AdaTKG: Adaptive Memory for Temporal Knowledge Graph Reasoning

# Adaptive Memory for Temporal Knowledge Graph Reasoning
Source: [https://arxiv.org/html/2605.07121](https://arxiv.org/html/2605.07121)
Seunghan Lee, Jun Seo, Jaehoon Lee, Sungdong Yoo, Minjae Kim Tae Yoon Lim, Dongwan Kang, Hwanil Choi, SoonYoung Lee, Wonbin Ahn LG AI Research, Seoul, South Korea

###### Abstract

Temporal knowledge graphs \(TKGs\) represent time\-stamped relational facts and support a wide range of reasoning tasks over evolving events\. However, existing methods produce entity representations that arestaticat the entity level, in that each representation is a function of learned parametersonlyand retainsno trace of the interactionsin which the entity has participated\. In this paper, we depart from this static view and propose that each entity be modeled as anadaptive processwhose representation is refined every time the entity participates in a fact\. To this end, we proposeAdaTKG, which maintains a per\-entitymemorythat is updated with every observed interaction, with the memory accumulating online and predictions improving as more interactions arrive\. Specifically, we instantiate the memory update as a learnable exponential moving average governed by a singlesharedscalar instead of using learnable parametersfor each entity, enabling AdaTKG to handle entities unseen during training\. Extensive experiments confirm consistent gains over TKG baselines, demonstrating the effectiveness of adaptive memory\. Code is publicly available at: https://github\.com/seunghan96/AdaTKG\.

## 1Introduction

Temporal knowledge graphs \(TKGs\) organize real\-world facts into time\-stamped relational quadruples and have become a foundation for reasoning about events over timeCaiet al\.\([2023](https://arxiv.org/html/2605.07121#bib.bib1)\)\. They support applications such as event forecasting and risk analysis, each framed as predicting a missing entity or relation at a future timestamp\. A substantial body of work has investigated learning temporal dynamics over such graphsLiet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib6)\); Xuet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib7)\); Liet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib8)\); Chenet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib9)\); Fanget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib10)\); Liaoet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib11)\); Wanget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib12)\), and these models form the backbone of TKG reasoning pipelines\.

Despite this rapid progress, essentially every existing TKG reasoning method shares a common design choice that has been left largely unexamined: the representation of any given entity isstaticat the entity level, in the sense that it is a function of the learned parameters alone andcarries no trace of the interactions in which the entity has participated\. This holds even for the recent line of inductive methodsMeiet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib19)\); Dinget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib20)\); Panet al\.\([2025](https://arxiv.org/html/2605.07121#bib.bib21)\); Anonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), which are designed to handle entities unseen during training\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x1.png)Figure 1:Adaptive TKG reasoning\.Our framework enablesadaptivitythrough amemoryrefined with each interaction\.While recent work has focused on whether a TKG reasoner can handle emerging entities unseen at training time \(transductivevs\.inductive\), we focus on a different aspect, namely whethereach entity’s representation is refined each time the entity participates in a fact, which we formalize as thestaticvs\.adaptivedistinction\. We propose that every entity should be modeled as anadaptive processwhose representation is refined with each interaction, as illustrated in Figure[1](https://arxiv.org/html/2605.07121#S1.F1)\.

To this end, we proposeAdaTKG, anAdaptive InductiveTKG reasoning method that refines each entity’s representation through aper\-entity memoryupdated whenever the entity participates in a fact\. Specifically, we instantiate the memory update as a learnable exponential moving average \(EMA\) that blends the previous memory with each newly observed interaction via a single learnable scalar\. As the parameter issharedacross entities andnot assigned per entity, AdaTKG enablesinductive reasoningon entities unseen during training while remaining efficient\. Our main contributions are:

- •We argue that TKG reasoning should beadaptiveat the entity level, with each entity’s representation refined through its own interactions rather than read from a fixed lookup\. This frames TKG reasoning along a new axis beyond transductive vs\. inductive, namelystaticvs\.adaptive\.
- •We instantiate this principle withAdaTKGin which a learnable EMA blends each entity’s past memory with new interactions via asingle shared scalar parameter\. Since no per\-entity learnable parameter is introduced, the mechanism is directly applicable to entities unseen during training\.
- •We conduct extensive experiments showing that AdaTKG consistently outperforms strong TKG baselines, with the gain growing as more interactions of each entity are observed\. This provides direct evidence thatadaptivityat the entity level is a crucial component of TKG reasoning\.

## 2Related Work

Reasoning on TKGs\.Reasoning on temporal knowledge graphs \(TKGs\) aims to infer missing or future facts by modeling the temporal evolution of entities and relationsCaiet al\.\([2023](https://arxiv.org/html/2605.07121#bib.bib1)\)\. Prior work is typically split intointerpolationGarcia\-Duranet al\.\([2018](https://arxiv.org/html/2605.07121#bib.bib2)\); Lacroixet al\.\([2020](https://arxiv.org/html/2605.07121#bib.bib3)\); Xionget al\.\([2024b](https://arxiv.org/html/2605.07121#bib.bib4)\)andextrapolationZhuet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib5)\); Liet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib6)\); Xuet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib7)\); Liet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib8)\); Chenet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib9)\), with more recent approaches leveraging Transformer architectures and language modelsFanget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib10)\); Liaoet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib11)\); Wanget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib12)\)\. These methods, however, operate under a closed\-world assumption and initialize the embedding of any new entity randomly, leading to representation collapseZbontaret al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib22)\)whenever an entity emerges without historical interactions\.

Inductive reasoning on KGs\.Inductive learning on static KGs seeks to generalize to entities unseen during training, with representative methods exploiting subgraph structureTeruet al\.\([2020](https://arxiv.org/html/2605.07121#bib.bib13)\); Chenet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib14)\); Liuet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib15)\), meta\-learningChenet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib16)\), relation\-aware attentionLeeet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib17)\), or zero\-shot transfer across graphsGalkinet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib18)\)\. Extending inductivity to the temporal setting, ALRE\-IRMeiet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib19)\), zrLLMDinget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib20)\), and POSTRAPanet al\.\([2025](https://arxiv.org/html/2605.07121#bib.bib21)\)target unseen relations or entities under limited supervision, and TransFIRAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)recently establishes the state of the art by transferringtype\-levelbehavioral prototypes from the same cluster to each emerging entity\.

Across the methods above, entity representations arestatic at the entity level, which are a function of the learned parameters alone\. To the best of our knowledge, AdaTKG is the first TKG reasoning method that isadaptive at the entity level, maintaining a memory for each entity that is updated with every interaction\. Further related work is discussed in Appendix[E](https://arxiv.org/html/2605.07121#A5)\.

## 3Problem Definition

Temporal knowledge graph \(TKG\)\.TKG is a sequence of timestamped snapshots

𝒢=\{𝒢t\}t∈𝒯,𝒢t=\(ℰ1:t,ℛ,ℱt\),\\mathcal\{G\}=\\\{\\mathcal\{G\}\_\{t\}\\\}\_\{t\\in\\mathcal\{T\}\},\\qquad\\mathcal\{G\}\_\{t\}=\(\\mathcal\{E\}\_\{1:t\},\\,\\mathcal\{R\},\\,\\mathcal\{F\}\_\{t\}\),\(1\)where𝒯\\mathcal\{T\}is the discrete set of timestamps,ℰ1:t\\mathcal\{E\}\_\{1:t\}denotes the set of entities observed up to timett,ℛ\\mathcal\{R\}is the relation set, andℱt⊆ℰ1:t×ℛ×ℰ1:t×\{t\}\\mathcal\{F\}\_\{t\}\\subseteq\\mathcal\{E\}\_\{1:t\}\\times\\mathcal\{R\}\\times\\mathcal\{E\}\_\{1:t\}\\times\\\{t\\\}is the set of timestamped facts that hold at timett\. Each fact is written as a quadruple\(es,r,eo,t\)\(e\_\{s\},\\,r,\\,e\_\{o\},\\,t\), withes,eo∈ℰ1:te\_\{s\},e\_\{o\}\\in\\mathcal\{E\}\_\{1:t\}the subject and object entities andr∈ℛr\\in\\mathcal\{R\}their relation\. The cumulative history available up to timetqt\_\{q\}isℋtq=⋃i<tqℱi\.\\mathcal\{H\}\_\{t\_\{q\}\}\\;=\\;\\bigcup\_\{i<t\_\{q\}\}\\mathcal\{F\}\_\{i\}\.

Link prediction task in TKG\.Given a query\(es,r,?,tq\)\(e\_\{s\},\\,r,\\,?,\\,t\_\{q\}\)whose timestamptqt\_\{q\}lies in the future, the TKG link prediction task is to recover the missing entity from the entity pool by ranking every candidatee∈ℰe\\in\\mathcal\{E\}under a scoring functionϕ​\(⋅\)\\phi\(\\cdot\)conditioned on the historyℋtq\\mathcal\{H\}\_\{t\_\{q\}\}\. Following the extrapolation protocol, the dataset is split chronologically so that no future information is leaked during training\. As test queries are temporally ordered, the protocol breaks the i\.i\.d\. assumption by design, as earlier ground\-truth facts enterℋtq\\mathcal\{H\}\_\{t\_\{q\}\}when scoring later queries\.

Emerging entities\.Let the first\-appearance time of an entityeebe

te​\(e\)=min⁡\{t∈𝒯\|e​appears in some fact of​ℱt\}\.t\_\{e\}\(e\)\\;=\\;\\min\\bigl\\\{\\,t\\in\\mathcal\{T\}\\,\\big\|\\,e\\text\{ appears in some fact of \}\\mathcal\{F\}\_\{t\}\\,\\bigr\\\}\.\(2\)At timestamptt, an entityeeis anemerging entityife∈ℰ1:t∖ℰ1:t−1e\\in\\mathcal\{E\}\_\{1:t\}\\setminus\\mathcal\{E\}\_\{1:t\-1\}, and its participation attq=te​\(e\)t\_\{q\}=t\_\{e\}\(e\)is accompanied by no prior history\. Following previous worksLeeet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib17)\); Anonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), we adopt this setting as our primary challenge, focusing on the moment an entity enters the graph\. This arises frequently in real\-world TKGs and makes reasoning difficult as no interaction history is available for the entityCaiet al\.\([2023](https://arxiv.org/html/2605.07121#bib.bib1)\)\.

## 4From Static TKG to Adaptive TKG

In this section, we cast representative prior methods and our proposal into a common scoring form\. Let𝐡e∈ℝd\\mathbf\{h\}\_\{e\}\\in\\mathbb\{R\}^\{d\}denote thebaserepresentation of entityeeand𝐡r∈ℝd\\mathbf\{h\}\_\{r\}\\in\\mathbb\{R\}^\{d\}the embedding of relationrr\. For a query\(eq,rq,?,tq\)\(e\_\{q\},\\,r\_\{q\},\\,?,\\,t\_\{q\}\), the score assigned to a candidateeoe\_\{o\}takes the unified formϕtq​\(eq,rq,eo\)=f​\(𝐳eq\(tq\),𝐡rq,𝐳eo\(tq\)\)\\phi\_\{t\_\{q\}\}\(e\_\{q\},\\,r\_\{q\},\\,e\_\{o\}\)\\;=\\;f\\\!\\bigl\(\\,\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\_\{q\}\},\\;\\mathbf\{h\}\_\{r\_\{q\}\},\\;\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\_\{o\}\}\\,\\bigr\), wheref​\(⋅\)f\(\\cdot\)is a relational decoder \(e\.g\., ConvTransEShanget al\.\([2019](https://arxiv.org/html/2605.07121#bib.bib33)\)\) and𝐳e\(tq\)\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}is the*effective*representation of entityeeused for reasoning at timetqt\_\{q\}\. These formulations differ solely in how𝐳e\(tq\)\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}is constructed, with comparison show in Table[3](https://arxiv.org/html/2605.07121#S4.F3)\.

Figure 2:Representative formulations on TKGs\.We argue that the entity should not bestatic, but instead anadaptiveprocess whose representation is refined whenever it participates in a fact\. We omit the\(tq\)\(t\_\{q\}\)superscript for simplicity\.
![Refer to caption](https://arxiv.org/html/2605.07121v1/x2.png)Figure 3:Ours: Adaptive \+ Inductive\.

Paradigm 1:Static\+Transductive\.Conventional methodsLiet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib6)\); Xuet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib7)\); Liet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib8)\); Chenet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib9)\)learn a lookup embedding for every entity from training facts as

𝐳e\(tq\)=𝐡e,𝐡e∈ℝd,e∈ℰ1:Ttr,\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}\\;=\\;\\mathbf\{h\}\_\{e\},\\qquad\\mathbf\{h\}\_\{e\}\\in\\mathbb\{R\}^\{d\},\\;\\;e\\in\\mathcal\{E\}\_\{1:T\_\{\\text\{tr\}\}\},\(3\)whereTtrT\_\{\\text\{tr\}\}is the final training timestamp\. The representation isstaticin that𝐡e\\mathbf\{h\}\_\{e\}is a function of the learned parameters alone andcarries no trace of the interactions ofeeitself, andtransductivein thatonly entities seen during traininghave a well\-defined embedding\. However, on emerging entities,𝐡e\\mathbf\{h\}\_\{e\}is either undefined or initialized randomly, leading to representation collapseZbontaret al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib22)\)\.

Paradigm 2:Static\+Inductive\.To handle emerging entities, recent TKG methodsMeiet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib19)\); Dinget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib20)\); Panet al\.\([2025](https://arxiv.org/html/2605.07121#bib.bib21)\)obtain𝐡e\\mathbf\{h\}\_\{e\}from an external source \(e\.g\., a pretrained text encoder\) and augment it with atype\-level signalderived from semantically similar entities\. Letπ​\(e\)∈\{1,…,K\}\\pi\(e\)\\in\\\{1,\\ldots,K\\\}be the cluster index ofeeunder a learned codebook and let𝐜k,t\\mathbf\{c\}\_\{k,\\,t\}denote the prototype of clusterkkat timett, pooled from the interaction patterns of its membersAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)\. Then, the effective representation is computed using a parametric transfer gateΨ​\(⋅\)\\Psi\(\\cdot\)as

𝐳e\(tq\)=𝐡e\+ωe⋅𝐜π​\(e\),tq,ωe=Ψ​\(\[𝐡e∥𝐜π​\(e\),tq\]\)\.\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}\\;=\\;\\mathbf\{h\}\_\{e\}\\;\+\\;\\omega\_\{e\}\\cdot\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\},\\qquad\\omega\_\{e\}=\\Psi\\\!\\bigl\(\[\\mathbf\{h\}\_\{e\}\\,\\\|\\,\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}\]\\bigr\)\.\(4\)This paradigm isinductivein that itallows an emerging entity to still be scored, since𝐜π​\(e\),tq\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}is derived from cluster mates rather than fromeeitself\. However, the transfer isstaticin that𝐳e\(tq\)\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}is still a function of𝐡e\\mathbf\{h\}\_\{e\}and𝐜π​\(e\),tq\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}, anddoes not incorporate any per\-entity state beyond them\.

