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

Conference: ICLR 2026
OpenReview: https://openreview.net/forum?id=HvOKarTubb
Code: To be confirmed
Area: Personalized Recommendation / Personalized Summarization
Keywords: Personalized Summarization, User Preference Modeling, Geometric Random Walk, Dual Memory Channels, Action Conditioning

TL;DR

This paper proposes the "Structured Walk Hypothesis" (SWH) to challenge the prevailing "Markovian Drift Hypothesis" (MDH) in personalized summarization. It introduces Walk2Pers, a lightweight encoder-decoder model that characterizes user preference evolution as an action-biased geometric walk with dual memory channels, decomposable into magnitude and orientation (continuity vs. novelty). It significantly outperforms specialized summarizers and Large Language Models (LLMs) across three benchmarks.

Background & Motivation

• Background: Personalized document summarization assists readers by focusing on "content of interest," which is subjective and time-varying. Leading approaches in news recommendation and summarization (e.g., graph diffusion RWR/Personalized PageRank, short-memory neural encoders like NAML/NRMS/EBNR, and prompted mid-sized LLMs) almost universally assume that user preferences follow a memoryless or short-memory random walk along the interaction graph—where each new state depends primarily on the most recent interaction.
• Limitations of Prior Work: The authors categorize these practices under the Markovian Drift Hypothesis (MDH): history is compressed into a final state/seed vector/hidden state/prompt window, causing long-range action dynamics to be overwritten. Graph diffusion lacks action semantics; neural encoders compress long histories into shallow memories; LLMs are constrained by prompt length and lack persistent reinforcement or inhibition. In datasets like PENS containing click/skip logs, user interests drift across fine-grained subtopics; including long histories in prompts degrades the performance of SOTA LLMs.
• Key Challenge: Preference evolution requires persistent, asymmetric memory of "likes" (click reinforcement) vs. "dislikes" (skip inhibition) and must distinguish whether evolution continues along the existing trajectory (continuity) or pivots (novelty). MDH fails both requirements by converging everything into a single-step drift.
• Goal: To test whether MDH holds for personalized summarization and to provide a more faithful, interpretable, and lightweight modeling alternative.
• Core Idea: Structured Walk Hypothesis (SWH)—updates to preference states caused by interactions (click/skip/summarize) are decomposed into (i) Magnitude (push intensity) + (ii) Orientation (continuity vs. novelty), supplemented by dual memory channels (reinforcement/inhibition) and a summary-request-specific drift term. This theoretically approximates a first-order action-conditioned kernel and is instantiated as Walk2Pers.

Method

Overall Architecture

The method abstracts user history into a two-layer structure: the lower User Interaction Graph (UIG) records nodes (user/document/summary) and action edges (click/skip/summarize/summGen); the upper layer compresses each interaction into a "behavior dual" b-cell b=⟨action, tail node⟩, forming a trajectory via nextBehavior edges. Walk2Pers utilizes a T5-base encoder-decoder framework: the SWH-Encoder performs memory-augmented geometric walks along the b-layer to obtain contextualized embeddings; the Predictor forecasts the next b-node; the Inverse Approximator extracts latent summary intents (s-nodes); the Contextualizer uses cross-attention to fuse summary intent, user history, and query documents; finally, a fine-tuned T5 decoder (top layers only) generates the personalized summary.

flowchart LR
  A[User Interaction Logs<br/>click/skip/summarize] --> B[UIG → b-cell Trajectory]
  B --> C[SWH-Encoder<br/>Dual Memory + Geometric Step]
  C --> D[Predictor<br/>Predict next b-node]
  D --> E[Inverse Approximator<br/>Extract latent s-node]
  E --> F[Contextualizer<br/>Cross-attention fusion]
  F --> G[T5 Decoder<br/>Top-layer fine-tuning]
  G --> H[Personalized Summary]

