Unlearning on Spatio-Temporal Graphs through Subgraph Virtual Edge Reconstruction

Unlearning on Spatio-Temporal Graphs through Subgraph Virtual Edge Reconstruction Qiming Guo✉ Texas A&M University - Corpus Christi Corpus Christi, Texas, USA qguo2@islander.tamucc.edu

Wenbo Sun

Chen Pan

Delft University of Technology Delft, Netherlands w.sun-2@tudelft.nl

University of Texas at San Antonio San Antonio, Texas, USA chen.pan@utsa.edu

Wenlu Wang✉

arXiv:2608.29369v1 [cs.LG] 29 Aug 2026

Ye Wang Biogen Cambridge, Massachusetts, USA ye.wang@biogen.com

Abstract Spatio-temporal graphs are widely used in modeling complex dynamic processes such as temporal forecasting, molecular dynamics, and healthcare monitoring. Recently, stringent privacy regulations such as GDPR and CCPA have introduced significant new challenges for existing spatio-temporal graph models, requiring complete unlearning of unauthorized data. Since each node in a spatio-temporal graph diffuses information globally across both spatial and temporal dimensions, existing unlearning methods primarily designed for static graphs and localized data removal cannot efficiently erase a single node without incurring costs nearly equivalent to full model retraining. To address this, we propose CallosumNet, a spatio-temporal graph unlearning framework biologically inspired by the corpus callosum structure. CallosumNet makes two key technical contributions: (1) it reconstructs subgraphs using biologically-inspired virtual edges; and (2) it restores interlinked spatio-temporal dependencies among subgraphs via a lightweight meta-graph integration layer. Empirical results on four diverse real-world datasets show that CallosumNet achieves complete unlearning while maintaining accuracy very close to the gold model. The code is publicly available at https://github.com/wenlu-lab/STGraphUnlearning.

CCS Concepts • Computing methodologies → Machine learning; • Information systems → Geographic information systems; • Security and privacy → Security services.

Texas A&M University - Corpus Christi Corpus Christi, Texas, USA wenlu.wang@tamucc.edu ACM Reference Format: Qiming Guo, Wenbo Sun, Chen Pan, Ye Wang, and Wenlu Wang. 2026. Unlearning on Spatio-Temporal Graphs through Subgraph Virtual Edge Reconstruction. In The 34th ACM International Conference on Advances in Geographic Information Systems (SIGSPATIAL ’26), November 03–06, 2026, Riverside, CA, USA. ACM, New York, NY, USA, 4 pages. https://doi.org/10. 1145/3841645.3843433

1

Introduction

Recent advanced spatio-temporal graph models effectively capture complex dynamic processes, such as urban traffic flows, molecular interactions, and healthcare monitoring, by harnessing both spatial adjacency and temporal continuity. However, the broad deployment of these powerful models increasingly faces stringent privacy regulations, such as the General Data Protection Regulation (GDPR) and the California Consumer Privacy Act (CCPA), which necessitate the complete removal or unlearning of sensitive user data upon request. Motivating scenario. Taking a mobile–location service (e.g., Google Maps) as an example, Figure 1(a) shows smartphones (nodes) forming a richly coupled spatio-temporal graph stream of time-stamped GPS signals. Suppose a subset of users revokes consent for their location data, necessitating the deletion of these devices and all incident edges, as shown in Figure 1(b). Simply dropping the raw records (Figure 1(c)) does not fully satisfy the deletion requirement, as it fails to eliminate the latent influence of the revoked users. High Accuracy

Keywords

Retraining Initiated

Retrained, Altered Features

RM 𝒱3

Machine Unlearning, Spatio-Temporal Graph, Graph Neural Networks, Privacy Compliance, GDPR

𝒱3

RM

𝒱1

𝒱2

𝒱1

b. Entities Marked for Removal

a. Complete ST-Graph Nodes |

This work is licensed under a Creative Commons Attribution 4.0 International License. SIGSPATIAL ’26, Riverside, CA, USA © 2026 Copyright held by the owner/author(s). ACM ISBN 979-8-4007-2950-8/2026/11 https://doi.org/10.1145/3841645.3843433

Fragmented ST-Graph

Removal Initiated

Edges

|

RM

Nodes to Remove

|

c. Entities Removed

Edges to Remove |

𝒱2

d. ST-Graph Retrained

Node Influence |

𝒱 1,2,3 Annotated Nodes

Figure 1: Unlearning on an ST-graph: (a) full graph; (b) consent-revoked nodes marked; (c) record deletion leaves residual model influence; (d) retraining purges it but fragments the graph and distorts remaining features (𝑣 1 –𝑣 3 ).