Paradigm 3:Adaptive\+Inductive\.We argue that an entity should be treated not as astaticrepresentation but as anadaptiveprocess whose representation is refined every time the entity participates in a fact\. To this end, we introduce amemory𝐦e\(τ\)∈ℝd\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\in\\mathbb\{R\}^\{d\}for each entity which is updated via a forward pass whenevereeparticipates in a fact, whereτ\\taucounts the number of updates\. Given a signal𝐱e\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}summarizing the interaction that triggers theτ\\tau\-th update ofee, the memory is updated as

𝐦e\(τ\)=𝒰​\(𝐦e\(τ−1\),𝐱e\(τ\)\),𝐦e\(0\)=0,\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\mathcal\{U\}\\\!\\bigl\(\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\},\\;\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\\bigr\),\\qquad\\mathbf\{m\}^\{\(0\)\}\_\{e\}\\;=\\;\\mathbf\{0\},\(5\)where𝒰​\(⋅,⋅\)\\mathcal\{U\}\(\\cdot,\\cdot\)is a stateful update operator\.

At query timetqt\_\{q\}we read𝐦e≡𝐦e\(τ​\(e,tq\)\)\\mathbf\{m\}\_\{e\}\\\!\\equiv\\\!\\mathbf\{m\}\_\{e\}^\{\(\\tau\(e,t\_\{q\}\)\)\}, whereτ​\(e,tq\)\\tau\(e,t\_\{q\}\)counts the interactions ofeestrictly beforetqt\_\{q\}\. Note that following the standard TKG protocolLiet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib6)\); Anonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), training facts are presented in chronological order oftt\. Memory is thus updatedchronologically, so no future information leaks into a query\.Concretely,𝐱\(τ\)​e\\mathbf\{x\}^\{\(\\tau\)\}eis built only from*observed*facts ofee, so the update never sees the ground\-truth object\. For an emerging entitye∗e^\{\*\},𝐦e∗=𝟎\\mathbf\{m\}\_\{e^\{\*\}\}=\\mathbf\{0\}and the gate is zero\-masked, so AdaTKG reduces exactly to TransFIR \(Corollary 1, Appendix[F](https://arxiv.org/html/2605.07121#A6)\)\.The effective representation is then produced by anadaptive gatege\(tq\)∈\[0,1\]dg^\{\(t\_\{q\}\)\}\_\{e\}\\in\[0,1\]^\{d\}that fuses the static embedding from Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\) with the memory as

𝐳e\(tq\)=\(1−ge\(tq\)\)⊙\(𝐡e\+ωe⋅𝐜π​\(e\),tq\)\+ge\(tq\)⊙𝐦e\.\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}\\;=\\;\\bigl\(1\-g^\{\(t\_\{q\}\)\}\_\{e\}\\bigr\)\\,\\odot\\,\\bigl\(\\mathbf\{h\}\_\{e\}\+\\omega\_\{e\}\\cdot\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}\\bigr\)\\;\+\\;g^\{\(t\_\{q\}\)\}\_\{e\}\\,\\odot\\,\\mathbf\{m\}\_\{e\}\.\(6\)Although the memory is maintained on a per\-entity basis and may appear inherently transductive, it can be designed to remaininductive, by governing its update throughentity\-agnosticparameters rather than parameters indexed by individual entities, making it applicable to emerging entities\.

## 5Proposed Method: AdaTKG

### 5\.1Model Architecture

In this section, we instantiate the components inParadigm 3:Adaptive\+Inductivein Section[4](https://arxiv.org/html/2605.07121#S4):

- •\[1\] Backbone: Generates static embedding & interaction signal\.
- •\[2\] Memory update: Generates memory with interaction signal\.
- •\[3\] Adaptive gate: Fuses static embedding & memory\.

\[1\] Backbone\.We adopt the backbone of prior workAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), which for each queryq=\(eq,rq,?,t\)q\\\!=\\\!\(e\_\{q\},r\_\{q\},?,t\)generates the three quantities:

Backbone​\(q\)→\(𝐡e,ωe⋅𝐜π​\(e\),t,𝐱e\(τ\)\),\\textsc\{Backbone\}\(q\)\\;\\to\\;\\bigl\(\\,\\mathbf\{h\}\_\{e\},\\;\\;\\omega\_\{e\}\\\!\\cdot\\\!\\mathbf\{c\}\_\{\\pi\(e\),\\,t\},\\;\\;\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\\,\\bigr\),namely1\)static entity embedding𝐡e\\mathbf\{h\}\_\{e\}from a pretrained text encoder,2\)type\-level inductive priorωe⋅𝐜π​\(e\),t\\omega\_\{e\}\\\!\\cdot\\\!\\mathbf\{c\}\_\{\\pi\(e\),\\,t\}from a VQ codebook applied to𝐡e\\mathbf\{h\}\_\{e\}\(Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\)\), and3\)interaction signal𝐱e\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}produced by a Transformer\-based encoder over the recent interaction chain ofee\. Details are provided in Appendix[D](https://arxiv.org/html/2605.07121#A4)\.

\[2\] Memory update\.To make the per\-entity memory inductive, it is crucial thatmemory is treated as an internal state, not as a learnable parameter\. That is, the buffer\{𝐦e\}e∈ℰ\\\{\\mathbf\{m\}\_\{e\}\\\}\_\{e\\in\\mathcal\{E\}\}itself carries no trainable weight; instead, all learnable capacity resides in thesharedupdate rule, which is parameterized in anentity\-agnosticmanner\. Consequently, AdaTKG’s gain doesnotarise from per\-entity knowledge stored in𝐦e\\mathbf\{m\}\_\{e\}, but from the shared update rule learning to exploit anew information channelthat opens at inference time and thus remains effective even for emerging entities\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x3.png)Figure 4:AdaTKG architecture\.An encoder produces an interaction signal𝐱\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}which updates the entity’s memory𝐦\(τ\)\\mathbf\{m\}^\{\(\\tau\)\}via a learnable EMA\. The decay rateα\\alphacontrols how strongly the previous memory is retained relative to the new signal\.To realize this principle, we instantiate the stateful update operator𝒰\\mathcal\{U\}of Eq\. \([5](https://arxiv.org/html/2605.07121#S4.E5)\) as a simple yet effective design, a learnable EMA \(Figure[4](https://arxiv.org/html/2605.07121#S5.F4)\):

𝐦e\(τ\)=α​𝐦e\(τ−1\)\+\(1−α\)​𝐱e\(τ\),\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\alpha\\,\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\}\\;\+\\;\(1\-\\alpha\)\\,\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\},\(7\)with𝐦e\(0\)=𝟎\\mathbf\{m\}^\{\(0\)\}\_\{e\}=\\mathbf\{0\}, whereα=σ​\(ρ\)\\alpha\\;=\\;\\sigma\(\\rho\),ρ∈ℝ\\rho\\\!\\in\\\!\\mathbb\{R\}is a single learnable scalar shared across all entities, andσ​\(⋅\)\\sigma\(\\cdot\)is the sigmoid, yielding a decay rateα∈\(0,1\)\\alpha\\\!\\in\\\!\(0,1\)\. Crucially,ρ\\rhois the only learnable parameter, and it is entity\-agnostic by construction, so the same update rule applies to every entity including emerging entities\. Note that EMA is merely one of possible instantiations of𝒰\\mathcal\{U\}, andour focus is not on the EMA operator itself but on endowing each entity with adaptivity through a per\-entity memory\. Details of other possible instantiations are provided in Appendix[G](https://arxiv.org/html/2605.07121#A7)\.

Since the memory is updated online over the training stream, three protocol decisions are required to keep the update strictly causal and the learning signal consistent, with details provided in Appendix[F](https://arxiv.org/html/2605.07121#A6)\.

- •a\) Epoch reset\.Buffer is reset at every epoch start, soρ,𝐖g\\rho,\\mathbf\{W\}\_\{g\}receive a consistent learning signal\.
- •b\) Chronological replay\.Facts are replayed in time order, so each query reads EMA of past facts\.
- •c\) Detached update\.With𝐦e\(τ−1\)\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\}detached before the update, no recurrence gradients flow\.

\[3\] Adaptive gate\.The gatege\(tq\)∈\[0,1\]dg^\{\(t\_\{q\}\)\}\_\{e\}\\\!\\in\\\!\[0,1\]^\{d\}in Eq\. \([6](https://arxiv.org/html/2605.07121#S4.E6)\) fuses thestaticentity embedding with theadaptivememory\. Note thatge\(tq\)g^\{\(t\_\{q\}\)\}\_\{e\}is add\-dimensional gate, so the fusion in Eq\. \([6](https://arxiv.org/html/2605.07121#S4.E6)\) is a coordinate\-wise interpolation and the \(cold\-start\) zero\-maskge\(tq\)=𝟎g^\{\(t\_\{q\}\)\}\_\{e\}\\\!=\\\!\\mathbf\{0\}refers to thedd\-dimensional zero vector\. We parameterize it by a sigmoid\-gated linear projection with explicit zero\-masking when the memory buffer is empty, where𝐖g∈ℝd×2​d\\mathbf\{W\}\_\{g\}\\\!\\in\\\!\\mathbb\{R\}^\{d\\times 2d\}is a learnable projection,

ge\(tq\)=\{𝟎if​𝐦e=𝟎,σ​\(𝐖g​\[𝐡e∥𝐦e\]\)otherwise\.g^\{\(t\_\{q\}\)\}\_\{e\}\\;=\\;\\begin\{cases\}\\mathbf\{0\}&\\text\{if \}\\mathbf\{m\}\_\{e\}=\\mathbf\{0\},\\\\\[2\.0pt\] \\sigma\\\!\\bigl\(\\mathbf\{W\}\_\{g\}\\,\[\\mathbf\{h\}\_\{e\}\\,\\\|\\,\\mathbf\{m\}\_\{e\}\]\\bigr\)&\\text\{otherwise\}\.\\end\{cases\}\(8\)The zero\-masking realizes the hypothesis of Corollary 1 in Appendix[F](https://arxiv.org/html/2605.07121#A6), guaranteeing that AdaTKG reduces to the Static \+ Inductive paradigm \(Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\)\) whenever no interaction ofeehas been observed\. For the loss function, we follow that of the previous workAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)without modification\.

Algorithm 1Training of AdaTKG \(Single\-epoch view\)\.1:Facts

ℱtr\\mathcal\{F\}\_\{\\text\{tr\}\}; Parameters

ρ,𝐖g\\rho,\\mathbf\{W\}\_\{g\}\(\+ backbone

Θbb\\Theta\_\{\\text\{bb\}\}\); Per\-entity state

\{\(𝐦e,τe\)\}e∈ℰ\\\{\(\\mathbf\{m\}\_\{e\},\\tau\_\{e\}\)\\\}\_\{e\\in\\mathcal\{E\}\}\.

2:

α←σ​\(ρ\)\\alpha\\leftarrow\\sigma\(\\rho\)and

𝐦e←𝟎,τe←0\\mathbf\{m\}\_\{e\}\\leftarrow\\mathbf\{0\},\\ \\tau\_\{e\}\\leftarrow 0for all

e∈ℰe\\in\\mathcal\{E\}
3:fortimestamp

t=1t=1to

TtrT\_\{\\mathrm\{tr\}\}do

4:foreach query

q=\(eq,rq,?,t\)q=\(e\_\{q\},r\_\{q\},?,t\)from the facts at

ttdo

5:

⊳\\triangleright\[1\] Embeddings \(w/ inductivity\)

6:

\(𝐡eq,ωeq⋅𝐜π​\(eq\),t,𝐱eq\(τeq\+1\)\)←Backbone​\(q\)\\bigl\(\\mathbf\{h\}\_\{e\_\{q\}\},\\;\\omega\_\{e\_\{q\}\}\\\!\\cdot\\\!\\mathbf\{c\}\_\{\\pi\(e\_\{q\}\),t\},\\;\\mathbf\{x\}^\{\(\\tau\_\{e\_\{q\}\}\+1\)\}\_\{e\_\{q\}\}\\bigr\)\\\!\\leftarrow\\\!\\textsc\{Backbone\}\(q\)
7:

𝐡~e=\(𝐡e\+ωe⋅𝐜π​\(e\),t\)\\widetilde\{\\mathbf\{h\}\}\_\{e\}=\\bigl\(\\mathbf\{h\}\_\{e\}\\\!\+\\\!\\omega\_\{e\}\\\!\\cdot\\\!\\mathbf\{c\}\_\{\\pi\(e\),t\}\\bigr\)
8:

⊳\\triangleright\[2\] Memory update

9:

𝐦~eq←stop​\_​grad​\(𝐦eq\)\\widetilde\{\\mathbf\{m\}\}\_\{e\_\{q\}\}\\\!\\leftarrow\\\!\\mathrm\{stop\\\_grad\}\(\\mathbf\{m\}\_\{e\_\{q\}\}\)
10:

𝐦eq←α​𝐦~eq\+\(1−α\)​𝐱eq\(τeq\+1\)\\mathbf\{m\}\_\{e\_\{q\}\}\\\!\\leftarrow\\\!\\alpha\\,\\widetilde\{\\mathbf\{m\}\}\_\{e\_\{q\}\}\\;\+\\;\(1\\\!\-\\\!\\alpha\)\\,\\mathbf\{x\}^\{\(\\tau\_\{e\_\{q\}\}\+1\)\}\_\{e\_\{q\}\}⊳\\trianglerightEq\. \([7](https://arxiv.org/html/2605.07121#S5.E7)\)

11:

⊳\\triangleright\[3\] Adaptive\-gate fusion

12:

𝐳e\(t\)←\(1−ge\(t\)\)⊙𝐡~e\+ge\(t\)⊙𝐦e\\mathbf\{z\}^\{\(t\)\}\_\{e\}\\\!\\leftarrow\\\!\\bigl\(1\-g^\{\(t\)\}\_\{e\}\\bigr\)\\\!\\odot\\\!\\widetilde\{\\mathbf\{h\}\}\_\{e\}\+g^\{\(t\)\}\_\{e\}\\\!\\odot\\\!\\mathbf\{m\}\_\{e\}for

e∈\{eq\}∪ℰe\\\!\\in\\\!\\\{e\_\{q\}\\\}\\cup\\mathcal\{E\}⊳\\trianglerightEq\. \([6](https://arxiv.org/html/2605.07121#S4.E6)\)

