Beyond Markovian Drifts: Action-Biased Geometric Walks with Memory for Personalized Summarization

Document summarization helps readers focus on the "content-of-interest", a *subjective* and *time-variant* quantity. Capturing this *dynamic subjectivity* requires modeling how user preferences evolve over time, thereby demanding *personalized summarization*. Recent news recommendation and summarization models often assume that preferences follow a *memoryless or short-memory random walk* on interaction graphs, i.e., a Markovian diffusion seeded at the latest interaction or compressed into a short hidden state or prompt. We ask whether such a hypothesis also holds for personalized summarization. To test this, we propose **Walk2Pers**, a lightweight encoder–decoder framework that extends the walk view with *action-conditioned geometric steps*, decomposed into (i) a *magnitude* controlling shift strength and (ii) an *orientation* capturing continuity vs. novelty. The process is mediated by dual memory lanes that reinforce consistent interests while suppressing disinterest, and is augmented with a drift term for summary requests. We show theoretically that such structured walks approximate first-order action-conditioned kernels, and empirically validate the hypothesis on PENS, OpenAI-Reddit, and PersonalSum. Using PerSEval, a personalization metric with strong human correlation, Walk2Pers outperforms specialized personalized summarizers by an average of $0.41 \uparrow$, and strong LLM baselines (DeepSeek-R1-14B, LLaMA-2-13B, Mistral-7B, Zephyr-7B) by $0.22 \uparrow$. Analyses further confirm cross-domain robustness ($0.19 \uparrow$ over the best LLM) and stability on long histories. Together, these results support viewing personalized summarization as an *action-biased geometric walk with memory*, offering both interpretability and efficiency.