SIGSPATIAL ’26, November 03–06, 2026, Riverside, CA, USA

Guo et al. 𝒱1 𝒱2 𝒱3 … 𝒱1 1 𝒱2 0 1 𝒱3 0 0 1 …

Steps 1. Construct Enhanced Sub-Graphs (ESC)

2 1

𝓔1

𝒱1 𝒱1… 𝒱32

𝒱1 … 𝒱32

Folds

Cross-Subgraph Edges

a. Original Graph b. Define ST Sub-Graphs Steps 2. Construct Global Ganglion Bridging (GGB)

𝒱2

𝒱1 … 𝒱8

𝒱1 … 𝒱6

𝒱1 … 𝒱8

𝒱1 … 𝒱9

𝒱1… 𝒱8

𝒱1… 𝒱6

𝒱1… 𝒱8

𝒱1… 𝒱9

adjenhanced

Key Nodes

Ganglion Node

𝓔2 𝒱1

𝒱1 𝒱2 𝒱3 … 𝒱1 1 𝒱2 1 1 𝒱3 1 0 1 …

d. Enhance Subgraphs

c. Build ST-Subgraphs

Enhanced Subgraphs

Virtual Nodes 4

adjoriginal

𝒱3

3

Ganglion Nodes 5

6

Key Node List 𝒱4 𝒱10 𝒱15 …

e. Build Ganglion Nodes Steps 3. Training, Integration, and Deployment

Meta-Graph Global Integration Slot

Global Integration Slot

f. Build Meta-Graph and Integration Slot

g. Mount SubModels onto Integration Slot

Inputs

Waitlist

Inputs

… 7

8

Parallel Training

9

Models Frozen

Update

h. Train and Freeze Sub Models

Meta-Graph Global Integration Slot i. Global Integration Slot Training

Global Integration Slot Predictions j. Deployment of CallosumNet

Figure 2: CallosumNet system construction. The original graph (a) is transformed into multiple enhanced local subgraphs (d) through ESC, and then the GGB method adds ganglion nodes and identifies key nodes to construct the meta-graph. Conversely, retraining the entire model from scratch after purging those records (Figure 1(d)) erases the influence but fragments longrange spatial and temporal paths, severely degrading accuracy and interpretability for the remaining users, with a prohibitively high retraining cost. In this study, we propose CallosumNet, inspired by the corpus callosum, a bundle of ∼2×108 axonal fibers that enables the two cerebral hemispheres to specialize independently while staying synchronized [1]. CallosumNet mirrors this organization through subgraph virtual edge reconstruction: it partitions the ST-graph into locally coherent subgraphs, each trained exclusively on its own data like an independent hemisphere, and then reconstructs the severed cross-partition dependencies through biologically-inspired virtual edges and a lightweight meta-graph integration layer—analogous to the corpus callosum bridging the two hemispheres. This design simultaneously enables exact unlearning (each node’s influence is confined to one subgraph) and preserves predictive accuracy (global context is recovered without sharing training data across subgraphs).

2

Related Work

Graph unlearning methods mainly fall into approximate and partitionbased approaches. Approximate methods, such as influence functions [11] and GNNDelete [5], avoid full retraining but provide only approximate removal and do not explicitly handle spatio-temporal dependencies. Partition-based methods, including SISA [2], GraphEraser [4], GraphRevoker [16], and STEPs [6], enable efficient or

exact unlearning by retraining only affected partitions, but partition boundaries can break spatial and temporal dependencies, while fixed aggregation cannot fully recover the lost context. CallosumNet addresses this gap by preserving cross-partition dependencies with virtual ganglion edges and restoring global context through a learnable bridging layer.

