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Time is Not a Label: Continuous Phase Rotation for Temporal Knowledge Graphs and Agentic Memory

Weixian Waylon Li, Jiaxin Zhang, Xianan Jim Yang, Tiejun Ma, Yiwen Guo

arXiv:2604.11544v1cs.CLcs.AI

TL;DR

Existing memory systems struggle to resolve changing facts without burying permanent knowledge, deleting history, or invoking an LLM at every ingestion step. RoMem addresses this with continuous phase rotation and a learned relation-volatility gate, achieving strong temporal knowledge-graph and agentic-memory results while preserving static knowledge and supporting zero-shot transfer.

  • Problem

    Existing systems model time as discrete metadata and cannot distinguish persistent relations from evolving ones while resolving temporal conflicts.

  • Method

    RoMem combines continuous geometric phase rotation with a Semantic Speed Gate that learns relation volatility from text embeddings in an append-only memory module.

  • Results

    RoMem achieves state-of-the-art ICEWS05-15 temporal knowledge graph completion at 72.6 MRR and improves agentic-memory performance across temporal, hybrid, static, and unseen-domain evaluations.

  • Takeaways & Limitations

    Geometric shadowing lets temporally aligned facts outrank obsolete contradictions without deletion, while static knowledge remains preserved and the module generalises zero-shot to unseen domains.

  • Takeaways & Limitations

    MultiTQ excludes 1A-Mem because it lacks native support for massive structured triple ingestion of approximately 11K triples.

Abstract

from arXiv · show

Structured memory representations such as knowledge graphs are central to autonomous agents and other long-lived systems. However, most existing approaches model time as discrete metadata, either sorting by recency (burying old-yet-permanent knowledge), simply overwriting outdated facts, or requiring an expensive LLM call at every ingestion step, leaving them unable to distinguish persistent facts from evolving ones. To address this, we introduce RoMem, a drop-in temporal knowledge graph module for structured memory systems, applicable to agentic memory and beyond. A pretrained Semantic Speed Gate maps each relation's text embedding to a volatility score, learning from data that evolving relations (e.g., "president of") should rotate fast while persistent ones (e.g., "born in") should remain stable. Combined with continuous phase rotation, this enables geometric shadowing: obsolete facts are rotated out of phase in complex vector space, so temporally correct facts naturally outrank contradictions without deletion. On temporal knowledge graph completion, RoMem achieves state-of-the-art results on ICEWS05-15 (72.6 MRR). Applied to agentic memory, it delivers 2-3x MRR and answer accuracy on temporal reasoning (MultiTQ), dominates hybrid benchmark (LoCoMo), preserves static memory with zero degradation (DMR-MSC), and generalises zero-shot to unseen financial domains (FinTMMBench).

1 Introduction

RoMem addresses the static-dynamic dilemma in graph-based memory by replacing discrete temporal metadata and destructive or LLM-mediated conflict handling with continuous geometric phase rotation. A Semantic Speed Gate learns relation volatility, enabling static facts to remain stable while obsolete dynamic facts are shadowed, with strong results across temporal knowledge graph and agentic-memory benchmarks.

  • 1 Introduction: Discrete timestamps treat all relations identically, forcing systems to choose among overwriting history, per-ingestion LLM arbitration, or recency sorting that can bury permanent facts.The paper frames this conflict between preserving historical context, avoiding repeated LLM calls, and retaining old-yet-permanent knowledge as the static-dynamic dilemma.
  • 1 Introduction: RoMem is a drop-in temporal reasoning module that internalises time as a continuous geometric operator in the knowledge-graph component.It resolves conflicts through geometry rather than database updates, while retaining an append-only memory architecture.
  • 1 Introduction: Continuous Geometric Shadowing rotates obsolete dynamic facts out of alignment while keeping static facts locked in phase.This lets temporally aligned facts outrank contradictions without deleting stored records.
  • 1 Introduction: The Semantic Speed Gate maps relation text embeddings to volatility scores, so static relations rotate slowly and dynamic relations rotate quickly.The learned per-relation scalar αr controls rotation speed and supports zero-shot generalisation to unseen relations and domains.
  • 1 Introduction: 72.6 MRR establishes state-of-the-art temporal knowledge graph completion on ICEWS05-15.In agentic memory, RoMem also delivers 2∼3× MRR and answer accuracy on MultiTQ, dominates LoCoMo, preserves DMR-MSC static memory, and generalises zero-shot on FinTMMBench.

