arXiv subjects

William H. W. Thompson

Publications and source records attributed to William H. W. Thompson.

4 recordsLinked to original sources

arXiv2026

Multiple latent orderings better predict language model preferences

Language models are frequently employed in settings where they are asked to make value judgments and choices. These observed choices often exhibit intransitivity: A model may prefer item $A$ to $B$ and $B$ to $C$, while also preferring $C$ to $A$. Existing work that models LLM preferences treats such inconsistencies as sampling noise around a single latent ordering. We instead propose that intransitivity reflects the aggregation of multiple latent, internally consistent orderings. We first show that observed inconsistencies cannot be explained by a single ordering under any monotone link function. We then introduce a noise-augmented mixture Bradley-Terry (MBT) model that infers latent preference components from repeated pairwise comparisons. Across seven models and four tasks, a mixture of orderings often explains structural inconsistencies better than single-utility models. We find that aggregate preferences often hide underlying preference heterogeneity. A case study on Moral Machine dilemmas shows that models which disagree on aggregate orderings can still share latent components. Together, these results suggest that LLMs reflect plural preferences. Alignment and evaluation pipelines that treat LLM preferences as a single function, therefore, risk averaging over coherent orderings that different users may endorse differently.

cs.LG↗

arXiv2026

Simpson's paradox explains the ubiquity of nonlinear, threshold, and complex contagions

Complex contagions describe systems where the probability or rate of contagious transmission is a nonlinear function of the exposure to contagious agents. These models were first studied theoretically but have since been used to capture effects such as nonconformism, social reinforcement or peer pressure in empirical data. However, recent studies have shown that local correlations (e.g., group structure or temporal burstiness) and heterogeneity (e.g., diversity of parameters or covariates) can give the illusion of nonlinear effects even when the dynamics is actually linear. We briefly review these studies to inform a new model and explanation for these effective models of complex contagions. We find global threshold dynamics and superlinear complex contagions even in populations where agents are distributed across social groups described solely by linear or even sublinear contagions. This effect can be understood as a manifestation of Simpson's paradox. Incidence data from heterogeneous groups can look superlinear once averaged over all groups, since the sampling of groups represented at high incidence is biased towards those with stronger local transmission. We then define what we call a Simpson's contagion: a contagion process that looks superlinear when observed over an entire population, but is mechanistically linear or even sublinear in all of its subgroups. By exploring these Simpson's contagions over mathematical case studies, our work contributes to the growing body of literature on the ubiquity of threshold and complex contagions as effective models, and our results stress the pitfall of model selection that ignores correlations and heterogeneity in populations.

physics.soc-ph↗

arXiv2025

Sensitivity analysis of epidemic forecasting and spreading on networks with probability generating functions

Epidemic forecasting tools embrace the stochasticity and heterogeneity of disease spread to predict the growth and size of outbreaks. Conceptually, stochasticity and heterogeneity are often modeled as branching processes or as percolation on contact networks. Mathematically, probability generating functions provide a flexible and efficient tool to describe these models and quickly produce forecasts. While their predictions are probabilistic-i.e., distributions of outcome-they depend deterministically on the input distribution of transmission statistics and/or contact structure. Since these inputs can be noisy data or models of high dimension, traditional sensitivity analyses are computationally prohibitive and are therefore rarely used. Here, we use statistical condition estimation to measure the sensitivity of stochastic polynomials representing noisy generating functions. In doing so, we can separate the stochasticity of their forecasts from potential noise in their input. For standard epidemic models, we find that predictions are most sensitive at the critical epidemic threshold (basic reproduction number $R_0 = 1$) only if the transmission is sufficiently homogeneous (dispersion parameter $k > 0.3$). Surprisingly, in heterogeneous systems ($k \leq 0.3$), the sensitivity is highest for values of $R_{0} > 1$. We expect our methods will improve the transparency and applicability of the growing utility of probability generating functions as epidemic forecasting tools.

q-bio.PE↗

arXiv2018

Lévy Flights of the Collective Imagination

We present a structured random-walk model that captures key aspects of how people communicate in groups. Our model takes the form of a correlated Lévy flight that quantifies the balance between focused discussion of an idea and long-distance leaps in semantic space. We apply our model to three cases of increasing structural complexity: philosophical texts by Aristotle, Hume, and Kant; four days of parliamentary debate during the French Revolution; and branching comment trees on the discussion website Reddit. In the philosophical and parliamentary cases, the model parameters that describe this balance converge under coarse-graining to limit regions that demonstrate the emergence of large-scale structure, a result which is robust to translation between languages. Meanwhile, we find that the political forum we consider on Reddit exhibits a debate-like pattern, while communities dedicated to the discussion of science and news show much less temporal order, and may make use of the emergent, tree-like topology of comment replies to structure their epistemic explorations. Our model allows us to quantify the ways in which social technologies such as parliamentary procedures and online commenting systems shape the joint exploration of ideas.

cs.SI↗