Related papers: The Certainty Bound: Structural Limits on Scientif…
The reproducibility of scientific findings are an important hallmark of quality and integrity in research. The scientific method requires hypotheses to be subjected to the most crucial tests, and for the results to be consistent across…
For decades, forensic statisticians have debated whether searching large DNA databases undermines the evidential value of a match. Modern surveillance faces an exponentially harder problem: screening populations across thousands of…
Data are essential for the experiments of relevant scientific publication recommendation methods but it is difficult to build ground truth data. A naturally promising solution is using publications that are referenced by researchers to…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation…
We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…
Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the…
The Open Science Collaboration recently reported that 36% of published findings from psychological studies were reproducible by independent researchers. We can use this information together with Bayes theorem to estimate the statistical…
The prevailing assumption of an exponential decay in large language model (LLM) reliability with sequence length, predicated on independent per-token error probabilities, posits an inherent limitation for long autoregressive outputs. Our…
Structural reliability analysis is concerned with estimation of the probability of a critical event taking place, described by $P(g(\textbf{X}) \leq 0)$ for some $n$-dimensional random variable $\textbf{X}$ and some real-valued function…
We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability $1/2$. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound,…
Classical measures of structural reliability, such as the probability of failure and the related reliability index, are still widely applied in practice. However, these measures are frequency-based only, and they do not give information…
Large language models (LLMs) generate fluent text across a wide range of tasks, but the fabrication of non-existent academic citations remains a critical and well-documented failure mode. Building on prior work that frames hallucination and…
Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their performance often deteriorates sharply in long-horizon tasks, exhibiting systematic breakdown beyond certain scales. Conventional explanations primarily…
We consider a robust analog of the planted clique problem. In this analog, a set $S$ of vertices is chosen and all edges in $S$ are included; then, edges between $S$ and the rest of the graph are included with probability $\frac{1}{2}$,…
This paper investigates the reliability of explanations generated by large language models (LLMs) when prompted to explain their previous output. We evaluate two kinds of such self-explanations - extractive and counterfactual - using three…
Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard…
Modern production systems are increasingly defined by dense networks of multi-tier sourcing dependencies, where localized upstream disruptions can cascade into system-wide collapses. While supply chain resilience has garnered significant…
Analysis pipelines commonly use high-level technologies that are popular when created, but are unlikely to be readable, executable, or sustainable in the long term. A set of criteria is introduced to address this problem: Completeness (no…
Model collapse, the progressive degradation of LLMs trained on their own outputs, has been characterized statistically but lacks a linguistic explanation for which structures degrade, in what order, and why. We show that iterated learning…