2 Related Work

Prior memory systems generally lack native handling for changing facts, while temporal knowledge-graph methods use discrete time operators that limit temporal flexibility and interpolation. RoMem is positioned against these approaches through continuous, relation-sensitive temporal modelling.

  • 2 Related Work: Graph-based memory systems provide scalable, controllable retrieval, whereas parametric approaches require costly retraining and offer less transparent retrieval.The related-work discussion situates RoMem among graph-based and parametric agentic-memory paradigms.
  • 2 Related Work: Existing memory systems handle changing facts through destructive overwriting, LLM arbitration, or recency sorting, without distinguishing permanent from evolving relations.These workarounds respectively erase history, add ingestion-time latency, or bury old-yet-permanent facts.
  • 2 Related Work: Discrete temporal operators such as RotatE, TeRo, and ChronoR require fixed temporal resolutions and cannot dynamically adjust their temporal representation during training.The paper identifies this as granularity rigidity caused by discrete lookup tables.
  • 2 Related Work: Discrete timestamp embeddings cannot interpolate between observed timestamps because they lack a continuous function connecting them.The paper illustrates the limitation with inferring September 22 from September 21 and 23.

3 Methodology: ROMEM

ROMEM replaces discrete temporal metadata with continuous phase rotation in an append-only knowledge graph, using relation-specific volatility to distinguish static from dynamic facts. Its two-phase training and geometric shadowing support temporal retrieval, contradiction resolution, and zero-shot transfer across relation forms.

  • Continuous Temporal Representation: ROMEM internalises temporal conflict resolution as continuous phase rotation, allowing contradictory facts to coexist and obsolete facts to be shadowed at query time.The architecture is append-only and supports historical retrieval through continuous timestamps.
  • Relation-Specific Dynamics: Static relations remain phase-stable while dynamic relations rotate rapidly, preventing permanent facts from being buried by recency and separating obsolete contradictions geometrically.The gate functions as a temporal clutch: αr approaches 0 for static relations and 1 for dynamic relations.
  • Functional Rotation: The rotation angle combines a learnable global time scale, relation volatility, continuous time, and a learnable inverse-frequency spectrum.The model embeds entities in R2d while interpreting them as complex vectors in Cd and applies element-wise phase shifts.
  • Semantic Speed Gate: A Semantic Speed Gate derives relation volatility from text embeddings, enabling zero-shot generalisation across linguistic variants such as “married” and “wedded”.Stable relations receive low rotation speeds, while changing relations receive high speeds.
  • Two-Phase Training: Two-phase training pretrains the gate on observed entity changes, then freezes it while learning the temporal spectrum and embeddings on the target dataset.The online objective combines triple scoring, temporal contrastive learning, and regularisation.
  • Inference-Time Retrieval: At retrieval, query-time phase alignment makes temporally relevant facts score highest while rotating obsolete facts out of focus, including when querying historical dates.This geometric shadowing avoids explicit deletion and restores past facts when the query timestamp is set accordingly.

4 Experiments

ROMEM is evaluated across temporal knowledge graph completion, temporal and hybrid agentic-memory tasks, static retrieval, and zero-shot financial-domain generalisation. Across these settings, it improves temporal performance while preserving non-temporal memory capabilities.

  • RQ1: TKGE Completion: ROMEM-ChronoR achieves 72.6 MRR on ICEWS05-15, exceeding vanilla ChronoR’s 68.4 MRR.
  • RQ1: TKGE Completion: ROMEM-DistMult reaches 62.1 MRR versus 45.6 MRR for static DistMult on ICEWS05-15.
  • RQ2: Temporal and Agentic Memory: On MultiTQ, ROMEM raises HippoRAG’s MRR from 0.203 to 0.337 and LLM@5 Accuracy from 0.112 to 0.366 under GPT-5-mini.
  • RQ2: Temporal and Agentic Memory: On LoCoMo, ROMEM improves Temporal Reasoning Recall@10 from 0.645 to 0.726 while achieving 0.768 Single Hop and 0.904 Open Domain performance.
  • RQ2: Temporal and Agentic Memory: On DMR-MSC, ROMEM slightly improves HippoRAG from 0.848 to 0.856 MRR and from 0.852 to 0.862 LLM@5 Accuracy.
  • RQ3: Domain Generalisation: On FinTMMBench, ROMEM achieves 0.728 MRR and 0.580 LLM@5 Accuracy, outperforming A-Mem’s 0.716 MRR and HippoRAG’s 0.690 MRR.