3

Methodology

We propose CallosumNet (Figure 2), a partition-and-integrate framework for spatio-temporal graph unlearning. Given an ST-GNN ′ trained on a graph G ′ = (V ′, E ′, X′ ) with features X′ ∈ R𝑇 ×𝑁 ×𝐹 over 𝑇 steps, and a deletion request U = (U𝑁 , U𝐸 ) of nodes and edges to erase, the goal is a model that behaves as if U had never been trained on. CallosumNet consists of two components: Enhanced Subgraph Construction (ESC) for graph decomposition, and Global Ganglion Bridging (GGB) to restore global coherence, organized in a three-step pipeline. 1. Divide (ESC). Enhanced Sub-graph Construction slices the original ST-graph into 𝑀 locally coherent sub-graphs along a correlationdriven backbone and patches every cut with virtual ganglion edges so that high-order spatial–temporal paths are preserved. 2. Link (GGB). Global Ganglion Bridging then assembles the sub-graphs into a lightweight meta-graph: it promotes the top-𝐾 key nodes, the interface boundary nodes, and the newly created ganglion nodes to meta-graph vertices and sparsely wires them together. Each sub-graph is trained independently (and can be frozen afterwards). Their embeddings are routed through a cross-fusion Transformer

Unlearning on Spatio-Temporal Graphs through Subgraph Virtual Edge Reconstruction

that sits on the meta-graph layer and outputs the final prediction. 3. Unlearning on demand. When a deletion request arrives, only the sub-graphs that contain the target nodes/edges are re-trained; the meta-graph parameters are fine-tuned, while untouched sub-graphs remain frozen. 1. Enhanced Subgraph Construction (ESC) decomposes G ′ into 𝑀 localized subgraphs while maintaining global dependencies through virtual ganglion edges. For each directed edge (𝑢, 𝑣) ∈ E ′ , we com-
Í ′ ′ pute a𝑊 -step temporal correlation 𝜌 (𝑢, 𝑣) = 𝑊1 𝑊 𝑡 =1 corr 𝑋𝑡,𝑢 , 𝑋𝑡 +1,𝑣 , Í and extract a backbone path D = arg max P (𝑢,𝑣) ∈ P 𝜌 (𝑢, 𝑣), where P ranges over all Hamiltonian paths on V ′ . Since this maximization is NP-hard, we solve it approximately via a greedy algorithm that iteratively appends the highest-correlation neighbor. Nodes are according to their backbone index: V𝑖 =  assigned to subgraphs ′ ′ 𝑣 ∈ D ⌊(𝑖−1) 𝑁𝑀 ⌋ ≤ idx(𝑣) < ⌊𝑖 𝑁𝑀 ⌋ , where 𝑁 ′ = |V ′ |. Edges internal to V𝑖 form A𝑖 ; the remainder are the cut set Ecut . Isolated vertices are re-connected to their two nearest neighbours on D, and for every (𝑢, 𝑣) ∈ Ecut we insert a virtual ganglion edge to preserve high-order dependencies. Additionally, ESC applies a K-Ring augmentation within each subgraph: boundary nodes (those incident to cut edges) are sorted by their angular positions in a spring-layout embedding and connected sequentially into a closed ring, so that boundary nodes— most affected by partitioning—stay mutually connected. The numh i ber of partitions is chosen by 𝑀 ∗ = arg min𝑀 Δcut + 𝛾 log 𝑀 , Í Δcut = (𝑢,𝑣) ∈ Ecut𝜌 (𝑢, 𝑣), with 𝛾 balancing correlation loss against model parallelism. Theorem 1. Minimising Δcut under equal-size constraints is NPhard, yet the greedy backbone yields a (1 − 𝑒1 ) approximation.
Theorem 2. ESC runs in 𝑂 𝑇 |E ′ |+𝑁 ′2 /𝑀 time and stores 𝑂 (𝑁 ′2 /𝑀) √ edges, which is sub-linear in 𝑁 ′ when 𝑀 = Θ( 𝑁 ′ ). Moreover it re
Δcut tains at least Infointra ≥ 1− TotalCorr TotalCorr of the total temporal correlation.

