Hallucinations and artificial text in LLM-generated outputs often appear as distributional deviations between prompt and response hidden-state distributions. Since prompts or retrieved contexts typically serve as reference samples and responses as query samples, with major differences in length, these asymmetries motivate the use of change test statistics that treat the two samples differently. We consider an asymmetric two-sample test ASK-NN based on the directed k-nearest-neighbor graph. Our statistic counts reference points whose nearest neighbor in the pooled sample is also a reference point. Under the permutation null, it admits an exact finite-sample conditional mean and variance; we further establish asymptotic normality and consistency under fixed alternatives. ASK-NN is computationally effective and easy to implement. Empirically, it is competitive with kernel and graph-based baselines on synthetic benchmarks, artificial-text detection, and LLM hallucination detection from token-level hidden states.
Test-time adaptive out-of-distribution (OOD) detectors update a memory bank from the unlabelled stream. We show this adaptation obeys a provable dynamical law. Modelling bank impurity as a generalized Pólya urn, we prove almost-sure convergence to a mean-field equilibrium whose s…
We propose a new approach to two-sample testing for deciding whether two sets of samples are drawn from the same distribution. The test is built on a statistical discrepancy based on the zero-flow criterion, termed zero-flow discrepancy (ZFD). We prove the validity of ZFD and pro…
As large language models (LLMs) are increasingly deployed, reliable and efficient mechanisms for distinguishing AI-generated text from human-written content have become essential. Statistical watermarking has emerged as a promising solution, yet most existing methods are typicall…
We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system. More precisely, we study discrete-time autonomous stochastic systems defining time-homogeneous Markov processes. We first focus on estimating the optimal one-step predic…
Imitation learning (IL)---training an agent to replicate expert behavior from demonstrations---underpins applications from robotics to language model training. Standard approaches such as Behavior Cloning (BC) are known to suffer from compounding errors and performance plateaus,…
We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distribution…