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.