Proof sketch. Virtual ganglion edges reconnect every isolated vertex to a neighbor with 𝐴′ [𝑢, 𝑣] > 0 (which exists since G ′ is Ð connected), and since E ′ = 𝑖 E𝑖 ∪ Ecut , the retained correlation is exactly TotalCorr − Δcut ; a balanced-cut lower bound Δcut ≥ 𝑐 ′ 𝑀 diam(G ) shows the greedy backbone is near-optimal. 2. Global Ganglion Bridging (GGB) reconstructs global spatiotemporal dependencies by stitching the 𝑀 sub-graphs into a lightweight meta-graph M = (Vmeta, Emeta ) with adjacency matrix Ameta . It integrates three types of vertices: (i) key nodes (top-𝐾 PageRank per sub-graph, 𝐾 = ⌈log |V𝑖 |⌉), (ii) boundary nodes incident to cut edges, and (iii) ganglion nodes, each parameterised by a two-layer MLP with ReLU. Let Eagg denote the original cross-partition edges (i.e., edges in Ecut that now connect boundary nodes across subgraphs), and Ekey the edges among key nodes within the same subgraph. The  meta-graph edges are then defined as Emeta = Eagg ∪ (𝑢, 𝑔), (𝑔, 𝑣) | 𝑔 ∈ Vganglion, 𝑢, 𝑣 ∈ Vkey ∪ Vboundary ∪ Ekey, and are sparsified until |Emeta | ≈ 𝑂 (𝑀 log 𝑀). Each sub-graph is encoded by a frozen STGCN [14] ℎ 𝑣 = STGCN(𝑋 ′ [:, 𝑣, :], A𝑖 ) optimised via Í 2 Lsub = 𝑣 ∈ V𝑖 \U 𝑦 𝑣 − pred𝑆𝑖 (𝑣) 2 + 𝜆reg ∥𝜃 𝑖 ∥ 22 ,

SIGSPATIAL ’26, November 03–06, 2026, Riverside, CA, USA

thereby isolating U. Token-level outputs and ganglion embeddings are fused through a cross-attention Transformer: ℎ final = 𝛼ℎ tok + (1 − 𝛼)ℎ gang ,
𝑦ˆ𝑣 = Transformer {ℎ𝑢′ , ℎ𝑔 }, Ameta , where 𝛼 is a learnable scalar initialised to 0.5 and clipped to [0, 1]. Í Í The overall loss is Lggb = 𝑣 ∥𝑦 𝑣 − 𝑦ˆ𝑣 ∥ 22 + 𝜆1 ∥Ameta ∥ 1 + 𝜆2 𝑔 ∥ℎ𝑔 ∥ 22, where 𝜆1, 𝜆2 ≥ 0 control sparsity and embedding regularization, respectively. Theorem 3 (Prediction error bound). For a graph G ′ partitioned into 𝑀 sub-graphs, √ Δcut 𝑀 𝑦ˆfull − 𝑦ˆGGB 2 ≤ 𝐶 approx 𝐻 𝐿 𝐷𝑔 where 𝐻 , 𝐿, 𝐷𝑔 are the fusion Transformer’s head count, depth, and ganglion width, and 𝐶 approx is an architecture-dependent constant (see proof sketch). This bound stays below 0.05 whenever 𝑀 ≤ 16 and 𝑁 ′ ≤ 104 . Theorem 4 (Unlearning stability). After erasing an arbitrary set U,   E ∥𝑦ˆ𝑣 − 𝑦ˆ𝑣unlearn ∥ 22 𝑣 ∉ U ≤