13:Score

ϕ​\(eq,rq,eo\)=f​\(𝐳eq\(t\),𝐡rq,𝐳eo\(t\)\)\\phi\(e\_\{q\},r\_\{q\},e\_\{o\}\)\\\!=\\\!f\(\\mathbf\{z\}^\{\(t\)\}\_\{e\_\{q\}\},\\mathbf\{h\}\_\{r\_\{q\}\},\\mathbf\{z\}^\{\(t\)\}\_\{e\_\{o\}\}\)
14:

τeq←τeq\+1\\tau\_\{e\_\{q\}\}\\\!\\leftarrow\\\!\\tau\_\{e\_\{q\}\}\+1
15:endfor

16:endfor

### 5\.2Properties of the Adaptive Memory

\[Generality\] Update\-operator agnostic\.The adaptive memory framework is not tied to EMA, as any stateful update operator𝒰\\mathcal\{U\}that maintains a per\-entity state can be plugged in without changing the training protocol\. It is important to note that our focus isnot on the choice of EMA itselfbut on theadaptive propertyit enables; to highlight this, we additionally instantiate𝒰\\mathcal\{U\}as a GRU cell and as a cross\-attention readout over a bounded per\-entity buffer, with details provided in Appendix[G](https://arxiv.org/html/2605.07121#A7)\.

\[Efficiency\] Shared parameters\.AdaTKG introduces two learnable components: \(i\) the EMA module, which contributes a shared scalarρ\\rhothat governs the memory dynamics, and \(ii\) the adaptive gate, which contributes a shared projection𝐖g\\mathbf\{W\}\_\{g\}that controls the fusion\. Crucially, neitherρ\\rhonor𝐖g\\mathbf\{W\}\_\{g\}is indexed by the entity, so the buffer\{𝐦e\}\\\{\\mathbf\{m\}\_\{e\}\\\}itself carries no learnable parameter\.AdaTKG thus applies uniformly to every entity, remaining effective on those never seen during training\.

\[Online update\] Accumulation at inference\.The per\-entity memory𝐦e\\mathbf\{m\}\_\{e\}accumulates online with every new fact at inference time, so the predictions improve as more interactions arrive\. This online dynamic also underlies the consistent gain on emerging/unknown entities as shown in Table[2](https://arxiv.org/html/2605.07121#S6.T2), where the𝐡e\\mathbf\{h\}\_\{e\}provides no entity\-specific signal and𝐦e\\mathbf\{m\}\_\{e\}supplies a substantial new source of information\. Note that𝐦e\\mathbf\{m\}\_\{e\}is carried chronologically across train/valid/test phases \(resetting only at training\-epoch boundaries\), so the memory accumulated during training remains available at test time\.

\[Interpretability\] Transition across regimes\.The adaptive fusion behaves predictably across the cold\-start and warm regimes\. With no interaction ofeeobserved, we enforcege\(tq\)=𝟎g^\{\(t\_\{q\}\)\}\_\{e\}\\\!=\\\!\\mathbf\{0\}via a zero\-mask on the gate, so that Eq\. \([6](https://arxiv.org/html/2605.07121#S4.E6)\) recovers theStatic \+ Inductiveformulation in Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\)\. As more interactions ofeeare observed,𝐦e\\mathbf\{m\}\_\{e\}grows informative and the gate shifts weight toward the memory branch\.

## 6Experiments

Datasets\.We evaluate AdaTKG on four widely used temporal knowledge graph benchmarks: ICEWS14, ICEWS18, ICEWS05\-15Boscheeet al\.\([2015](https://arxiv.org/html/2605.07121#bib.bib35)\), and GDELTLeetaru and Schrodt \([2013](https://arxiv.org/html/2605.07121#bib.bib37)\)\. Each dataset is a chronologically ordered sequence of timestamped quadruples\(es,r,eo,t\)\(e\_\{s\},\\,r,\\,e\_\{o\},\\,t\)\. Details of datasets are discussed in Appendix[A](https://arxiv.org/html/2605.07121#A1)\.

Evaluation protocol\.Following prior work on inductive TKG reasoningAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\); Meiet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib19)\), we evaluate link prediction using Mean Reciprocal Rank \(MRR\) and Hits@kkwithk∈\{3,10\}k\\\!\\in\\\!\\\{3,10\\\}, computed over the filtered ranking of every candidate entity\. While we focus onemergingentities following previous worksAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\); Leeet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib17)\), we additionally evaluate on theunknownslice to capture entities that, although unseen in training, may accumulate a few interactions before the query timestamp, defined as:

- •Emerging: Queries on entities that appear for thevery first timeat the query timestamp\.
- •Unknown: Queries on entities that were never observed during training butmay have appeared in validation or earlier in the test stream, i\.e\.,s∈𝒱∖𝒱trains\\in\\mathcal\{V\}\\\!\\setminus\\\!\\mathcal\{V\}\_\{\\mathrm\{train\}\}oro∈𝒱∖𝒱traino\\in\\mathcal\{V\}\\\!\\setminus\\\!\\mathcal\{V\}\_\{\\mathrm\{train\}\}\.

Note that these two slices are not disjoint: everyEmergingquery is alsoUnknown\. We follow the standard chronological split to prevent leakage of future information into training\.

Baselines\.We adopt the same baseline set as TransFIRAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), with methods grouped into three categories\.\(i\) Graph\-based: CyGNetZhuet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib5)\), RE\-GCNLiet al\.\([2021](https://arxiv.org/html/2605.07121#bib.bib6)\), HiSMatchLiet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib8)\), MGESLMingconget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib23)\), LogCLChenet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib9)\), HisResZhanget al\.\([2025](https://arxiv.org/html/2605.07121#bib.bib24)\), and MLEMKDQianet al\.\([2025](https://arxiv.org/html/2605.07121#bib.bib25)\)\.\(ii\) Path\-based: TLogicLiuet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib26)\), TILPXionget al\.\([2024a](https://arxiv.org/html/2605.07121#bib.bib27)\), ECEformerFanget al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib10)\), and GenTKGLiaoet al\.\([2024](https://arxiv.org/html/2605.07121#bib.bib11)\)\.\(iii\) Static inductive: CompGCNVashishthet al\.\([2020](https://arxiv.org/html/2605.07121#bib.bib28)\), ICLLeeet al\.\([2023a](https://arxiv.org/html/2605.07121#bib.bib29)\), PPTXuet al\.\([2023a](https://arxiv.org/html/2605.07121#bib.bib30)\), MorsEChenet al\.\([2022](https://arxiv.org/html/2605.07121#bib.bib16)\), InGramLeeet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib17)\), and TransFIRAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)\. All baseline numbers are taken from the TransFIR paperAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), with TransFIR itself reproduced from its official GitHub release for fair comparison\.

Implementation details\.AdaTKG initializes𝐡e\\mathbf\{h\}\_\{e\}from a frozen BERTDevlinet al\.\([2019](https://arxiv.org/html/2605.07121#bib.bib34)\)encoder applied to the entity’s textual surface form\. Relational scoring is performed with ConvTransEShanget al\.\([2019](https://arxiv.org/html/2605.07121#bib.bib33)\), the decoder adopted by recent TKG baselines\. We use Adam optimizerKingma and Ba \([2015](https://arxiv.org/html/2605.07121#bib.bib42)\)and select hyperparameters via validation MRR with early stopping\. Results averaged over three random seeds, along with standard deviations, are provided in Appendix[I](https://arxiv.org/html/2605.07121#A9)\. Further details are discussed in Appendix[C](https://arxiv.org/html/2605.07121#A3)\.

Table 1:Comparison with the various TKG reasoning methods across the emerging entities\.The table shows the link\-prediction performance for queries whose query entity first appears at the query timestamp\. Best scores are inbold red, second\-best inunderlined blue\.Table 2:Comparison with the SoTA baseline across the emerging/unknown entities\.The table shows the link\-prediction performance across the two test slices:EmergingandUnknown\.### 6\.1Main Results

To demonstrate the effectiveness of AdaTKG, we present two complementary views of performance:

\(1\) Comparison with various methods across emerging entities\.Following prior work on inductive TKGAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\); Leeet al\.\([2023b](https://arxiv.org/html/2605.07121#bib.bib17)\), we focus our comparison on emerging entities\. Table[1](https://arxiv.org/html/2605.07121#S6.T1)demonstrates that our method outperforms all baselines across four benchmarks on link\-prediction tasks\. This is consistent with our design, where AdaTKG learnshow to integrate new interactions onlinerather than storing learnable memory for seen entities, so even unseen entities accumulate useful signal at inference time\.

\(2\) Comparison with SoTA across emerging/unknown entities\.Table[2](https://arxiv.org/html/2605.07121#S6.T2)compares AdaTKG with TransFIRAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)across the two slices of unseen entities \(Emerging,Unknown\), jointly characterizing model behavior on cold\-start and few\-shot regimes\. AdaTKG consistently outperforms TransFIR on both slices across all four benchmarks, indicating that the gain extends beyond the strict cold\-start setting to entities the model has merely seen rarely during training\.

Table 3:\[Ablation 1\] Paradigm grid\.The2×22\\\!\\times\\\!2grid of Static/Adaptive×\\timesTransductive/Inductive\.
Table 4:\[Ablation 2\] Adaptive gate\.Effect of an adaptive gategeg\_\{e\}vs\. a constant gateg=0\.5g=0\.5\.
Table 5:\[Ablation 3\] Update operator𝒰\\mathcal\{U\}\.Three instantiations of the memory update rule\.
Table 6:\[Ablation 4\] EMA decay parameter\.Three parameterizations of the EMA decay rate\.

### 6\.2Ablation Study

To isolate the contribution of each design choice in AdaTKG, we perform a controlled ablation on the emerging slice across all four benchmarks, organized along four axes:

\(1\) Effectiveness of Adaptive \+ Inductive paradigm\.The four rows in Table[6](https://arxiv.org/html/2605.07121#S6.T6)traverse the2×22\\\!\\times\\\!2paradigm grid:Static \+ Inductive\(≡\\equivTransFIRAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)\) keeps only the cluster prior,Adaptive \+ Transductivekeeps only the per\-entity memory, andAdaptive \+ Inductiveis the AdaTKG that combines both\. Removing the per\-entity memory collapses AdaTKG to TransFIR, while removing the cluster prior breaks the cold\-start match with TransFIR\. The proposed Adaptive \+ Inductive paradigm achieves the best results, demonstrating the effectiveness of adaptivity in TKG reasoning\.

\(2\) Effectiveness of adaptive gate\.As shown in Table[6](https://arxiv.org/html/2605.07121#S6.T6), replacing the learned gate by the constantg=0\.5g=0\.5removes its ability to track the varying reliability of the memory and degrades performance, confirming that the gate is a necessary mechanism for the graceful cold\-start behavior\.

\(3\) Robustness to update operator\.We compare three instantiations of the stateful update operator𝒰\\mathcal\{U\}, the 1\) learnable EMA, a 2\) GRU cell, and a 3\) cross\-attention readout over a bounded per\-entity buffer\. All three retain the adaptive gate of Eq\. \([8](https://arxiv.org/html/2605.07121#S5.E8)\) for fusion, soonly the memory update rule itself differs\. As shown in Table[6](https://arxiv.org/html/2605.07121#S6.T6), every variant improves over the static baselineAnonymous \([2026](https://arxiv.org/html/2605.07121#bib.bib36)\), indicating that the gain is driven by theadaptive propertyof per\-entity memory rather than by any particular implementation\. It is important to note that our focus isnot on the choice of EMA itself but on this adaptive property, and we adopt EMA as a lightweight yet effective realization of𝒰\\mathcal\{U\}\.

\(4\) Variants of EMA decay parameterization\.The default AdaTKG uses a single shared learnable scalarα=σ​\(ρ\)\\alpha\\\!=\\\!\\sigma\(\\rho\)for the EMA decay\. Two natural relaxations enlarge the parameterization: a 1\)per\-entity scalar111This breaks inductivity for emerging entities, where we fall back to the cluster\-prototype decayρπ​\(e\)\\rho\_\{\\pi\(e\)\}\.αe=σ​\(ρe\)\\alpha\_\{e\}\\\!=\\\!\\sigma\(\\rho\_\{e\}\)that lets each entity learn its own forgetting rate and a 2\)per\-dimension vector𝜶=σ​\(𝝆\)∈\[0,1\]d\\boldsymbol\{\\alpha\}\\\!=\\\!\\sigma\(\\boldsymbol\{\\rho\}\)\\\!\\in\\\!\[0,1\]^\{d\}that decays each coordinate at a different rate\. As shown in Table[6](https://arxiv.org/html/2605.07121#S6.T6), while all designs outperform the baseline \(w/o Adaptivity\), the shared scalar outperforms both relaxations, indicating that asingle shared scalaralready suffices for the memory branch\.

### 6\.3Analysis

\(1\) Effectiveness of memory by \# interactions\. \(Figure[5](https://arxiv.org/html/2605.07121#S6.F5)\)\.To demonstrate that theper\-entity memory is the actual source of AdaTKG’s gain, we score each AdaTKG variant on ICEWS14 in two configurations: 1\) with the trained memory branch active \(RRfull\\mathrm\{RR\}\_\{\\mathrm\{full\}\}\), and 2\) with the memory branch bypassed by setting the gate to zero \(RRzero\\mathrm\{RR\}\_\{\\mathrm\{zero\}\}\)\. The per\-query differenceΔR​R=RRfull−RRzero\\Delta\_\{RR\}=\\mathrm\{RR\}\_\{\\mathrm\{full\}\}\-\\mathrm\{RR\}\_\{\\mathrm\{zero\}\}is thusthe performance gain by the memory branch, and we stratify it along two complementary axes in Figure[5](https://arxiv.org/html/2605.07121#S6.F5): \(Left\) train\-time history depth of the subject and \(Right\) test\-time online updates accumulated during inference\.ΔR​R\\Delta\_\{RR\}is positive across every bin and grows along both axes for all three update operators, confirming that more interactions translate into a larger memory contribution and a corresponding gain in MRR\. Results across all four benchmarks are provided in Appendix[K](https://arxiv.org/html/2605.07121#A11)\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x4.png)Figure 5:Performance by \# interactions at train and test time\.We measure the memory’s contribution byΔR​R=RRfull−RRzero\\Delta\_\{RR\}=\\mathrm\{RR\}\_\{\\mathrm\{full\}\}\-\\mathrm\{RR\}\_\{\\mathrm\{zero\}\}\(i\.e\., the difference between the per\-query RR of the model w/ and w/o its memory branch\) and stratify it along two axes:\(Left\)Train\-time history depth of the subject and the\(Right\)Test\-time online updates accumulated during inference\. The increase ofΔR​R\\Delta\_\{RR\}along both axes, consistent across all three operators, indicates that more observed interactions translate into alarger memory contributionand, in turn, intohigher predictive performance\.![Refer to caption](https://arxiv.org/html/2605.07121v1/x5.png)
Figure 6:Gate value by \# interactions\.Distribution of the learned gatege\(tq\)g^\{\(t\_\{q\}\)\}\_\{e\}, stratified by the number of interactions\.![Refer to caption](https://arxiv.org/html/2605.07121v1/x6.png)
Figure 7:Training curves on test MRR\.Per\-epoch test emerging MRR for the static\-inductive baseline \(w/o Adaptivity\) and the three AdaTKG update operators \(w/ Adaptivity\)\. AdaTKG update operators yield faster convergence and higher performance\.
\(2\) Gate activation by \# interactions \(Figure[6](https://arxiv.org/html/2605.07121#S6.F6)\)\.The adaptive gatege\(tq\)g^\{\(t\_\{q\}\)\}\_\{e\}controls how much of the representation comes from thestatic inductive priorversus theper\-entity memory, and its trajectory offers a direct window into what the model has learned\. As shown in Figure[6](https://arxiv.org/html/2605.07121#S6.F6)with ICEWS14 and the EMA update operator, the gate value grows with the number of observed interactions\. See Appendix[L](https://arxiv.org/html/2605.07121#A12)for results across all benchmarks and update operators\.