Key Designs

1. Unified Update for Structured Walk: Decomposing "One-step Drift" into a Triad of Geometric Step, Memory, and Drift. MDH assumes the next state depends only on the previous state: \(e^{(t+1)}_{b,u}=f(e^{(t)}_{b,u}, a^{(t)}, q)+\epsilon^{(t)}\), where history is folded into a recency prior \(q\). SWH rewrites this into an additive family:

\[e^{(t+1)}_{b,u}=e^{(t)}_{b,u}+\underbrace{\mathrm{mag}(a^{(t)})\big(\cos\theta(a^{(t)})\,u^{(t)}+\sin\theta(a^{(t)})\,o^{(t)}\big)}_{\Phi:\ \text{Geometric step, Continuity vs. Novelty}}+\underbrace{\Psi(h^+_t,h^-_t)}_{\Psi:\ \text{Dual Memory}}+\underbrace{\delta\cdot\mathbb{I}[a^{(t)}=\text{summGen}]}_{\Delta:\ \text{Summary Drift}}\]

Where \(\mathrm{mag}(\cdot)\) controls step size (single click = small step, repeated = large), and the rotation angle \(\theta\) interpolates between the momentum axis \(u^{(t)}\) (continuation of interest) and the orthogonal novelty axis \(o^{(t)}\) (pivot). This decomposition draws from JODIE's trajectory dynamics and RotatE/ChronoR's angular relations but adds explicit action bias and memory.

2. Dual Memory Channels Ψ and Summary Drift Δ: Asymmetric Reinforcement and Inhibition. Walk2Pers uses two channels to represent history \(h^{(t)}=\omega^{(t)}h^{(+,t)}+(1-\omega^{(t)})h^{(-,t)}\) (\(\omega\) is learnable). The positive channel accumulates reinforcement signals from clicks, while the negative channel accumulates inhibition from skips, using asymmetric update rules:

\[h^{(+,t_i)}=h^{(+,t_{i-1})}+m^{(t_i)}\odot c^{(t_i)}_{tl};\qquad h^{(-,t_i)}=h^{(-,t_{i-1})}\odot(1-m^{(t_i)})+c^{(t_i)}_{tl}\]

Gate \(m^{(t_i)}=\mathrm{SoftMax}(W_h h^{(t_{i-1})}+W_c c^{(t_i)}_{tl})\). Summary requests (summGen) trigger a drift vector \(\Delta^{(t)}=(I-e^{(t-1)}_{tl})\cdot e^{(t)}_{tl}\), pushing the preference state toward a more concise representation.

3. Action-Biased b-cell and Geometric Step Implementation. Nodes are initialized with T5-base; actions are encoded as 4D one-hot vectors. The b-cell fuses action gating and tail-node content \(c^{(t_i)}_{tl}=\tanh(f^{(a,t_i)}\odot e^{(t_i)}_{tl})\), where \(f^{(a,t_i)}=\mathrm{AGD}(e_a,t_i)\odot h^{(t)}\) leverages the action gates of the AGD baseline. The encoder is supervised by two objectives: a next-node prediction head \(\mathcal{L}_{next}\) and a position classification alignment term \(\mathcal{L}_{align}\) to ensure intermediate b-nodes can be recovered from contextualized embeddings: \(\mathcal{L}_{enc}=\alpha\mathcal{L}_{align}+(1-\alpha)\mathcal{L}_{next}\).

4. User-Contextualized Attention (T5-UCA): Rewriting Documents via Preference Prisms. The decoder leverages T5-base with two variants: T5-CA uses cross-attention to contextualize documents with latent summary intents; T5-UCA further uses the user trajectory state to gate document embeddings—suppressing aspects aligned with negative memory \(h^-\) and amplifying those aligned with \(h^+\). This ensures Alice and Bob receive different summaries for the same document.