Δcut |U| (|V ′ | − |U|) 𝐻 𝐿 𝐷𝑔

√︁ and the fine-tune converges to an 𝜀-accurate solution, 𝜀 = 𝐺 2 /(2𝜂 𝑇ep ), for gradient bound 𝐺, learning rate 𝜂, and 𝑇ep fine-tuning epochs. Theorem 5 (Model complexity). GGB contributes O (𝑀 log 𝑀 𝐷𝑔2 ) additional parameters on top of the O (𝑁𝑑 2 /𝑀) parameters of the
sub-graphs, and its per-batch FLOPs are O 𝐵𝑇 [ |E |/𝑀+𝑀 log 𝑀 ] 𝑑 . √ √ With 𝑀 = 𝑁 this yields a sub-linear (≈ 1/ 𝑁 ) speed-up compared to a full-graph ST-GNN. Proof sketch. Theorem 3 follows from the Transformer’s universal approximation property [15]; Theorem 4’s rate is standard Adam analysis under bounded gradients; Theorem 5 counts 𝑂 (𝑑 2 𝑁 /𝑀) parameters per sub-graph and 𝑂 (𝑀 log 𝑀 𝐷𝑔2 ) for the meta-Transformer, √ √ so 𝑀 = 𝑁 gives 𝑂 ( 𝑁𝑑 2 ) total. 3. Unlearning On Demand As shown in Figure 3, upon receiving a deletion request U, CallosumNet executes three steps: (i) Locate and remove. The target nodes and edges are identified and zeroed out in their host subgraph(s); untouched subgraphs remain frozen. (ii) Reconstruct and retrain. ESC re-enhances the affected subgraph(s) with virtual ganglion edges and K-Ring connections, then retrains and freezes them. (iii) Reset GGB. The ganglion MLPs and crossfusion Transformer are reinitialized and fine-tuned (1–3 epochs) on all subgraph outputs, completing the erasure. Since each sub-model trains exclusively on its own partition, U’s training signal resides only in its host subgraph(s) and the GGB layer; retraining both leaves the model identical in distribution to one retrained from ˆ U) = 0, by the same shard-isolation argument as scratch, i.e., 𝐼 (𝑦; SISA [2].

4

Evaluation

We evaluate on four spatio-temporal graph datasets (23–3,220 nodes): RWW [7], PeMS08 [9], Global Weather [12], and Human Mobility Flow [10], against SISA [2], STEPs [6], GraphEraser [4], and GraphRevoker [16]. The gold model retrains the backbone from scratch on the post-deletion graph and thus carries zero residual

SIGSPATIAL ’26, November 03–06, 2026, Riverside, CA, USA

Guo et al.

Virtual Node Nodes to Sub Graph Unlearn ID Virtual Edge SubG3 𝒱18 Nodes to Remove K-Ring SubG7 𝒱32 RM 1. Identification of …V𝒱1… …𝒱18… Nodes for Unlearning … … V𝒱1 𝒱18 1

𝒱18

RM

3

2

Replace!

Drop!

Inputs

4

Virtual Node1

2. Original Sub4. Reconstruct Sub-Graph3 3. Sub-Graph3 Graph3 with Node after Node Removal with Virtual Nodes & Edges to Unlearn & K-Ring

4. New Reconstructed & Frozen Sub-Graph3 Replacement 5

Reset & Update Meta-Graph Global Integration Slot

Global Integration Slot Predictions 6. Deployment: CallosumNet Normal Operation after Fully Completing the Assigned Unlearning Tasks and Resetting Subgraphs + Global Integration Slot

5. Reset & Update Integration Slot

Subgraph Replacement & Global Integration Slot Reset/Update

Unlearning and Subgraph Reconstruction

Figure 3: CallosumNet unlearning process influence; Rate 𝑟 is the fraction of nodes deleted uniformly at random (5 fixed seeds), so 𝑟 =0% isolates partitioning overhead and 𝑟 =10% measures post-unlearning accuracy. As Table 1 summarizes, CallosumNet degrades MAE by only 3.7% on average, versus 28.9% for the best baseline (SISA) and over 170% for the rest; on Mobility (𝑁 =3,220) it also cuts unlearning time from 12,640 s (full retraining) to 3,631 s at 𝑀=16.

5

Conclusion

CallosumNet delivers exact spatio-temporal graph unlearning with near-gold accuracy and sub-linear unlearning cost. Limitations include the static-adjacency assumption and meta-graph overhead at large 𝑀; future work targets dynamic topologies and edge-/featurelevel deletion requests.

Acknowledgments This work was partially supported by the NSF award No.2318641 and No.2112631.

Table 1: Average relative MAE degradation (%) versus the gold model, averaged over four backbones (STGCN [14], STGAT [13], ST-GATV2 [3], ST-SAGE [8]). Negative values indicate that the method outperforms the gold model. Dataset

Rate

SISA

GR

Ours

RWW

0% 10%

+65.3% +276.4% +734.0% +725.8% +57.1% +302.4% +708.9% +664.8%

+0.0% −3.2%

PeMS08

0% 10%

+19.1% +183.9% +107.5% +216.1% +13.7% +211.6% +99.0% +211.2%

+1.1% +1.0%

Weather

0% 10%

+9.6% +10.6%

+66.8% +66.1%

+4.2% +5.1%

Mobility

0% 10%

+27.4% +150.5% +28.2% +152.8%

+75.0% +251.8% +81.3% +231.7%

+7.2% +14.4%

+28.9%

+237.8%

+3.7%

Overall Avg

STEPs

+55.1% +55.3%

+173.5%

GE

+47.5% +49.3%

GE = GraphEraser, GR = GraphRevoker, Ours = CallosumNet.