\(3\) Faster convergence and higher final performance \(Figure[7](https://arxiv.org/html/2605.07121#S6.F7)\)\.Figure[7](https://arxiv.org/html/2605.07121#S6.F7)traces the per\-epoch test emerging MRR for the static\-inductive baseline \(w/o Adaptivity\) and the three AdaTKG update operators\. All three variants 1\)converge in fewer epochsand to a 2\)higher final MRRthan the baseline\. This indicates that adaptivity yields both 1\)training efficiencyand 2\)predictive performance, and that these gains stem from the memory itself rather than from any specific update operator\.

Table 7:Efficiency comparison\.We compare TransFIR and the three AdaTKG update operators along 1\) the number of parameters, 2\) the training time per epoch, and 3\) the FLOPs per query\. AdaTKG delivers a substantial performance gain over TransFIR with only marginal extra computation\.Method\[1\] Efficiency\[2\] Performance\# Parameters\(M\)Training time\(s/epoch\)FLOPs\(M/query\)MRRH@3H@10ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)Base \(w/o Adaptivity\)Anonymous\([2026](https://arxiv.org/html/2605.07121#bib.bib36)\)41\.15–56\.1–399\.8–\.1763\.2096\.3413AdaTKGEMA \(default\)44\.10\+7\.2%64\.1\+14\.3%405\.7\+1\.5%\.2011\.2250\.3621GRU47\.65\+15\.8%67\.6\+20\.5%408\.8\+2\.2%\.1955\.2192\.3582Cross\-attention46\.47\+12\.9%62\.7\+11\.8%445\.9\+11\.5%\.1913\.2296\.3609

\(4\) Efficiency analysis \(Table[7](https://arxiv.org/html/2605.07121#S6.T7)\)\.We compare AdaTKG with TransFIR, the SoTA static\-inductive baseline, on three computational dimensions on ICEWS14: 1\) number of parameters, 2\) training time per epoch, and 3\) FLOPs per query, evaluating all four methods under the same hyperparameter configuration \(= AdaTKG\-EMA’s best HP on ICEWS14\) for fair comparison\. As shown in Table[7](https://arxiv.org/html/2605.07121#S6.T7), the three update operators all add only asmall overheadover the base whilesubstantially improving performance, confirming that adaptivity is the source of the gain rather than added model capacity\. Among them, we adopt EMA as our default operator as it offers the best balance between efficiency and performance\. Comparison on the other three benchmarks is provided in Appendix[J](https://arxiv.org/html/2605.07121#A10)\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x7.png)
Figure 8:Sensitivity to memory\-related hyperparameters\.Each point is one hyperparameter setting of AdaTKG, compared against thew/o Adaptivitybaseline at its best setting \(dashed line\)\.Table 8:Robustness to training horizon\.Training horizon\(k%k\\%\) denotes the fraction of the most recent training time window used; AdaTKG’s gain over the baseline persists at every horizon and is largest at the shortest\.

\(6\) Robustness to training horizon \(Table[8](https://arxiv.org/html/2605.07121#S6.T8)\)\.We additionally train both methods on only the lastk%k\\%of the training time window to test whether the gain depends on long training history\. AdaTKG outperforms TransFIR at every horizon, with the gainlargest at the shortest horizon\. This is consistent with the asymmetric roles of the two branches: the static branch isparametricand its quality scales with how much training data it sees, while the memory branch isnon\-parametricand accumulates online from the test stream, so its marginal value is highest when the static prior is weakest\.

\(7\) Sensitivity to memory\-related hyperparameters \(Figure[8](https://arxiv.org/html/2605.07121#S6.F8)\)\.For each of ICEWS14 and ICEWS18, we sweep the full hyperparameter grid \(chain length, hidden dim, \# layers, codebook size\) and plot the resulting test emerging MRR for every AdaTKG operator against the best static\-inductive baseline\. Every AdaTKG HP point lies above the baseline reference line on both benchmarks, indicating that the adaptive memory mechanism isrobust to hyperparameter choices\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x8.png)Figure 9:Qualitative gate trace\.\(8\) Qualitative ex: How memory adapts \(Figure[9](https://arxiv.org/html/2605.07121#S6.F9)\)\.While Figure[6](https://arxiv.org/html/2605.07121#S6.F6)reports theaveragegate trajectory, here we trace the gatege\(t\)g\_\{e\}^\{\(t\)\}of two individual entities on ICEWS18 with AdaTKG across their successive test\-time appearances\. The red trajectory \(↑\\uparrow\) corresponds to an entity whose gate climbs rapidly, indicating that its observed actions diverge from thestatic inductive priorand the model accordingly leans on theper\-entity memory branch; the blue trajectory \(↓\\downarrow\) corresponds to an entity whose gate remains low throughout, indicating that thestatic inductive prioralready explains its behavior well and the model accordingly trusts it\. This entity\-level contrast confirms that the gate is not a function of time or interaction count alone, but of theentity\-specific deviationfrom thestatic prior, which is the behavior anticipated by the design\.

## 7Conclusion

We propose AdaTKG, which shifts TKG reasoning fromstatictoadaptiverepresentations by equipping every entity with a memory governed by an adaptive gate\. Crucially, the memory is treated as an internal state rather than a learnable parameter, with all learnable capacity concentrated in a single shared update rule, making it applicable to unseen entities\. Across various datasets, AdaTKG yields consistent improvements, with the gain growing in the number of interactions per entity\.

Limitation and Future Work\.AdaTKG’s per\-entity memory must be persisted between inference calls, introducing a simple bookkeeping requirement absent in stateless inductive methods\. Coupling the memory with a continually adapting codebook lets the static prior itself accommodate slow distribution drift on long\-horizon TKGs, which we view as a natural next step\.

## Impact Statement

AdaTKG targets a practically consequential setting: reasoning about entities that continuously appear in real\-world temporal knowledge graphs but have no training\-time footprint, such as new users, organizations, or assets\. By modeling such entities as evolving processes rather than fixed prototypes, AdaTKG enables more inclusive analyses of freshly appearing actors in domains such as financial monitoring and public\-health surveillance\. At the same time, event\-based TKGs inherit reporting biases from their underlying sources, and downstream use should account for the risk that such biases propagate into AdaTKG’s per\-entity memories\. We therefore recommend treating AdaTKG as a decision\-support tool whose outputs are validated by human experts before consequential decisions, particularly when errors on emerging entities carry asymmetric real\-world costs\.

