HawkesLLM: Semantic Uncertainty Propagation in Agentic Text Simulation

A significant challenge in agentic AI is prospective memory: the ability to execute an intention at a specific future cue or state while other activities are ongoing. We introduce PM-Bench, a text-based benchmark for measuring prospective memory capabilities in modern LLM agents. Inspired by the Virtual Week paradigm from cognitive science, PM-Bench evaluates how well LLM agents maintain user intentions, execute delayed intentions, and monitor latent environment changes. Over the course of a simulated seven-day week, agents must continue an ongoing activity while deciding whether any deferred task is due. We compare eight state-of-the-art LLMs on PM-Bench under eight different agent configurations. PM-Bench proves challenging across all settings: the best method, a GPT-5.4 agent, reaches only 65.1% F1 score under our evaluation. Furthermore, no single strategy for improving prospective memory dominates across models. We release PM-Bench as a controlled testbed for diagnosing these failures and developing training or inference-time interventions that support reliable prospective behavior.

LLM agents often degrade over long episodes: as trajectories grow, they revisit explored states, repeat failed actions, and lose strategies that previously worked. Test-time training (TTT) offers a way to adapt model weights to the evolving task state, but existing LLM TTT methods largely adapt once to a fixed input. We study continuous TTT in multi-turn agent episodes, where each update changes the policy that generates later training text. This creates a self-training loop that helps when new trajectory information appears, but can amplify drift when the agent gets stuck and repeatedly trains on similar text. We find that update-text repetition distinguishes these regimes and introduce Agentic Test-Time Training (aTTT), a token-level reweighting method that downweights the loss on tokens appearing in repeated $n$-grams from prior updates while leaving novel tokens fully weighted. To run such updates inside live episodes, we build a concurrent serving system using vLLM's runtime LoRA API, limiting overhead to 1.9$\times$ the no-TTT cost. aTTT improves success by up to 5.0 points on ALFWorld and 4.9 points on SWE-bench Lite. The gains concentrate where models already have task competence but drift over long trajectories, suggesting that aTTT mainly preserves existing competence rather than teaching new abilities.

Uncertainty quantification (UQ) methods for language models are typically evaluated on single-turn outputs, where uncertainty is attached to one generated answer. For LLM agents, however, the unit of observation is an interactive trajectory, where the model can ask clarifying questions, call tools, update state, and make intermediate decisions whose errors propagate to the final outcome. We study whether three common families of single-turn UQ methods transfer to this setting. Across five LLMs and four multi-turn tool-use datasets from BFCL-v4 and $τ^2$-bench, we evaluate white-box scorers based on action-token probabilities, black-box consistency scorers based on resampled trajectories, and reflexive scorers based on model self-assessment of the trajectory. We find that transfer is often useful but uneven. Token-probability scores are highly sensitive to the choice of aggregator used across turns, reflexive scores provide the strongest low-cost baseline in most evaluated settings, and black-box self-consistency is often the strongest UQ family, with trajectory-equivalence and action-set consistency typically ranking highest among its variants. These results suggest that UQ methods developed for single generations should be revalidated at the trajectory level, with careful attention to the consistency measurement, aggregator choice, and computational budget.