitive load when studying a complex format.

cs.PL↗
arXiv2022

The Topology of Circular Synthetic Aperture Sonar Targets

This report presents a connection between the physical acoustics of an object and the topology of the space of echoes resulting from a circular synthetic aperture sonar (CSAS) collection of that object. A simple theoretical model is developed that yields a precise, yet qualitative, description of the space of echoes. This theoretical model is validated in simulation and with experimental data from a laboratory sonar system.

eess.SP↗
arXiv2022

Statistical detection of format dialects using the weighted Dowker complex

This paper provides an experimentally validated, probabilistic model of file behavior when consumed by a set of pre-existing parsers. File behavior is measured by way of a standardized set of Boolean "messages" produced as the files are read. By thresholding the posterior probability that a file exhibiting a particular set of messages is from a particular dialect, our model yields a practical classification algorithm for two dialects. We demonstrate that this thresholding algorithm for two dialects can be bootstrapped from a training set consisting primarily of one dialect. Both the (parametric) theoretical and the (non-parametric) empirical distributions of file behaviors for one dialect yield good classification performance, and outperform classification based on simply counting messages. Our theoretical framework relies on statistical independence of messages within each dialect. Violations of this assumption are detectable and allow a format analyst to identify "boundaries" between dialects. A format analyst can therefore greatly reduce the number of files they need to consider when crafting new criteria for dialect detection, since they need only consider the files that exhibit ambiguous message patterns.

cs.CE↗