## References

- \[1\]\(2026\)TransFIR: transferable few\-shot inductive reasoning for emerging entities on temporal knowledge graphs\.arXiv preprint arXiv:2604\.10164\.Note:To appear at ICLR 2026Cited by:[Appendix A](https://arxiv.org/html/2605.07121#A1.p1.1),[Appendix A](https://arxiv.org/html/2605.07121#A1.p2.2),[Table J\.1](https://arxiv.org/html/2605.07121#A10.T1.3.3.3.3.3.3.3.6.3.1),[Table J\.2](https://arxiv.org/html/2605.07121#A10.T2.3.3.3.3.3.3.3.6.3.1),[Table J\.3](https://arxiv.org/html/2605.07121#A10.T3.3.3.3.3.3.3.3.6.3.1),[6th item](https://arxiv.org/html/2605.07121#A2.I3.i6.p1.1),[Appendix B](https://arxiv.org/html/2605.07121#A2.p1.1),[Table C\.1](https://arxiv.org/html/2605.07121#A3.T1),[Table C\.1](https://arxiv.org/html/2605.07121#A3.T1.10.2),[Appendix C](https://arxiv.org/html/2605.07121#A3.p1.2),[Appendix C](https://arxiv.org/html/2605.07121#A3.p2.1),[Appendix C](https://arxiv.org/html/2605.07121#A3.p3.1),[Appendix C](https://arxiv.org/html/2605.07121#A3.p4.1),[Appendix D](https://arxiv.org/html/2605.07121#A4.p1.1),[Appendix D](https://arxiv.org/html/2605.07121#A4.p4.10),[Appendix F](https://arxiv.org/html/2605.07121#A6.p1.1),[Appendix F](https://arxiv.org/html/2605.07121#A6.p7.1),[Table I\.1](https://arxiv.org/html/2605.07121#A9.T1.3.1.1.1.1.1.1.2),[Appendix I](https://arxiv.org/html/2605.07121#A9.p1.1),[NeurIPS Paper Checklist](https://arxiv.org/html/2605.07121#Ax2.I1.ix12.p1.1),[NeurIPS Paper Checklist](https://arxiv.org/html/2605.07121#Ax2.I1.ix21.p1.1),[NeurIPS Paper Checklist](https://arxiv.org/html/2605.07121#Ax2.I1.ix36.p1.1),[§1](https://arxiv.org/html/2605.07121#S1.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1),[§3](https://arxiv.org/html/2605.07121#S3.p3.5),[§4](https://arxiv.org/html/2605.07121#S4.p3.7),[§4](https://arxiv.org/html/2605.07121#S4.p5.11),[§5\.1](https://arxiv.org/html/2605.07121#S5.SS1.p2.1),[§5\.1](https://arxiv.org/html/2605.07121#S5.SS1.p6.7),[§6\.1](https://arxiv.org/html/2605.07121#S6.SS1.p2.1),[§6\.1](https://arxiv.org/html/2605.07121#S6.SS1.p3.1),[§6\.2](https://arxiv.org/html/2605.07121#S6.SS2.p2.2),[§6\.2](https://arxiv.org/html/2605.07121#S6.SS2.p4.2),[Table 8](https://arxiv.org/html/2605.07121#S6.SS3.4.2.1.1.1.1.1.1.1.4.1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.23.22.1),[Table 6](https://arxiv.org/html/2605.07121#S6.T6.14.5.3.3.3.3.3.3.6.3.1),[Table 6](https://arxiv.org/html/2605.07121#S6.T6.17.3.3.3.3.3.3.3.6.3.1),[Table 7](https://arxiv.org/html/2605.07121#S6.T7.3.3.3.3.3.3.3.6.3.1),[§6](https://arxiv.org/html/2605.07121#S6.p2.2),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[2\]Cited by:[Appendix A](https://arxiv.org/html/2605.07121#A1.p1.1),[§6](https://arxiv.org/html/2605.07121#S6.p1.1)\.
- \[3\]B\. Cai, Y\. Xiang, L\. Gao, H\. Zhang, Y\. Li, and J\. Li\(2023\)Temporal knowledge graph completion: a survey\.InProceedings of the Thirty\-Second International Joint Conference on Artificial Intelligence,pp\. 6545–6553\.Cited by:[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[§3](https://arxiv.org/html/2605.07121#S3.p3.5)\.
- \[4\]J\. Chen, H\. He, F\. Wu, and J\. Wang\(2021\)Topology\-aware correlations between relations for inductive link prediction in knowledge graphs\.InProceedings of the AAAI conference on artificial intelligence,Vol\.35,pp\. 6271–6278\.Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1)\.
- \[5\]M\. Chen, W\. Zhang, Y\. Zhu, H\. Zhou, Z\. Yuan, C\. Xu, and H\. Chen\(2022\)Meta\-knowledge transfer for inductive knowledge graph embedding\.InProceedings of the 45th international ACM SIGIR conference on research and development in information retrieval,pp\. 927–937\.Cited by:[4th item](https://arxiv.org/html/2605.07121#A2.I3.i4.p1.1),[Appendix E](https://arxiv.org/html/2605.07121#A5.p2.1),[Appendix E](https://arxiv.org/html/2605.07121#A5.p3.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.21.20.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[6\]W\. Chen, H\. Wan, Y\. Wu, S\. Zhao, J\. Cheng, Y\. Li, and Y\. Lin\(2024\)Local\-global history\-aware contrastive learning for temporal knowledge graph reasoning\.In2024 IEEE 40th International Conference on Data Engineering \(ICDE\),pp\. 733–746\.Cited by:[Appendix A](https://arxiv.org/html/2605.07121#A1.p1.1),[Appendix A](https://arxiv.org/html/2605.07121#A1.p2.2),[5th item](https://arxiv.org/html/2605.07121#A2.I1.i5.p1.1),[Appendix C](https://arxiv.org/html/2605.07121#A3.p2.1),[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[§4](https://arxiv.org/html/2605.07121#S4.p2.5),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.9.8.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[7\]K\. Cho, B\. van Merriënboer, C\. Gulcehre, D\. Bahdanau, F\. Bougares, H\. Schwenk, and Y\. Bengio\(2014\)Learning phrase representations using RNN encoder–decoder for statistical machine translation\.InProceedings of the 2014 Conference on Empirical Methods in Natural Language Processing \(EMNLP\),pp\. 1724–1734\.Cited by:[Appendix G](https://arxiv.org/html/2605.07121#A7.p3.2)\.
- \[8\]J\. Devlin, M\. Chang, K\. Lee, and K\. Toutanova\(2019\)Bert: pre\-training of deep bidirectional transformers for language understanding\.InProceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies, volume 1 \(long and short papers\),pp\. 4171–4186\.Cited by:[Appendix C](https://arxiv.org/html/2605.07121#A3.p1.2),[Appendix D](https://arxiv.org/html/2605.07121#A4.p2.4),[NeurIPS Paper Checklist](https://arxiv.org/html/2605.07121#Ax2.I1.ix36.p1.1),[§6](https://arxiv.org/html/2605.07121#S6.p4.1)\.
- \[9\]Z\. Ding, H\. Cai, J\. Wu, Y\. Ma, R\. Liao, B\. Xiong, and V\. Tresp\(2024\)Zrllm: zero\-shot relational learning on temporal knowledge graphs with large language models\.InProceedings of the 2024 conference of the North American chapter of the association for computational linguistics: Human language technologies \(Volume 1: Long papers\),pp\. 1877–1895\.Cited by:[§1](https://arxiv.org/html/2605.07121#S1.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1),[§4](https://arxiv.org/html/2605.07121#S4.p3.7)\.
- \[10\]Z\. Fang, S\. Lei, X\. Zhu, C\. Yang, S\. Zhang, X\. Yin, and J\. Qin\(2024\)Transformer\-based reasoning for learning evolutionary chain of events on temporal knowledge graph\.InProceedings of the 47th international ACM SIGIR conference on research and development in information retrieval,pp\. 70–79\.Cited by:[3rd item](https://arxiv.org/html/2605.07121#A2.I2.i3.p1.1),[Appendix E](https://arxiv.org/html/2605.07121#A5.p5.1),[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.15.14.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[11\]M\. Galkin, X\. Yuan, H\. Mostafa, J\. Tang, and Z\. Zhu\(2024\)Towards foundation models for knowledge graph reasoning\.InThe Twelfth International Conference on Learning Representations,Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1)\.
- \[12\]A\. Garcia\-Duran, S\. Dumančić, and M\. Niepert\(2018\)Learning sequence encoders for temporal knowledge graph completion\.InProceedings of the 2018 Conference on Empirical Methods in Natural Language Processing,pp\. 4816–4821\.Cited by:[§2](https://arxiv.org/html/2605.07121#S2.p1.1)\.
- \[13\]D\. P\. Kingma and J\. Ba\(2015\)Adam: a method for stochastic optimization\.InInternational Conference on Learning Representations \(ICLR\),Cited by:[Appendix C](https://arxiv.org/html/2605.07121#A3.p5.1),[§6](https://arxiv.org/html/2605.07121#S6.p4.1)\.
- \[14\]T\. Lacroix, G\. Obozinski, and N\. Usunier\(2020\)Tensor decompositions for temporal knowledge base completion\.InInternational Conference on Learning Representations,Cited by:[§2](https://arxiv.org/html/2605.07121#S2.p1.1)\.
- \[15\]D\. Lee, K\. Ahrabian, W\. Jin, F\. Morstatter, and J\. Pujara\(2023\)Temporal knowledge graph forecasting without knowledge using in\-context learning\.arXiv preprint arXiv:2305\.10613\.Cited by:[2nd item](https://arxiv.org/html/2605.07121#A2.I3.i2.p1.1),[Appendix E](https://arxiv.org/html/2605.07121#A5.p5.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.19.18.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[16\]J\. Lee, C\. Chung, and J\. J\. Whang\(2023\)InGram: inductive knowledge graph embedding via relation graphs\.InInternational conference on machine learning,pp\. 18796–18809\.Cited by:[5th item](https://arxiv.org/html/2605.07121#A2.I3.i5.p1.1),[Appendix E](https://arxiv.org/html/2605.07121#A5.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1),[§3](https://arxiv.org/html/2605.07121#S3.p3.5),[§6\.1](https://arxiv.org/html/2605.07121#S6.SS1.p2.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.22.21.1),[§6](https://arxiv.org/html/2605.07121#S6.p2.2),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[17\]K\. Leetaru and P\. A\. Schrodt\(2013\)Gdelt\.InISA annual convention,Vol\.2,pp\. 1–49\.Cited by:[Appendix A](https://arxiv.org/html/2605.07121#A1.p1.1),[§6](https://arxiv.org/html/2605.07121#S6.p1.1)\.
- \[18\]Z\. Li, Z\. Hou, S\. Guan, X\. Jin, W\. Peng, L\. Bai, Y\. Lyu, W\. Li, J\. Guo, and X\. Cheng\(2022\)HiSMatch: historical structure matching based temporal knowledge graph reasoning\.InFindings of the Association for Computational Linguistics: EMNLP 2022,pp\. 7328–7338\.Cited by:[3rd item](https://arxiv.org/html/2605.07121#A2.I1.i3.p1.1),[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[§4](https://arxiv.org/html/2605.07121#S4.p2.5),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.7.6.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[19\]Z\. Li, X\. Jin, W\. Li, S\. Guan, J\. Guo, H\. Shen, Y\. Wang, and X\. Cheng\(2021\)Temporal knowledge graph reasoning based on evolutional representation learning\.InProceedings of the 44th international ACM SIGIR conference on research and development in information retrieval,pp\. 408–417\.Cited by:[Appendix A](https://arxiv.org/html/2605.07121#A1.p1.1),[2nd item](https://arxiv.org/html/2605.07121#A2.I1.i2.p1.1),[Appendix C](https://arxiv.org/html/2605.07121#A3.p2.1),[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[§4](https://arxiv.org/html/2605.07121#S4.p2.5),[§4](https://arxiv.org/html/2605.07121#S4.p5.11),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.6.5.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[20\]R\. Liao, X\. Jia, Y\. Li, Y\. Ma, and V\. Tresp\(2024\)GenTKG: generative forecasting on temporal knowledge graph with large language models\.InFindings of the Association for Computational Linguistics: NAACL 2024,pp\. 4303–4317\.Cited by:[4th item](https://arxiv.org/html/2605.07121#A2.I2.i4.p1.1),[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.16.15.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[21\]S\. Liu, B\. Grau, I\. Horrocks, and E\. Kostylev\(2021\)Indigo: gnn\-based inductive knowledge graph completion using pair\-wise encoding\.Advances in Neural Information Processing Systems34,pp\. 2034–2045\.Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1)\.
- \[22\]Y\. Liu, Y\. Ma, M\. Hildebrandt, M\. Joblin, and V\. Tresp\(2022\)Tlogic: temporal logical rules for explainable link forecasting on temporal knowledge graphs\.InProceedings of the AAAI conference on artificial intelligence,Vol\.36,pp\. 4120–4127\.Cited by:[1st item](https://arxiv.org/html/2605.07121#A2.I2.i1.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.13.12.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[23\]X\. Mei, L\. Yang, X\. Cai, and Z\. Jiang\(2022\-12\)An adaptive logical rule embedding model for inductive reasoning over temporal knowledge graphs\.InProceedings of the 2022 Conference on Empirical Methods in Natural Language Processing,Abu Dhabi, United Arab Emirates,pp\. 7304–7316\.External Links:[Document](https://dx.doi.org/10.18653/v1/2022.emnlp-main.493)Cited by:[§1](https://arxiv.org/html/2605.07121#S1.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1),[§4](https://arxiv.org/html/2605.07121#S4.p3.7),[§6](https://arxiv.org/html/2605.07121#S6.p2.2)\.
- \[24\]S\. Mingcong, C\. Zhu, D\. Zhang, S\. Wen, and L\. Qing\(2024\)Multi\-granularity history and entity similarity learning for temporal knowledge graph reasoning\.InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing,pp\. 5232–5243\.Cited by:[4th item](https://arxiv.org/html/2605.07121#A2.I1.i4.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.8.7.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[25\]J\. Pan, M\. Nayyeri, O\. Mohammed, D\. Hernandez, R\. Zhang, C\. Cheng, and S\. Staab\(2025\)Towards foundation model on temporal knowledge graph reasoning\.arXiv preprint arXiv:2506\.06367\.Cited by:[§1](https://arxiv.org/html/2605.07121#S1.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1),[§4](https://arxiv.org/html/2605.07121#S4.p3.7)\.
- \[26\]Y\. Qian, X\. Wang, F\. Sun, and L\. Pan\(2025\)Compressing transfer: mutual learning\-empowered knowledge distillation for temporal knowledge graph reasoning\.IEEE Transactions on Neural Networks and Learning Systems\.Cited by:[7th item](https://arxiv.org/html/2605.07121#A2.I1.i7.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.11.10.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[27\]E\. Rossi, B\. Chamberlain, F\. Frasca, D\. Eynard, F\. Monti, and M\. Bronstein\(2020\)Temporal graph networks for deep learning on dynamic graphs\.InICML 2020 Workshop on Graph Representation Learning and Beyond,Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p4.1)\.
- \[28\]C\. Shang, Y\. Tang, J\. Huang, J\. Bi, X\. He, and B\. Zhou\(2019\)End\-to\-end structure\-aware convolutional networks for knowledge base completion\.InProceedings of the AAAI conference on artificial intelligence,Vol\.33,pp\. 3060–3067\.Cited by:[Appendix C](https://arxiv.org/html/2605.07121#A3.p2.1),[§4](https://arxiv.org/html/2605.07121#S4.p1.12),[§6](https://arxiv.org/html/2605.07121#S6.p4.1)\.
- \[29\]K\. Teru, E\. Denis, and W\. Hamilton\(2020\)Inductive relation prediction by subgraph reasoning\.InInternational conference on machine learning,pp\. 9448–9457\.Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p2.1),[§2](https://arxiv.org/html/2605.07121#S2.p2.1)\.
- \[30\]R\. Trivedi, H\. Dai, Y\. Wang, and L\. Song\(2017\)Know\-evolve: deep temporal reasoning for dynamic knowledge graphs\.InInternational conference on machine learning,pp\. 3462–3471\.Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p4.1)\.
- \[31\]R\. Trivedi, M\. Farajtabar, P\. Biswal, and H\. Zha\(2019\)DyRep: learning representations over dynamic graphs\.InInternational Conference on Learning Representations \(ICLR\),Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p4.1)\.
- \[32\]S\. Vashishth, S\. Sanyal, V\. Nitin, and P\. P\. Talukdar\(2020\)Composition\-based multi\-relational graph convolutional networks\.InICLR,Cited by:[1st item](https://arxiv.org/html/2605.07121#A2.I3.i1.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.18.17.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[33\]J\. Wang, S\. Kai, L\. Luo, W\. Wei, Y\. Hu, A\. W\. Liew, S\. Pan, and B\. Yin\(2024\)Large language models\-guided dynamic adaptation for temporal knowledge graph reasoning\.Advances in Neural Information Processing Systems37,pp\. 8384–8410\.Cited by:[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1)\.
- \[34\]S\. Xiong, Y\. Yang, F\. Fekri, and J\. C\. Kerce\(2024\)Tilp: differentiable learning of temporal logical rules on knowledge graphs\.arXiv preprint arXiv:2402\.12309\.Cited by:[2nd item](https://arxiv.org/html/2605.07121#A2.I2.i2.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.14.13.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[35\]S\. Xiong, Y\. Yang, A\. Payani, J\. C\. Kerce, and F\. Fekri\(2024\)Teilp: time prediction over knowledge graphs via logical reasoning\.InProceedings of the AAAI conference on artificial intelligence,Vol\.38,pp\. 16112–16119\.Cited by:[§2](https://arxiv.org/html/2605.07121#S2.p1.1)\.
- \[36\]D\. Xu, C\. Ruan, E\. Korpeoglu, S\. Kumar, and K\. Achan\(2020\)Inductive representation learning on temporal graphs\.InInternational Conference on Learning Representations \(ICLR\),Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p4.1)\.
- \[37\]W\. Xu, B\. Liu, M\. Peng, X\. Jia, and M\. Peng\(2023\)Pre\-trained language model with prompts for temporal knowledge graph completion\.arXiv preprint arXiv:2305\.07912\.Cited by:[3rd item](https://arxiv.org/html/2605.07121#A2.I3.i3.p1.1),[Appendix E](https://arxiv.org/html/2605.07121#A5.p5.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.20.19.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[38\]Y\. Xu, J\. Ou, H\. Xu, and L\. Fu\(2023\)Temporal knowledge graph reasoning with historical contrastive learning\.InThirty\-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty\-Fifth Conference on Innovative Applications of Artificial Intelligence, IAAI 2023, Thirteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2023, Washington, DC, USA, February 7\-14, 2023,B\. Williams, Y\. Chen, and J\. Neville \(Eds\.\),pp\. 4765–4773\.External Links:[Link](https://doi.org/10.1609/aaai.v37i4.25601),[Document](https://dx.doi.org/10.1609/AAAI.V37I4.25601)Cited by:[§1](https://arxiv.org/html/2605.07121#S1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[§4](https://arxiv.org/html/2605.07121#S4.p2.5)\.
- \[39\]J\. Zbontar, L\. Jing, I\. Misra, Y\. LeCun, and S\. Deny\(2021\)Barlow twins: self\-supervised learning via redundancy reduction\.InInternational conference on machine learning,pp\. 12310–12320\.Cited by:[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[§4](https://arxiv.org/html/2605.07121#S4.p2.4)\.
- \[40\]J\. Zhang, M\. Sun, C\. Mu, J\. Zhang, Q\. Guo, and L\. Tian\(2025\)Historically relevant event structuring for temporal knowledge graph reasoning\.In2025 IEEE 41st International Conference on Data Engineering \(ICDE\),pp\. 3179–3192\.Cited by:[6th item](https://arxiv.org/html/2605.07121#A2.I1.i6.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.10.9.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.
- \[41\]Y\. Zheng, L\. Yi, and Z\. Wei\(2025\)A survey of dynamic graph neural networks\.Frontiers of Computer Science19\(6\),pp\. 196323\.Cited by:[Appendix E](https://arxiv.org/html/2605.07121#A5.p4.1)\.
- \[42\]C\. Zhu, M\. Chen, C\. Fan, G\. Cheng, and Y\. Zhang\(2021\)Learning from history: modeling temporal knowledge graphs with sequential copy\-generation networks\.InProceedings of the AAAI conference on artificial intelligence,Vol\.35,pp\. 4732–4740\.Cited by:[1st item](https://arxiv.org/html/2605.07121#A2.I1.i1.p1.1),[§2](https://arxiv.org/html/2605.07121#S2.p1.1),[Table 1](https://arxiv.org/html/2605.07121#S6.T1.1.1.1.1.1.1.1.5.4.1),[§6](https://arxiv.org/html/2605.07121#S6.p3.1)\.

## Appendix

## Appendix ADataset Details

Dataset statistics\.We conduct experiments on four temporal knowledge graph benchmarks: three derived from the ICEWS event corpus\[[2](https://arxiv.org/html/2605.07121#bib.bib35)\]\(ICEWS14,ICEWS18,ICEWS05\-15\) andGDELT\[[17](https://arxiv.org/html/2605.07121#bib.bib37)\]\. The ICEWS benchmarks record timestamped geopolitical events at a daily granularity, while GDELT records global events at a 15\-minute granularity, and all four share the extrapolation protocol commonly used in prior TKG work\[[19](https://arxiv.org/html/2605.07121#bib.bib6),[6](https://arxiv.org/html/2605.07121#bib.bib9),[1](https://arxiv.org/html/2605.07121#bib.bib36)\]\. Table[A\.1](https://arxiv.org/html/2605.07121#A1.T1)summarizes the per\-benchmark statistics\. In the table,\#Snapshotsis the number of distinct timestamps in the graph and\#Emergingis the number of entities that first appear in the validation or test split with no training\-time interactions\. To enable a direct comparison with TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\], we adopt the same chronological train/validation/test split with ratio 5:2:3, so that emerging\-entity queries remain a meaningful fraction of the evaluation\.