+304.3%

References [1] Francisco Aboitiz, Arnold B. Scheibel, Robin S. Fisher, and Eran Zaidel. 1992. Fiber Composition of the Human Corpus Callosum. Brain Research 598, 1–2 (1992), 143–153. [2] Lucas Bourtoule, Varun Chandrasekaran, Christopher A Choquette-Choo, Hengrui Jia, Adelin Travers, Baiwu Zhang, David Lie, and Nicolas Papernot. 2021. Machine unlearning. In 2021 IEEE symposium on security and privacy (SP). IEEE, 141–159. [3] Shaked Brody, Uri Alon, and Eran Yahav. 2022. How Attentive are Graph Attention Networks?. In International Conference on Learning Representations (ICLR). [4] Min Chen, Zhikun Zhang, Tianhao Wang, Michael Backes, Mathias Humbert, and Yang Zhang. 2022. Graph unlearning. In Proceedings of the 2022 ACM SIGSAC conference on computer and communications security. 499–513. [5] Jiali Cheng, George Dasoulas, Huan He, Chirag Agarwal, and Marinka Zitnik. 2023. GNNDelete: A General Strategy for Unlearning in Graph Neural Networks. In International Conference on Learning Representations (ICLR). [6] Qiming Guo, Chen Pan, Hua Zhang, and Wenlu Wang. 2025. Efficient Unlearning for Spatio-temporal Graph (Student Abstract). Proceedings of the AAAI Conference on Artificial Intelligence 39, 28 (Apr. 2025), 29382–29384. doi:10.1609/aaai.v39i28. 35259 [7] Qiming Guo and Wenlu Wang. 2024. HydroNet: A Spatio-temporal Graph Neural Network for Modeling Hydraulic Dependencies in Urban Wastewater Systems. In Proceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems. 717–718. [8] William L. Hamilton, Rex Ying, and Jure Leskovec. 2017. Inductive Representation Learning on Large Graphs. In Advances in Neural Information Processing Systems (NeurIPS), Vol. 30. [9] Hengyuan He. 2025. California Traffic Network Datasets: METR-LA, PEMS-BAY, PEMS04 and PEMS08 for Traffic Speed and Flow Analysis. doi:10.21227/j49q-ch56 [10] Yuhao Kang, Song Gao, Yunlei Liang, Mingxiao Li, and Jake Kruse. 2020. Multiscale Dynamic Human Mobility Flow Dataset in the U.S. during the COVID-19 Epidemic. Scientific Data (2020), 1–13. Issue 390. [11] Pang Wei Koh and Percy Liang. 2017. Understanding Black-box Predictions via Influence Functions. In ICML. [12] NOAA Physical Sciences Laboratory. 2025. CPC Global Temperature and Precipitation datasets. Accessed: 2025-05-15. https: //downloads.psl.noaa.gov/Datasets/cpc_global_temp/Summary,https: //downloads.psl.noaa.gov/Datasets/cpc_global_precip [13] Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. 2018. Graph Attention Networks. In International Conference on Learning Representations (ICLR). [14] Bing Yu, Haoteng Yin, and Zhanxing Zhu. 2018. Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting. International Joint Conference on Artificial Intelligence (IJCAI) (2018), 3634–3640. doi:10.24963/ijcai.2018/505 [15] Chulhee Yun, Sashank Bhojanapalli, Ankit Singh Rawat, Sashank J. Reddi, and Sanjiv Kumar. 2020. Are Transformers Universal Approximators of Sequence-toSequence Functions? International Conference on Learning Representations (2020). https://openreview.net/pdf?id=ByxZX0KtDr [16] He Zhang, Bang Wu, Xiangwen Yang, Xingliang Yuan, Xiaoning Liu, and Xun Yi. 2025. Dynamic Graph Unlearning: A General and Efficient Post-Processing Method via Gradient Transformation. In Proceedings of the ACM on Web Conference 2025. 931–944.

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