5 Conclusion

The paper identifies discrete temporal metadata and costly workarounds as limitations of graph-based memory, then presents ROMEM as a continuous geometric alternative. ROMEM preserves static facts, rotates obsolete facts out of phase, and operates as a drop-in KG module.

  • Discrete metadata applies the same temporal policy to all relations, while overwriting and per-ingestion LLM calls do not scale.
  • ROMEM learns relational volatility from text embeddings and uses continuous phase rotation to preserve static facts while shadowing obsolete ones.
  • ROMEM achieves state-of-the-art TKGE results, improves temporal reasoning, preserves static knowledge, and generalises zero-shot to unseen domains.
  • ROMEM provides a standard scoring interface and can replace the KG component in graph-based or hierarchical memory systems.

A Scoring, Training, and Gate Formulations

This appendix describes ROMEM’s efficient scoring variants, training objectives, semantic-gate pretraining, and LLM-based extraction and answer-generation procedures.

  • A.1 Scoring Variants: The unrotation trick converts a temporally rotated query into one vector, enabling a single matrix multiplication for efficient 1-vs-N retrieval.
  • A.1 Scoring Variants: The DistMult variant sets k=1 and removes the inverse relation table, using self-adversarial negative sampling and global L3 regularisation.
  • A.2 Training Objectives: ChronoR training uses 1-vs-all cross-entropy with a timestamp-dependent query, while the structural loss detaches the gate αr.
  • A.2 Training Objectives: Conflict-aware negative sampling prioritises competing tails from the same (h, r) group to discriminate mutually exclusive facts.
  • A.2 Training Objectives: Regularisation combines backbone-specific penalties with a gate term that encourages αr toward zero for non-competing relation slots.
  • A.2 Training Objectives: The time-contrastive loss sharpens temporal discrimination through a Gaussian target kernel whose width decays from 0.5 yr to 0.02 yr.
  • A.3 Semantic Speed Gate Pretraining: The semantic speed gate is pretrained from changed-tail observations grouped by (h, r), then frozen during online TKGE training.
  • B. Information Extraction and Answer Generation: ROMEM uses LLM stages for entity, temporal-triple, and query-time extraction, while benchmark answer generation uses task-specific prompts and JSON outputs.

C Benchmark Datasets

The evaluation spans temporal graph completion, heavy temporal reasoning, conversational memory, hybrid reasoning, static retrieval, and financial temporal QA. The datasets differ in scale, modality, and temporal complexity.

  • ICEWS05-15 contains geopolitical event triples from 2005–2015 with 368,962 training, 46,275 validation, and 46,092 test triples.
  • MultiTQ builds on 461,329 temporal quads and 4,017 timestamps, with 54,584 temporal questions across multiple temporal relations and granularities.
  • The agentic-memory MultiTQ evaluation samples 500 questions and ingests 11,074 facts incrementally per time snapshot.
  • LoCoMo contains 10 synthetic multi-session conversations and 1,986 questions spanning single-hop, multi-hop, temporal, open-domain, and adversarial categories.
  • DMR-MSC contains 500 multi-session dialogues and serves as a static-memory test of conversational retrieval.
  • FinTMMBench contains 5,676 questions over NASDAQ-100 companies and 162,311 documents across news, financial tables, stock prices, and charts.

D Evaluation Metrics and Answer Verification

The evaluation reports retrieval metrics across temporal KG completion and agentic-memory benchmarks, then verifies answer quality using benchmark-specific matching or judge procedures.

  • Temporal KG completion reports MRR and Hits@k for k ∈ {1, 3, 10} under the standard filtered setting.
  • Agentic-memory retrieval reports MRR and Hits@k over retrieved facts for MultiTQ and DMR-MSC, with one gold answer per query.
  • LoCoMo uses Recall@10, measuring the fraction of gold evidence passages found among the top-10 retrieved documents per question category.
  • FinTMMBench reports Recall@k for k ∈ {1, 3, 5, 10} and MRR against gold source-document UUIDs.
  • Answer quality is measured with LLM@k Accuracy at k ∈ {5, 10}, using a two-stage LLM judge for DMR-MSC and FinTMMBench and a rule-based verifier for MultiTQ.
  • D.1 LLM Judge: The LLM-judge fast path labels an answer correct when the normalized gold answer is a substring of the generated answer, otherwise invoking GPT-5.2.