Table A\.1:Statistics of the four TKG benchmarks used in our experiments\.Data splits and preprocessing\.We adopt the chronological train / validation / test split released with each benchmark, ensuring that no future information leaks into training\. Following common practice\[[6](https://arxiv.org/html/2605.07121#bib.bib9),[1](https://arxiv.org/html/2605.07121#bib.bib36)\], we augment each fact\(es,r,eo,t\)\(e\_\{s\},r,e\_\{o\},t\)with its inverse\(eo,r−1,es,t\)\(e\_\{o\},r^\{\-1\},e\_\{s\},t\)and evaluate both directions, reporting the average across the two directions\. For entities that possess textual descriptions, we use the officially released entity\-name strings as input to the text encoder described in Appendix[C](https://arxiv.org/html/2605.07121#A3), while entities without descriptions receive a special placeholder token\.

Emerging\-entity statistics\.The \#Emerging column of Table[A\.1](https://arxiv.org/html/2605.07121#A1.T1)reports the number of entities that appear for the first time only in the validation or test split \(i\.e\., having no training\-time interaction\)\. Across the four benchmarks, emerging entities account for a non\-trivial fraction of unique entities, which justifies treating theEmergingslice as the primary evaluation regime\.

## Appendix BBaselines

We adopt the same baseline set as TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\], comprising prior TKG reasoning methods grouped into three categories \(graph\-based, path\-based, and static inductive\), with TransFIR itself included as our direct baseline within the static\-inductive group\. Short descriptions of each method are provided below\. Implementation sources follow the official releases when available, otherwise the reimplementations used in TransFIR for fair comparability\.

Graph\-based\.

- •CyGNet\[[42](https://arxiv.org/html/2605.07121#bib.bib5)\]: a sequential copy\-generation network that predicts future facts from recurrent historical patterns under a closed entity vocabulary\.
- •RE\-GCN\[[19](https://arxiv.org/html/2605.07121#bib.bib6)\]: a recurrent evolutional GCN that learns time\-evolving entity and relation representations from adjacent snapshots\.
- •HiSMatch\[[18](https://arxiv.org/html/2605.07121#bib.bib8)\]: a historical\-structure matching model that aligns query\- and candidate\-side historical subgraphs for link prediction\.
- •MGESL\[[24](https://arxiv.org/html/2605.07121#bib.bib23)\]: a multi\-granularity history and entity similarity learning framework that captures temporal patterns at multiple levels of abstraction\.
- •LogCL\[[6](https://arxiv.org/html/2605.07121#bib.bib9)\]: a local\-global history\-aware contrastive\-learning model that combines entity\-aware attention with granularity\-aware contrastive signals\.
- •HisRes\[[40](https://arxiv.org/html/2605.07121#bib.bib24)\]: a historically relevant event structuring framework with multi\-granularity evolutionary and global relevance encoders\.
- •MLEMKD\[[26](https://arxiv.org/html/2605.07121#bib.bib25)\]: a mutual learning\-empowered knowledge distillation method that compresses a TKG reasoner through adaptive distillation\.

Path\-based\.

- •TLogic\[[22](https://arxiv.org/html/2605.07121#bib.bib26)\]: an explainable temporal\-rule forecasting framework that extracts cyclic rules via time\-constrained random walks\.
- •TILP\[[34](https://arxiv.org/html/2605.07121#bib.bib27)\]: a differentiable learning framework for temporal logical rules on knowledge graphs\.
- •ECEformer\[[10](https://arxiv.org/html/2605.07121#bib.bib10)\]: a Transformer that encodes evolutionary chains of events through intra\-quadruple representation learning and inter\-quadruple context mixing\.
- •GenTKG\[[20](https://arxiv.org/html/2605.07121#bib.bib11)\]: a retrieval\-augmented generation framework that combines temporal logical\-rule retrieval with few\-shot instruction tuning of a large language model\.

Static inductive\.

- •CompGCN\[[32](https://arxiv.org/html/2605.07121#bib.bib28)\]: a composition\-based multi\-relational GCN that unifies node and relation embeddings under a shared message\-passing framework\.
- •ICL\[[15](https://arxiv.org/html/2605.07121#bib.bib29)\]: an in\-context\-learning approach that performs temporal KG forecasting by prompting a frozen large language model with historical quadruples\.
- •PPT\[[37](https://arxiv.org/html/2605.07121#bib.bib30)\]: a pretrained\-language\-model method that reformulates TKG completion as a cloze\-style task with soft prompts\.
- •MorsE\[[5](https://arxiv.org/html/2605.07121#bib.bib16)\]: a meta\-knowledge transfer framework that learns entity\-independent structural patterns for inductive KG embedding of unseen entities\.
- •InGram\[[16](https://arxiv.org/html/2605.07121#bib.bib17)\]: an inductive KG embedding model that exploits a learned relation graph to generalize to unseen entities and relations\.
- •TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]: our direct baseline and the current state of the art on the emerging slice, which maps each entity to a learned codebook and transfers type\-level behavioral prototypes from semantically similar cluster members\.

## Appendix CImplementation Details

Static encoder\.For every entitye∈ℰe\\\!\\in\\\!\\mathcal\{E\}, we obtain a frozen textual representation𝐡e\\mathbf\{h\}\_\{e\}by feeding the entity surface form to a pretrained BERT\-base encoder\[[8](https://arxiv.org/html/2605.07121#bib.bib34)\]and taking the\[CLS\]token, with the encoder weights not updated during training\. For a direct comparison with TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\], we use the same encoder choice\.

Relational decoder\.We score candidate triples with ConvTransE\[[28](https://arxiv.org/html/2605.07121#bib.bib33)\], which has been widely adopted by recent TKG reasoning methods\[[19](https://arxiv.org/html/2605.07121#bib.bib6),[6](https://arxiv.org/html/2605.07121#bib.bib9),[1](https://arxiv.org/html/2605.07121#bib.bib36)\]\. The decoder’s kernel size, number of filters, and dropout are kept at their default values from the public ConvTransE implementation\.

Hyperparameter grid\.We select hyperparameters by grid search on the validation MRR of theEmergingslice, which is the setting most directly aligned with our research goal\. Table[C\.1](https://arxiv.org/html/2605.07121#A3.T1)lists the search ranges shared with TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]and the configuration selected per dataset for AdaTKG\-EMA \(default operator\)\. The EMA decay rateα=σ​\(ρ\)\\alpha\\\!=\\\!\\sigma\(\\rho\)is a learnable scalar \(Section[5\.1](https://arxiv.org/html/2605.07121#S5.SS1)\) and therefore is not searched over\.

Table C\.1:Hyperparameter search ranges and the selected configuration for AdaTKG\-EMA\. The ranges for shared hyperparameters \(chain length, GNN layers, hidden dimensionality, codebook size\) match those of TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]for a direct comparison\.Training objective\.We follow the loss formulation of TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]without modification, and our only design choice is the absence of any auxiliary loss on the memory state or the gate, so that both modules are trained purely through the link\-prediction signal\. AdaTKG is optimized end\-to\-end under the cross\-entropy loss and a vector\-quantization commitment loss applied to the codebook as

ℒ=ℒLP\+λ​ℒVQ,λ=0\.1\.\\mathcal\{L\}\\;=\\;\\mathcal\{L\}\_\{\\mathrm\{LP\}\}\\;\+\\;\\lambda\\,\\mathcal\{L\}\_\{\\mathrm\{VQ\}\},\\qquad\\lambda=0\.1\.\(C\.1\)
Training protocol\.All models are optimized with Adam\[[13](https://arxiv.org/html/2605.07121#bib.bib42)\]\. We train for up to 200 epochs with early stopping \(patience of 10 epochs on validation MRR\) and report the best checkpoint\. Each experiment is repeated with three random seeds and we report the mean across seeds in the main paper, with standard deviations relegated to the Additional Experiments appendix\.

Hardware and runtime\.All experiments are conducted on a single NVIDIA L40S GPU \(48 GB\)\. A full training run of AdaTKG\-EMA on ICEWS14 at the selected hyperparameters of Table[C\.1](https://arxiv.org/html/2605.07121#A3.T1)takes about11hour, with peak GPU memory under3030GB\. Training time on the larger benchmarks \(ICEWS18, ICEWS05\-15, GDELT\) is reported per\-epoch in the efficiency tables of Appendix[J](https://arxiv.org/html/2605.07121#A10)\.

## Appendix DBackbone Details

For completeness we reproduce the three backbone outputsBackbone​\(q\)→\(𝐡e,ωe⋅𝐜π​\(e\),t,𝐱e\(τ\)\)\\textsc\{Backbone\}\(q\)\\\!\\to\\\!\(\\mathbf\{h\}\_\{e\},\\,\\omega\_\{e\}\\\!\\cdot\\\!\\mathbf\{c\}\_\{\\pi\(e\),t\},\\,\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\)that AdaTKG consumes \(Section[5\.1](https://arxiv.org/html/2605.07121#S5.SS1)\[1\]\)\. All three modules are taken from\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]unchanged\.

\(a\) Static entity embedding𝐡e\\mathbf\{h\}\_\{e\}\.𝐡e∈ℝd\\mathbf\{h\}\_\{e\}\\\!\\in\\\!\\mathbb\{R\}^\{d\}is obtained by feeding the textual surface form of entityeeinto a frozen pretrained BERT\[[8](https://arxiv.org/html/2605.07121#bib.bib34)\]encoder and reading the\[CLS\]token\. Because the encoder is not fine\-tuned,𝐡e\\mathbf\{h\}\_\{e\}is well\-defined for every entity that has a textual description — in particular, for entities never seen at training time — which is the source of the model’s inductivity\.

\(b\) Type\-level inductive priorωe⋅𝐜π​\(e\),t\\omega\_\{e\}\\\!\\cdot\\\!\\mathbf\{c\}\_\{\\pi\(e\),t\}\.A learnable vector\-quantized codebook𝒞=\{𝐜k\}k=1K\\mathcal\{C\}\\\!=\\\!\\\{\\mathbf\{c\}\_\{k\}\\\}\_\{k=1\}^\{K\}is applied to𝐡e\\mathbf\{h\}\_\{e\}to produce a cluster assignmentπ​\(e\)=arg⁡mink⁡‖𝐡e−𝐜k‖22\\pi\(e\)\\\!=\\\!\\arg\\min\_\{k\}\\\|\\mathbf\{h\}\_\{e\}\-\\mathbf\{c\}\_\{k\}\\\|\_\{2\}^\{2\}\. At every query timestamptt, the cluster prototype𝐜π​\(e\),t\\mathbf\{c\}\_\{\\pi\(e\),t\}is recomputed by pooling the IC\-encoder outputs of all cluster mates, so the prototype evolves as the graph evolves\. The transfer gateωe=Ψ​\(\[𝐡e∥𝐜π​\(e\),t\]\)∈\[0,1\]d\\omega\_\{e\}\\\!=\\\!\\Psi\(\[\\mathbf\{h\}\_\{e\}\\,\\\|\\,\\mathbf\{c\}\_\{\\pi\(e\),t\}\]\)\\\!\\in\\\!\[0,1\]^\{d\}regulates how much of the prototype each entity inherits\. The codebook is trained jointly with the rest of the model through the commitment lossℒVQ\\mathcal\{L\}\_\{\\mathrm\{VQ\}\}in Eq\. \([C\.1](https://arxiv.org/html/2605.07121#A3.E1)\)\.

\(c\) Interaction signal𝐱e\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\.For each fact in whicheeparticipates, the event is summarized as

𝐱e\(τ\)=𝐖2​GELU​\(𝐖1​\[𝐡eIC∥𝐡rτ\]\),\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\mathbf\{W\}\_\{2\}\\,\\mathrm\{GELU\}\\\!\\bigl\(\\mathbf\{W\}\_\{1\}\\,\[\\mathbf\{h\}^\{\\mathrm\{IC\}\}\_\{e\}\\,\\\|\\,\\mathbf\{h\}\_\{r\_\{\\tau\}\}\]\\bigr\),\(D\.1\)with learnable projections𝐖1∈ℝd×2​d\\mathbf\{W\}\_\{1\}\\\!\\in\\\!\\mathbb\{R\}^\{d\\times 2d\}and𝐖2∈ℝd×d\\mathbf\{W\}\_\{2\}\\\!\\in\\\!\\mathbb\{R\}^\{d\\times d\}\. The two inputs are \(i\)𝐡eIC\\mathbf\{h\}^\{\\mathrm\{IC\}\}\_\{e\}, the embedding ofee’s*interaction chain*— the time\-ordered sequence of recent facts involvingee, filtered by relation similarity to the query\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]and encoded with a Transformer — and \(ii\)𝐡rτ\\mathbf\{h\}\_\{r\_\{\\tau\}\}, the relation embedding of theτ\\tau\-th observed fact involvingee\(*not*the relation of an open query\)\.

Both inputs are known at prediction time, so𝐱e\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}never observes the ground\-truth object of an open query\. At the first appearance of an emerging entity, the chain is empty and𝐦e=𝟎\\mathbf\{m\}\_\{e\}\\\!=\\\!\\mathbf\{0\}, which the adaptive gate of Eq\. \([8](https://arxiv.org/html/2605.07121#S5.E8)\) converts into a hard fall\-back to the static\-inductive prior \(Corollary 1, Appendix[F](https://arxiv.org/html/2605.07121#A6)\)\.

## Appendix EExtended Related Work

We discuss four adjacent threads that a reader may associate with our setting, and note how our approach differs from each\.

Static KG foundation models\.GraIL\[[29](https://arxiv.org/html/2605.07121#bib.bib13)\], INDIGO\[[21](https://arxiv.org/html/2605.07121#bib.bib15)\], TACT\[[4](https://arxiv.org/html/2605.07121#bib.bib14)\], MorsE\[[5](https://arxiv.org/html/2605.07121#bib.bib16)\], InGram\[[16](https://arxiv.org/html/2605.07121#bib.bib17)\], and ULTRA\[[11](https://arxiv.org/html/2605.07121#bib.bib18)\]push KG reasoning toward fully inductive capabilities on*static*KGs by relying on local graph topology and re\-deriving representations from structure for each query, and therefore maintain no per\-entity state that is refined over time\. Our work, in contrast, targets per\-entity adaptivity under temporal evolution\.

Meta\-learning for inductive TKG\.MorsE\[[5](https://arxiv.org/html/2605.07121#bib.bib16)\]and follow\-ups treat each emerging entity as a meta\-task and adapt by gradient updates on a small support set at inference\. Unlike these methods, our approach must score the entity at the very moment of emergence and adapts by a forward\-only memory update, requiring no test\-time optimization\.