Key Experimental Results

Main Results

Next b-node prediction task (PENS, 151 candidates):

Category	Model	AUC	MRR	nDCG@5	nDCG@10
MDH	NAML	0.498	0.001	0.0004	0.0007
MDH	NRMS	0.499	0.0009	0.0002	0.0004
MDH	EBNR	0.499	0.0009	0.0003	0.0005
MDH	SMD (Ours)	0.415	0.094	0.052	0.065
MDH	AGD (Ours)	0.446	0.113	0.069	0.073
SWH	Walk2Pers-Enc. w/o Geo	0.474	0.121	0.082	0.132
SWH	Walk2Pers-Enc. Full	0.532	0.23	0.198	0.249

PENS Personalized Summarization (PerSEval metrics):

Category	Model	PSE-JSD	PSE-SU4	PSE-METEOR
Oracle (Clues)	BigBird-Pegasus	0.253	0.143	0.168
LLM (2-shot)	DeepSeek-14B	0.248	0.094	0.097
LLM (2-shot)	Gemini-2.5-Flash	0.222	0.104	0.124
MDH Encoders	AGD + T5-UCA	0.286	0.214	0.248
SWH (Ours)	Walk2Pers Full + T5-UCA	0.452	0.383	0.449

Ablation Study

Variant	PSE-JSD	PSE-SU4	PSE-METEOR
AGD + T5-UCA (Pure MDH)	0.286	0.214	0.248
Walk2Pers w/o Geometric + T5-UCA	0.306	0.334	0.321
Walk2Pers Full + T5-CA	0.418	0.341	0.422
Walk2Pers Full + T5-UCA	0.452	0.383	0.449

Key Findings

• RQ1: MDH is insufficient. Short-memory neural encoders (NAML/NRMS/EBNR) show AUC near random (≈0.5) and ranking metrics near zero (MRR≤0.001), indicating compressed hidden states carry almost no predictive signal.
• RQ2: SWH components provide systematic Gain. Adding dual memory and drift (w/o geometric) surpasses AGD; adding geometric magnitude-orientation steps yields a significant jump in performance.
• RQ3: Superiority over LLMs. Ours significantly outperforms all LLMs (e.g., +0.20/0.29/0.35 over DeepSeek-14B), while chain-of-thought prompting often lags behind MDH baselines.
• Cross-task Transferability: Walk2Pers trained for summarization outperforms dedicated baselines on the MIND news recommendation leaderboard (MRR +1.2, nDCG@10 +3.5).

Highlights & Insights

• Hypothesis-Driven Research: Instead of simply stacking models, the paper explicitly names and tests the prevalent MDH before proposing the falsifiable SWH.
• Geometric Interpretability: Decomposing updates into magnitude and orientation makes preference shifts readable, unlike opaque hidden states.
• Asymmetric Dual Memory: Splitting "likes" and "dislikes" into channels with different update rules aligns with psychological reinforcement/inhibition and persists across long histories.
• Lightweight Strength: A T5-base-scale framework outperforms 13B-235B LLMs, suggesting structural priors are more critical than scale for this task.

Limitations & Future Work

• Evaluation relies heavily on PerSEval; the trade-off between personalization and absolute summary quality (e.g., ROUGE) or fluency is not fully detailed.
• Action sets are restricted to four one-hot types; fine-grained or implicit feedback (e.g., dwell time) is not explored.
• Geometric steps introduce hyperparameters (\(\alpha, \omega, \theta\)), whose sensitivity across datasets is primarily discussed in the appendix.

Related Work & Insights

• Personalized Summarization Metrics: PerSEval is adopted for its high correlation with human judgment.
• Dynamic Embedding and Angular Modeling: Inspired by JODIE’s trajectory dynamics and RotatE’s angular relations.
• Insight: Explicit memory channels combined with geometric decomposition may replace implicit attention/GRU aggregation in sequential/session recommendations, particularly for long-range asymmetric feedback.

Rating

• Novelty: ⭐⭐⭐⭐ Explicitly challenges MDH and proposes a geometric-memory alternative.
• Experimental Thoroughness: ⭐⭐⭐⭐ Multi-dataset, multi-task validation against MDH, specialized models, and LLMs.
• Writing Quality: ⭐⭐⭐⭐ Clear progression from hypothesis to formula to instantiation.
• Value: ⭐⭐⭐⭐ Demonstrates that lightweight models with proper priors can beat LLMs; transferable to recommendation tasks.

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