E Implementation Configurations and Hyperparameters

The implementation evaluates agentic-memory systems under API-based and open-source configurations while reformulating temporal retrieval so static inner-product indices remain usable.

  • Implementation configurations: The OpenAI configuration uses GPT-5-mini and text-embedding-3-small for graph construction and embedding, while the Server configuration uses LLaMA-3.1-70B-Instruct and BAAI/BGE-M3.
  • Implementation configurations: GPT-5.2 supplies the answer LLM and LLM judge in both configurations to ensure fair comparison across baselines.
  • Baselines: The baselines are Mem0, Zep, and HippoRAG, with RoMem building on HippoRAG’s graph-construction pipeline.
  • Retrieval reformulation: Temporal retrieval transfers the rotation entirely to a candidate-independent query vector, preserving compatibility with optimized MIPS architectures and static candidate indices.
  • Retrieval reformulation: O(d) query preprocessing followed by O(N · d) static inner-product search avoids candidate-side temporal transformation.
  • Retrieval reformulation: The resulting formulation works with exact or approximate inner-product search libraries such as FAISS without rebuilding indices across queries.

F.4 A Stylised Analysis of Pairwise Temporal Interpolation

The stylised analysis models temporal competition between two historical facts as continuous multi-frequency rotations and derives conditions for a unique, monotonic interpolation crossover.

  • Continuous rotations can interpolate knowledge between historical observations by producing a smooth decision boundary for unobserved intermediate timestamps.
  • The scoring function is algebraically equivalent to a multi-frequency synchronized cosine expansion across independent rotational subspaces.
  • The effective angular velocity combines the global time scale, inverse frequency, and relation-specific semantic speed gate.
  • Under correct historical anchors and a strict half-period frequency bound, the pairwise confidence gap decreases monotonically between consecutive timestamps.
  • A unique crossover timestamp exists, with the model preferring the first fact before it and the second fact after it.
  • The theoretical crossover need not occur at the midpoint because its location depends on learned embedding parameters and phase structure.

G.1 Dynamic Relation: Score Crossover

The dynamic relation example shows continuous geometric shadowing: an older fact’s score declines while a newer fact’s score rises, producing a crossover without deleting either fact.

  • αr(Consult) = 0.87 identifies “Consult” as a highly dynamic relation.
  • The crossover occurs around 2009, after which Xi geometrically shadows Blair; its location is not necessarily the midpoint of the observation windows.
  • Both contradictory facts remain in append-only memory while rotation continuously modulates their alignment with query time.
  • Raw versus smoothed traces: Raw quarterly scores can cross multiple times because high-frequency components violate the half-period bound and shared entity embeddings introduce phase interference.
  • Raw versus smoothed traces: A 5-quarter rolling average suppresses high-frequency residuals and reveals a single clean crossover consistent with the theoretical prediction.

G.2 Gate Inspection: Learned Relational Volatility

The Semantic Speed Gate assigns relation-specific volatility scores, including to unseen relations, and preserves static memory despite an event-heavy pretraining corpus. Its learned gradient distinguishes episodic interactions from more sustained conditions without manual annotation.

  • The gate assigns high volatility to frequently changing relations and low volatility to inherently stable relations without manual annotation.
  • Higher αr denotes faster rotation, with Table 5 separating relations seen during ICEWS05-15 pretraining from unseen relations evaluated zero-shot.The table caption defines the score direction and the seen/unseen split.
  • Within ICEWS05-15’s event-driven relations, “Consult” (0.87) and “Host a visit” (0.86) receive higher αr than “Cooperate militarily” (0.09) and “Cooperate economically” (0.16).The corpus contains few semantically static relations, so this gradient appears within an event-heavy spectrum.
  • For unseen relations, the gate assigns high αr to “met with” (0.71) and “visited” (0.64), but low αr to “citizen of” (0.17) and “species” (0.22).The reported zero-shot transfer uses text embeddings rather than relation IDs.
  • DMR-MSC shows zero degradation on purely static conversational memory, validating that low αr suppresses rotation and preserves static fact retrieval.
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