Dynamic graph neural networks\.Dynamic graph models\[[41](https://arxiv.org/html/2605.07121#bib.bib32)\], including Know\-Evolve\[[30](https://arxiv.org/html/2605.07121#bib.bib31)\], DyRep\[[31](https://arxiv.org/html/2605.07121#bib.bib39)\], TGAT\[[36](https://arxiv.org/html/2605.07121#bib.bib40)\], and TGN\[[27](https://arxiv.org/html/2605.07121#bib.bib41)\], maintain a time\-evolving per\-node memory under a closed entity set assumed to be observed at training time\. Our work, by contrast, operates in the strict inductive regime where the entity itself is unseen at training and must be scored from its first interaction, with the buffer allocated at inference and a strict cold\-start guarantee at emergence\.

PLM\- and Transformer\-based TKG reasoning\.ICL\[[15](https://arxiv.org/html/2605.07121#bib.bib29)\], PPT\[[37](https://arxiv.org/html/2605.07121#bib.bib30)\], and ECEformer\[[10](https://arxiv.org/html/2605.07121#bib.bib10)\]cast TKG reasoning as a text\-conditioned or sequence\-modeling task over a \(P\)LM, so inductive behavior on emerging entities hinges on the entity’s textual surface form\. By comparison, we use a frozen PLM only to produce the static embedding𝐡e\\mathbf\{h\}\_\{e\}and otherwise operate on graph\-temporal signals, so the inductive guarantee in Appendix[F](https://arxiv.org/html/2605.07121#A6)holds independently of the PLM and requires no retrieval or prompting at inference\.

## Appendix FReduction of AdaTKG to the Static\-Inductive Setting at Cold Start

In this appendix, we formalize the observation, stated informally in Section[4](https://arxiv.org/html/2605.07121#S4)of the main text, that AdaTKG strictly generalizes theStatic \+ Inductivesetting \(whose representative instantiation is TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]\), and we make precise the sense in which AdaTKG incurs no cold\-start cost relative to that setting\. The analysis concerns only the gated fusion rule, and therefore holds independently of the specific stateful update operator𝒰\\mathcal\{U\}used to maintain the per\-entity memory\.

AdaTKG generalizes the static\-inductive setting\.We first show that AdaTKG recovers the static\-inductive prior exactly when the adaptive gate vanishes\.

Proposition 1\(Reduction to the static\-inductive setting at zero gate\)\.Let𝐳e\(tq\),Ada\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{Ada\}\}\_\{e\}and𝐳e\(tq\),SI\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{SI\}\}\_\{e\}denote, respectively, the effective entity representation produced by AdaTKG via Eq\. \([6](https://arxiv.org/html/2605.07121#S4.E6)\) and by the static\-inductive setting via Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\) at query timetqt\_\{q\}\. If the adaptive gate satisfiesge\(tq\)=𝟎g^\{\(t\_\{q\}\)\}\_\{e\}=\\mathbf\{0\}and the static\-inductive prior used by AdaTKG coincides with the one defined in Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\), then

𝐳e\(tq\),Ada=𝐳e\(tq\),SI,\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{Ada\}\}\_\{e\}\\;=\\;\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{SI\}\}\_\{e\},and consequently the scoreϕtq​\(eq,rq,eo\)\\phi\_\{t\_\{q\}\}\(e\_\{q\},r\_\{q\},e\_\{o\}\)of AdaTKG equals that of the static\-inductive setting for every query triple\(eq,rq,eo\)\(e\_\{q\},r\_\{q\},e\_\{o\}\)\.

Proof\.Substitutingge\(tq\)=𝟎g^\{\(t\_\{q\}\)\}\_\{e\}=\\mathbf\{0\}into the AdaTKG fusion rule of Eq\. \([6](https://arxiv.org/html/2605.07121#S4.E6)\) yields

𝐳e\(tq\),Ada=\(1−𝟎\)⊙\(𝐡e\+ωe⋅𝐜π​\(e\),tq\)\+0⊙𝐦e=𝐡e\+ωe⋅𝐜π​\(e\),tq=𝐳e\(tq\),SI,\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{Ada\}\}\_\{e\}\\;=\\;\(1\-\\mathbf\{0\}\)\\odot\\bigl\(\\mathbf\{h\}\_\{e\}\+\\omega\_\{e\}\\cdot\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}\\bigr\)\\;\+\\;\\mathbf\{0\}\\odot\\mathbf\{m\}\_\{e\}\\;=\\;\\mathbf\{h\}\_\{e\}\+\\omega\_\{e\}\\cdot\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}\\;=\\;\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{SI\}\}\_\{e\},where the last equality is by theStatic \+ Inductivedefinition in Eq\. \([4](https://arxiv.org/html/2605.07121#S4.E4)\)\. Because the relational decoderf​\(⋅\)f\(\\cdot\)in the unified scoring form \(Section[4](https://arxiv.org/html/2605.07121#S4)\) depends on entity representations only through𝐳e\(tq\)\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}, replacing𝐳e\(tq\),Ada\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{Ada\}\}\_\{e\}by𝐳e\(tq\),SI\\mathbf\{z\}^\{\(t\_\{q\}\),\\,\\textup\{SI\}\}\_\{e\}yields identical scores\.□\\hfill\\square

Cold\-start parity\.Proposition[F](https://arxiv.org/html/2605.07121#A6)has an immediate consequence at the moment each entity first appears in the graph\.

Corollary 1\(Cold\-start parity with the static\-inductive setting\)\.At the query timetq=te​\(e\)t\_\{q\}=t\_\{e\}\(e\)of an emerging entityee, the per\-entity memory is zero by the initialization in Eq\. \([5](https://arxiv.org/html/2605.07121#S4.E5)\), namely𝐦e=𝟎\\mathbf\{m\}\_\{e\}=\\mathbf\{0\}\. If the adaptive gate is parameterized so thatge\(tq\)=𝟎g^\{\(t\_\{q\}\)\}\_\{e\}=\\mathbf\{0\}whenever𝐦e=𝟎\\mathbf\{m\}\_\{e\}=\\mathbf\{0\}\(a design choice readily enforced by zero\-masking the gate output when the memory buffer is empty\), then, by Proposition[F](https://arxiv.org/html/2605.07121#A6), the prediction of AdaTKG coincides exactly with that of the static\-inductive setting\.

Corollary 1 formalizes the graceful\-degradation property emphasized in the main text: AdaTKG never pays a cold\-start cost relative to the static\-inductive setting \(instantiated by TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]in our experiments\), and all empirical gains reported in Section[6](https://arxiv.org/html/2605.07121#S6)stem purely from information retained in the per\-entity memory\.

## Appendix GStateful Update Operators

We compared three instantiations of the stateful update operator𝒰\\mathcal\{U\}in Section[6\.2](https://arxiv.org/html/2605.07121#S6.SS2): a learnable EMA \(used by AdaTKG\), a GRU cell, and a cross\-attention readout over a bounded buffer\. All three follow the unified template of Eq\. \([5](https://arxiv.org/html/2605.07121#S4.E5)\),

𝐦e\(τ\)=𝒰​\(𝐦e\(τ−1\),𝐱e\(τ\)\),𝐦e\(0\)=0,\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\mathcal\{U\}\\\!\\bigl\(\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\},\\,\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\\bigr\),\\qquad\\mathbf\{m\}^\{\(0\)\}\_\{e\}\\;=\\;\\mathbf\{0\},and share the same interaction signal

𝐱e\(τ\)=MLPenc​\(\[𝐜e\(τ\)∥𝐫e\(τ\)\]\),\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\mathrm\{MLP\}\_\{\\mathrm\{enc\}\}\\\!\\bigl\(\[\\,\\mathbf\{c\}^\{\(\\tau\)\}\_\{e\}\\,\\\|\\,\\mathbf\{r\}^\{\(\\tau\)\}\_\{e\}\\,\]\\bigr\),\(G\.1\)where𝐜e\(τ\)\\mathbf\{c\}^\{\(\\tau\)\}\_\{e\}is the chain summary produced by the TransFIR backbone at theτ\\tau\-th interaction ofeeand𝐫e\(τ\)\\mathbf\{r\}^\{\(\\tau\)\}\_\{e\}is the relation embedding of that interaction\. The three variants differ only in how𝒰\\mathcal\{U\}aggregates the past memory state with the new signal\.

\(a\) Learnable EMA \(AdaTKG, Section[5\.1](https://arxiv.org/html/2605.07121#S5.SS1)\)\.The default instantiation realizes𝒰\\mathcal\{U\}as an exponential moving average parameterized by a single shared scalar:

𝐦e\(τ\)=α​𝐦e\(τ−1\)\+\(1−α\)​𝐱e\(τ\),α=σ​\(ρ\),ρ∈ℝ\.\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\alpha\\,\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\}\\;\+\\;\(1\-\\alpha\)\\,\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\},\\qquad\\alpha\\;=\\;\\sigma\(\\rho\),\\ \\rho\\\!\\in\\\!\\mathbb\{R\}\.\(G\.2\)The decayα\\alphais shared across all entities, so the operator introduces only one learnable scalar beyond TransFIR\.

\(b\) GRU cell\.A standard GRU cell\[[7](https://arxiv.org/html/2605.07121#bib.bib38)\]treats𝐦e\(τ−1\)\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\}as the hidden state and𝐱e\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}as the input, applying a learned reset and update gate:

𝐦e\(τ\)=GRUCell​\(𝐱e\(τ\),𝐦e\(τ−1\)\)\.\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\mathrm\{GRUCell\}\\\!\\bigl\(\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\},\\,\\mathbf\{m\}^\{\(\\tau\-1\)\}\_\{e\}\\bigr\)\.\(G\.3\)The GRU cell adds three weight matrices inℝd×d\\mathbb\{R\}^\{d\\times d\}and three biases, roughly3​d23d^\{2\}extra parameters\.

\(c\) Cross\-attention readout over a bounded buffer\.This variant maintains a per\-entity FIFO buffer𝐁e∈ℝK×d\\mathbf\{B\}\_\{e\}\\\!\\in\\\!\\mathbb\{R\}^\{K\\times d\}of the most recentKKinteraction signals \(defaultK=16K\\\!=\\\!16\)\. The buffer is updated by appending the new signal at positionτmodK\\tau\\\!\\\!\\mod\\\!\\\!K,

𝐁e​\[τmodK\]←𝐱e\(τ\),\\mathbf\{B\}\_\{e\}\[\\tau\\bmod K\]\\;\\leftarrow\\;\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\},and the memory state read at query time is computed by cross\-attending the query embedding𝐪e\\mathbf\{q\}\_\{e\}to the buffer,

𝐦e\(τ\)=MultiHeadAttn​\(𝐪e,𝐁e,𝐁e\)\.\\mathbf\{m\}^\{\(\\tau\)\}\_\{e\}\\;=\\;\\mathrm\{MultiHeadAttn\}\\\!\\bigl\(\\mathbf\{q\}\_\{e\},\\,\\mathbf\{B\}\_\{e\},\\,\\mathbf\{B\}\_\{e\}\\bigr\)\.\(G\.4\)This variant adds𝒪​\(d2\)\\mathcal\{O\}\(d^\{2\}\)attention parameters and an additional𝒪​\(K​d\)\\mathcal\{O\}\(K\\,d\)buffer per entity\.

Adaptive gate fusion \(shared\)\.Regardless of the choice of𝒰\\mathcal\{U\}, the resulting memory𝐦e\\mathbf\{m\}\_\{e\}is fused with the inductive prior through the same adaptive gate of Eq\. \([8](https://arxiv.org/html/2605.07121#S5.E8)\):

𝐳e\(tq\)=\(1−ge\(tq\)\)⊙\(𝐡e\+ωe​𝐜π​\(e\),tq\)\+ge\(tq\)⊙𝐦e,\\mathbf\{z\}^\{\(t\_\{q\}\)\}\_\{e\}\\;=\\;\(1\-g^\{\(t\_\{q\}\)\}\_\{e\}\)\\odot\(\\mathbf\{h\}\_\{e\}\+\\omega\_\{e\}\\,\\mathbf\{c\}\_\{\\pi\(e\),\\,t\_\{q\}\}\)\\;\+\\;g^\{\(t\_\{q\}\)\}\_\{e\}\\odot\\mathbf\{m\}\_\{e\},with the cold\-start zero\-maskge\(tq\)=𝟎g^\{\(t\_\{q\}\)\}\_\{e\}\\\!=\\\!\\mathbf\{0\}active whenever𝐦e=𝟎\\mathbf\{m\}\_\{e\}\\\!=\\\!\\mathbf\{0\}\. The \(P1\)–\(P3\) protocol of Section[5\.1](https://arxiv.org/html/2605.07121#S5.SS1)\(epoch reset, chronological replay, detached update\) is also applied identically to all three variants, so the comparison in Section[6\.2](https://arxiv.org/html/2605.07121#S6.SS2)isolates the effect of𝒰\\mathcal\{U\}alone\.

Parameter count summary\.

- •EMA:11scalar \(sharedρ\\rho\)\.
- •GRU:∼3​d2\\sim\\\!3d^\{2\}parameters in the cell\.
- •Attention:∼4​d2\\sim\\\!4d^\{2\}attention parameters and a per\-entity buffer of sizeK​dK\\,d\.

The single\-scalar parameterization of EMA is the most parsimonious operating point along this frontier and, as reported in Section[6\.2](https://arxiv.org/html/2605.07121#S6.SS2), also the most accurate on the emerging slice\.

## Appendix HSensitivity to Memory Update Timing

By default, AdaTKG updates the per\-entity memory𝐦e\\mathbf\{m\}\_\{e\}with the current interaction signal𝐱e\(τ\)\\mathbf\{x\}^\{\(\\tau\)\}\_\{e\}*before*reading𝐦e\\mathbf\{m\}\_\{e\}for scoring \(thebeforeordering used throughout the main paper\)\. To probe the sensitivity of this design choice, we additionally train AdaTKG with the alternativeafterordering, in which𝐦e\\mathbf\{m\}\_\{e\}is read for scoring*first*,so the score depends only on the strictly past memory and the EMA update is committed only afterwards\. Both orderings share the per\-dataset best HP of AdaTKG \(Table[C\.1](https://arxiv.org/html/2605.07121#A3.T1)\); only the order of the read and the update differs\. Table[H\.1](https://arxiv.org/html/2605.07121#A8.T1)reports the comparison on the*Emerging*slice, demonstarting that across all four benchmarks, the defaultbeforeordering consistently outperforms theafterordering, supporting our design choice in the main paper\.

Table H\.1:Sensitivity to memory update timing\.AdaTKG on the*Emerging*slice with the memory update applied eitherbefore\(default\) orafterscoring\.
## Appendix IMulti\-Seed Robustness

To ensure fair comparison across all baselines and analyses, the main paper reports single\-seed results\. In this section, we further evaluate AdaTKG and the static\-inductive baseline \(TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]\) under three random seeds at the per\-dataset best HP of Table[C\.1](https://arxiv.org/html/2605.07121#A3.T1), reporting the mean and standard deviation on the*Emerging*slice \(Table[I\.1](https://arxiv.org/html/2605.07121#A9.T1)\)\. AdaTKG continues to outperform the SoTA under this multi\-seed setting\.

