Modeling the Arrival Time of Information-Bearing Events in Natural Language

Large language models (LLMs) are increasingly used in daily applications, from content generation to code writing, where each interaction treats the model as stateless, generating responses independently without memory. Yet human writing is inherently longitudinal: authors' styles and cognitive states evolve across months and years. This raises a central question: can LLMs reproduce such temporal structure across extended time periods? We construct and publicly release a longitudinal dataset of 412 human authors and 6,086 documents spanning 2012--2024 across three domains (academic abstracts, blogs, news) and compare them to trajectories generated by three representative LLMs under standard and history-conditioned generation settings. Using drift and variance-based metrics over semantic, lexical, and cognitive-emotional representations, we find temporal flattening in LLM-generated text. LLMs produce greater lexical diversity but exhibit substantially reduced semantic and cognitive-emotional drift relative to humans. These differences are highly predictive: temporal variability patterns alone achieve 94% accuracy and 98% ROC-AUC in distinguishing human from LLM trajectories. Our results demonstrate that temporal flattening persists regardless of whether LLMs generate independently or with access to incremental history, revealing a fundamental property of current deployment paradigms. This gap has direct implications for applications requiring authentic temporal structure, such as synthetic training data and longitudinal text modeling.

The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model learns in training and exploits in inference. In this work, we use these probabilities to situate LLMs within the mathematical theory of stochastic processes. We use this framework to design a model-agnostic probabilistic token attribution measure, using Bayes rule to invert the next-token log-probabilities so as to capture the models internal representation of the distribution over token sequences. The representation is independent of the models computational structure. This representation yields the conditional probability of the response given the prompt, and of the response given the prompt with a token marginalized away. Our attribution score is the log of the ratio of these probabilities. We further compute the entropies of a single prompts token distributions, conditioned on the remaining context. The interplay between entropy and attribution score sheds light on LLM behavior. We evaluate 8 models across 7 prompts and investigate anomalies, token sensitivity, response stability, model stability, and training convergence, thereby improving interpretability and guiding users to focus on uncertain or unstable parts of the generation.

Diffusion language models expose an explicit denoising trajectory, making it possible to ask when different kinds of information become measurable during generation. We study three independent 32-step runs of LLaDA-8B-Base on masked WikiText-103 text, each with 1{,}000 probe-training sequences and 200 held-out evaluation sequences. From saved trajectories, we derive four temporal measurements: token commitment; linear recoverability of part-of-speech (POS), coarse semantic category, and token identity; confidence and entropy dynamics; and sensitivity under mid-trajectory re-masking. Across seeds, the same ordering recurs: content categories stabilize earlier than function-heavy categories, POS and coarse semantic labels remain substantially more linearly recoverable than exact lexical identity under our probe setup, uncertainty remains higher for tokens that ultimately resolve incorrectly even though late confidence becomes less calibrated, and perturbation sensitivity peaks in the middle of the trajectory. A direct/collateral decomposition shows that this peak is overwhelmingly local to the perturbed positions themselves. In this LLaDA+WikiText setting, denoising time is therefore a useful analysis axis: under our measurements, coarse labels are recovered earlier and more robustly than lexical identity, trajectory-level uncertainty tracks eventual correctness, and mid-trajectory states are the most intervention-sensitive.