Jacob Miller

Jacob Miller, Vahan Huroyan, Stephen Kobourov

We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underlying data, which may not be known in advance. For a given graph, LGS aims to find a good balance between the local and global structure to preserve. We evaluate the performance of LGS with synthetic and real-world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online.

Alex Meiburg, Jing Chen, Jacob Miller et al.

Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable features arising from their quantum-inspired nature, tensor network generative models have previously been largely restricted to binary or categorical data, limiting their utility in real-world modeling problems. We overcome this by introducing a new family of tensor network generative models for continuous data, which are capable of learning from distributions containing continuous random variables. We develop our method in the setting of matrix product states, first deriving a universal expressivity theorem proving the ability of this model family to approximate any reasonably smooth probability density function with arbitrary precision. We then benchmark the performance of this model on several synthetic and real-world datasets, finding that the model learns and generalizes well on distributions of continuous and discrete variables. We develop methods for modeling different data domains, and introduce a trainable compression layer which is found to increase model performance given limited memory or computational resources. Overall, our methods give important theoretical and empirical evidence of the efficacy of quantum-inspired methods for the rapidly growing field of generative learning.

Jacob Miller, Markus Wallinger, Ludwig Felder et al.

In this paper, we test whether Multimodal Large Language Models (MLLMs) can match human-subject performance in tasks involving the perception of properties in network layouts. Specifically, we replicate a human-subject experiment about perceiving quality (namely stress) in network layouts using GPT-4o, Gemini-2.5 and Qwen2.5. Our experiments show that giving MLLMs the same study information as trained human participants yields performance comparable to that of human experts and exceeds that of untrained non-experts. Additionally, we show that prompt engineering that deviates from the human-subject experiment can lead to better-than-human performance in some settings. Interestingly, like human subjects, the MLLMs seem to rely on visual proxies rather than computing the actual value of stress, indicating some sense or facsimile of perception. Explanations from the models are similar to those used by the human participants (e.g., an even distribution of nodes and uniform edge lengths).

Kiran Smelser, Jacob Miller, Stephen Kobourov

Stress is among the most commonly employed quality metrics and optimization criteria for dimension reduction projections of high dimensional data. Complex, high dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two dimensional scatter plots that visually capture some properties of the data. Because visually determining the accuracy of these plots is challenging, researchers often use quality metrics to measure projection accuracy or faithfulness to the full data. One of the most commonly employed metrics, normalized stress, is sensitive to uniform scaling of the projection, despite this act not meaningfully changing anything about the projection. We investigate the effect of scaling on stress and other distance based quality metrics analytically and empirically by showing just how much the values change and how this affects dimension reduction technique evaluations. We introduce a simple technique to make normalized stress scale invariant and show that it accurately captures expected behavior on a small benchmark.

Timo Brand, Henry Förster, Stephen G. Kobourov et al.

We evaluate how visualizations can influence the judgment of MLLMs about the presence or absence of bridges in a network. We show that the inclusion of visualization improves confidence over a structured text-based input that could theoretically be helpful for answering the question. On the other hand, we observe that standard visualization techniques create a strong bias towards accepting or refuting the presence of a bridge -- independently of whether or not a bridge actually exists in the network. While our results indicate that the inclusion of visualization techniques can effectively influence the MLLM's judgment without compromising its self-reported confidence, they also imply that practitioners must be careful of allowing users to include visualizations in generative AI applications so as to avoid undesired hallucinations.

Kiran Smelser, Kaviru Gunaratne, Jacob Miller et al.

Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots that visually capture some properties of the data. Because visually determining the accuracy of these plots is challenging, researchers often use quality metrics to measure the projection's accuracy and faithfulness to the original data. One of the most commonly employed metrics, normalized stress, is sensitive to uniform scaling (stretching, shrinking) of the projection, despite this act not meaningfully changing anything about the projection. Another quality metric, the Kullback--Leibler (KL) divergence used in the popular t-Distributed Stochastic Neighbor Embedding (t-SNE) technique, is also susceptible to this scale sensitivity. We investigate the effect of scaling on stress and KL divergence analytically and empirically by showing just how much the values change and how this affects dimension reduction technique evaluations. We introduce a simple technique to make both metrics scale-invariant and show that it accurately captures expected behavior on a small benchmark.