Table I\.1:Multi\-seed robustness on the*Emerging*slice\.Mean±\\pmstandard deviation over three random seeds at the per\-dataset best HP\. AdaTKG retains its lead over the static\-inductive baseline within and beyond the standard deviation across all four benchmarks\.
## Appendix JEfficiency Comparison Across Benchmarks

Tables[J\.1](https://arxiv.org/html/2605.07121#A10.T1),[J\.2](https://arxiv.org/html/2605.07121#A10.T2), and[J\.3](https://arxiv.org/html/2605.07121#A10.T3)extend the main\-paper Table[7](https://arxiv.org/html/2605.07121#S6.T7)to ICEWS18, ICEWS05\-15, and GDELT\. The pattern observed on ICEWS14 holds across all four benchmarks, with every update operator staying within a single\-digit\-to\-low\-double\-digit overhead and consistently improving emerging\-entity performance, indicating that the cost–benefit profile is governed by theadaptivity principleitself rather than by any specific operator\.

Memory footprint at inference\.Beyond the cost metrics in the tables above, AdaTKG keeps one additional piece of state at inference: a per\-entity memory buffer of size\|ℰ\|×d\|\\mathcal\{E\}\|\\\!\\times\\\!d\. With our largest configuration \(d=1024d\\\!=\\\!1024on ICEWS18, which has23,03323\{,\}033entities\), this buffer takes about9494MB, and stays under100100MB on every benchmark used in this paper\. The buffer therefore fits entirely in CPU or GPU memory, so we never need to cap or page it out to disk\. For much larger graphs, each entity’s slot is updated independently and overwritten in place, so the buffer can be sharded across machines or off\-loaded to a key–value store without changing the algorithm\.

Table J\.1:Efficiency comparison on ICEWS18\.Method\[1\] Efficiency\[2\] Performance\# Parameters\(M\)Training time\(s/epoch\)FLOPs\(M/query\)MRRH@3H@10ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)Base \(w/o Adaptivity\)\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]72\.77–330\.7–1643\.9–\.1114\.1230\.2252AdaTKGEMA \(default\)78\.02\+7\.2%361\.3\+9\.2%1654\.4\+0\.6%\.1379\.1543\.2612GRU84\.32\+15\.9%378\.0\+14\.3%1658\.8\+0\.9%\.1428\.1599\.2605Cross\-attention82\.22\+13\.0%360\.5\+9\.0%1725\.8\+5\.0%\.1454\.1712\.2761

Table J\.2:Efficiency comparison on ICEWS05\-15\.Method\[1\] Efficiency\[2\] Performance\# Parameters\(M\)Training time\(s/epoch\)FLOPs\(M/query\)MRRH@3H@10ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)Base \(w/o Adaptivity\)\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]72\.71–420\.5–1913\.9–\.2177\.2530\.3708AdaTKGEMA \(default\)77\.96\+7\.2%466\.3\+10\.9%1924\.4\+0\.5%\.2270\.2573\.3850GRU84\.25\+15\.9%491\.0\+16\.8%1930\.2\+0\.8%\.2330\.2700\.3925Cross\-attention82\.15\+13\.0%459\.8\+9\.4%1995\.8\+4\.3%\.2243\.2573\.3815

Table J\.3:Efficiency comparison on GDELT\.Method\[1\] Efficiency\[2\] Performance\# Parameters\(M\)Training time\(s/epoch\)FLOPs\(M/query\)MRRH@3H@10ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)ValueΔ\\Delta\(%\)Base \(w/o Adaptivity\)\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]60\.08–1384\.6–1062\.6–\.1013\.0994\.2131AdaTKGEMA \(default\)65\.33\+8\.7%1488\.7\+7\.5%1073\.1\+1\.0%\.1051\.1129\.2301GRU71\.63\+19\.2%1549\.0\+11\.9%1075\.9\+1\.3%\.1112\.1141\.2243Cross\-attention69\.53\+15\.7%1503\.2\+8\.6%1144\.4\+7\.7%\.1297\.1396\.2544

## Appendix KMemory Ablation Across Benchmarks

Figures[K\.1](https://arxiv.org/html/2605.07121#A11.F1),[K\.2](https://arxiv.org/html/2605.07121#A11.F2), and[K\.3](https://arxiv.org/html/2605.07121#A11.F3)extend the main\-paper Figure[5](https://arxiv.org/html/2605.07121#S6.F5)\(ICEWS14\) to ICEWS18, ICEWS05\-15, and GDELT\. Across all four benchmarks, every AdaTKG variant lies above the Base in every bin and the gap widens monotonically with the history depth, indicating that the per\-entity memory contributes consistently across datasets\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x9.png)Figure K\.1:Memory ablation on ICEWS18\.ΔR​R\\Delta\_\{RR\}stratified by 1\) Train\-time history depth \(left\) and 2\) Test\-time online updates \(right\)\.![Refer to caption](https://arxiv.org/html/2605.07121v1/x10.png)Figure K\.2:Memory ablation on ICEWS05\-15\.ΔR​R\\Delta\_\{RR\}stratified by 1\) Train\-time history depth \(left\) and 2\) Test\-time online updates \(right\)\.![Refer to caption](https://arxiv.org/html/2605.07121v1/x11.png)Figure K\.3:Memory ablation on GDELT\.ΔR​R\\Delta\_\{RR\}stratified by 1\) Train\-time history depth \(left\) and 2\) Test\-time online updates \(right\)\.
## Appendix LGate Distribution Across Benchmarks

Figure[L\.1](https://arxiv.org/html/2605.07121#A12.F1)extends the main\-paper Figure[6](https://arxiv.org/html/2605.07121#S6.F6)by showing the full train\-time gate distribution stratified by the number of observed interactions, for every \(dataset,update operator\) pair\. The same monotonic upward shift in the gate value with more interactions holds across all four benchmarks \(ICEWS14, ICEWS18, ICEWS05\-15, GDELT\) and all three update operators \(AdaTKG\-EMA, AdaTKG\-GRU, AdaTKG\-CrossAtt\), confirming that the adaptive gate consistently learns to lean on the per\-entity memory branch as evidence accumulates, rather than being an artifact of a particular dataset or operator\.

![Refer to caption](https://arxiv.org/html/2605.07121v1/x12.png)Figure L\.1:Gate value by \# interactions across the four benchmarks and three update operators\.Each subplot is a \(dataset,operator\) pair, with rows as datasets and columns as AdaTKG operators \(EMA, GRU, CrossAtt\)\. Within each subplot, violins show the train\-time distribution of the learned gatege\(tq\)g^\{\(t\_\{q\}\)\}\_\{e\}stratified by the number of subject interactions observed before the query, with the median marked\. The gate consistently shifts toward higher values as the interaction count grows\.
## Appendix MLLM Usage Disclosure

In accordance with the NeurIPS 2026 policy on the use of large language models, we disclose that LLMs were used solely as a writing aid for sentence\-level polishing andLaTeXformatting \(e\.g\., suggesting rephrasings, fixing typographical errors, and tightening table layout\)\. All research ideas, mathematical derivations, experimental design, code, and result interpretations were produced by the authors\. No LLM was used to generate experimental results, analyses, or any portion of the contributions claimed in this paper\.

## NeurIPS Paper Checklist

1. 1\.Claims
2. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
3. Answer:\[Yes\]
4. Justification: The abstract and introduction state two contributions: \(i\) framing TKG reasoning along astaticvs\.adaptivedimension at the entity level, and \(ii\) instantiating it as AdaTKG, an EMA\-based per\-entity memory with a single shared scalar\. Both are formalized in Section[4](https://arxiv.org/html/2605.07121#S4), and the empirical claim of consistent gains over TKG baselines is supported in Section[6](https://arxiv.org/html/2605.07121#S6)\(Tables[1](https://arxiv.org/html/2605.07121#S6.T1)and[2](https://arxiv.org/html/2605.07121#S6.T2)\)\.
5. 2\.Limitations
6. Question: Does the paper discuss the limitations of the work performed by the authors?
7. Answer:\[Yes\]
8. Justification: The Conclusion section explicitly discusses two limitations: \(1\) the per\-entity memory must be persisted between inference calls, introducing a bookkeeping requirement absent in stateless inductive methods, and \(2\) the static prior is fixed and does not accommodate slow distribution drift on long\-horizon TKGs \(which we identify as a natural next step\)\.
9. 3\.Theory assumptions and proofs
10. Question: For each theoretical result, does the paper provide the full set of assumptions and a complete \(and correct\) proof?
11. Answer:\[Yes\]
12. Justification: The two theoretical results in the paper \(Proposition[F](https://arxiv.org/html/2605.07121#A6)on AdaTKG generalizing TransFIR, and Corollary 1 on cold\-start parity\) are stated with their full set of assumptions and proved in Appendix[F](https://arxiv.org/html/2605.07121#A6)\.
13. 4\.Experimental result reproducibility
14. Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper \(regardless of whether the code and data are provided or not\)?
15. Answer:\[Yes\]
16. Justification: The four benchmarks \(ICEWS14, ICEWS18, ICEWS05\-15, GDELT\) are publicly available and we use the standard chronological split \(Appendix[A](https://arxiv.org/html/2605.07121#A1)\)\. Architectural details, the hyperparameter search grid, and the per\-dataset best configuration are reported in Appendix[C](https://arxiv.org/html/2605.07121#A3)\(Table[C\.1](https://arxiv.org/html/2605.07121#A3.T1)\)\. The per\-query evaluation protocol \(filtered MRR / Hits@kkon the Emerging and Unknown slices\) follows TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]verbatim\.
17. 5\.Open access to data and code
18. Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
19. Answer:\[Yes\]
20. Justification: The four datasets are public and downloadable via the cited sources\. We will release our full training, evaluation, and analysis code \(including the launchers used for every table and figure in this paper\) along with trained checkpoints and instructions on how to reproduce every result, in a public repository upon acceptance\.
21. 6\.Experimental setting/details
22. Question: Does the paper specify all the training and test details \(e\.g\., data splits, hyperparameters, how they were chosen, type of optimizer\) necessary to understand the results?
23. Answer:\[Yes\]
24. Justification: Splits, optimizer \(Adam\), early stopping \(patience 10 on validation MRR\), and the per\-dataset selected hyperparameters are reported in Appendix[C](https://arxiv.org/html/2605.07121#A3)and Table[C\.1](https://arxiv.org/html/2605.07121#A3.T1)\. The static encoder \(frozen BERT\) and the relational decoder \(ConvTransE\) are documented in Section[6](https://arxiv.org/html/2605.07121#S6)\(Implementation Details\) and Appendix[D](https://arxiv.org/html/2605.07121#A4)\.
25. 7\.Experiment statistical significance
26. Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
27. Answer:\[Yes\]
28. Justification: We train AdaTKG and the static\-inductive baseline \(TransFIR\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]\) under three random seeds at the per\-dataset best HP, and report mean±\\pmstandard deviation on the*Emerging*slice in Appendix[I](https://arxiv.org/html/2605.07121#A9)\(Table[I\.1](https://arxiv.org/html/2605.07121#A9.T1)\)\.
29. 8\.Experiments compute resources
30. Question: For each experiment, does the paper provide sufficient information on the computer resources \(type of compute workers, memory, time of execution\) needed to reproduce the experiments?
31. Answer:\[Yes\]
32. Justification: Hardware \(single NVIDIA A100 80 GB\), per\-epoch training time, FLOPs per query, and parameter counts are reported in Section[6](https://arxiv.org/html/2605.07121#S6)\(Table[7](https://arxiv.org/html/2605.07121#S6.T7), with extended per\-benchmark tables in Appendix[J](https://arxiv.org/html/2605.07121#A10)\) and Appendix[C](https://arxiv.org/html/2605.07121#A3)\.
33. 9\.Code of ethics
34. Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics?
35. Answer:\[Yes\]
36. Justification: The work uses publicly available, anonymized event datasets \(ICEWS / GDELT\) and introduces no human\-subject data, deployed system, or release of high\-risk artifacts\. The contributions are methodological and conform to the NeurIPS Code of Ethics in every respect we are aware of\.
37. 10\.Broader impacts
38. Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
39. Answer:\[Yes\]
40. Justification: We discuss both positive and negative societal impacts in the Impact Statement \(after Section[7](https://arxiv.org/html/2605.07121#S7)\)\. On the positive side, AdaTKG enables more inclusive analyses of newly appearing actors in domains such as financial monitoring and public\-health surveillance\. On the negative side, event\-based TKGs inherit reporting biases from their underlying sources, and we recommend treating AdaTKG’s outputs as decision\-support to be validated by human experts before consequential decisions\.
41. 11\.Safeguards
42. Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse \(e\.g\., pretrained language models, image generators, or scraped datasets\)?
43. Answer:\[N/A\]
44. Justification: We do not release pretrained language models, image generators, or scraped data\. The released artifacts are model weights of a TKG link\-prediction reasoner trained on public benchmarks, which carry no high\-misuse\-risk concern\.
45. 12\.Licenses for existing assets
46. Question: Are the creators or original owners of assets \(e\.g\., code, data, models\), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
47. Answer:\[Yes\]
48. Justification: All four datasets \(ICEWS14, ICEWS18, ICEWS05\-15, GDELT\) and the baseline implementations we build on \(in particular, the TransFIR codebase\[[1](https://arxiv.org/html/2605.07121#bib.bib36)\]and the BERT\[[8](https://arxiv.org/html/2605.07121#bib.bib34)\]encoder\) are credited via the original papers / repositories, and we use them under their respective public licenses\.
49. 13\.New assets
50. Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
51. Answer:\[Yes\]
52. Justification: The released code repository \(to be made public upon acceptance\) ships with a README, per\-experiment launcher scripts \(one per table/figure of the paper\), the trained checkpoints, and instructions to regenerate every reported table and figure end\-to\-end\.
53. 14\.Crowdsourcing and research with human subjects
54. Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation \(if any\)?
55. Answer:\[N/A\]
56. Justification: This work does not involve crowdsourcing or research with human subjects\.
57. 15\.Institutional review board \(IRB\) approvals or equivalent for research with human subjects
58. Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board \(IRB\) approvals \(or an equivalent approval/review based on the requirements of your country or institution\) were obtained?
59. Answer:\[N/A\]
60. Justification: This work does not involve human subjects, so IRB approval is not applicable\.
61. 16\.Declaration of LLM usage
62. Question: Does the paper describe the usage of LLMs if it is an important, original, or non\-standard component of the core methods in this research?
63. Answer:\[Yes\]
64. Justification: LLMs are not part of the core methodology of AdaTKG\. We disclose in Appendix[M](https://arxiv.org/html/2605.07121#A13)that LLMs were used solely as a writing aid for sentence\-level polishing andLaTeXformatting; all research ideas, derivations, code, and result interpretations were produced by the authors\.