Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networks

Carlo Abate; Filippo Maria Bianchi; Ivan Marisca

arxiv: 2512.12642 · v2 · submitted 2025-12-14 · 💻 cs.LG

Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networks

Carlo Abate , Ivan Marisca , Filippo Maria Bianchi This is my paper

Pith reviewed 2026-05-16 22:45 UTC · model grok-4.3

classification 💻 cs.LG

keywords graph poolinggraph neural networksPyTorch Geometricsoftware librarySRCL decompositionhierarchical poolingGNN models

0 comments

The pith

Torch Geometric Pool unifies graph pooling methods through an SRCL interface in PyTorch Geometric.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents Torch Geometric Pool as a library built on PyTorch Geometric to handle graph pooling in neural networks. Pooling approaches differ widely in how they group nodes into supernodes, process batches, produce outputs, and incorporate extra losses. These inconsistencies complicate comparing methods or reusing model code. tgp introduces a shared interface by breaking pooling down into Select-Reduce-Connect-Lift steps. The library supplies twenty hierarchical poolers, uniform output structures, readout modules, dense pooling support, and tools for caching and pre-coarsening.

Core claim

Torch Geometric Pool supplies a common software interface for graph pooling by decomposing operations into the Select-Reduce-Connect-Lift (SRCL) sequence, which accommodates twenty distinct hierarchical poolers along with standardized outputs and utilities for batch handling, readout, and pre-coarsening.

What carries the argument

The SRCL decomposition, which factors pooling into node selection, feature reduction, edge reconnection, and output lifting stages to create a uniform software contract.

If this is right

Model code can switch between different pooling methods by changing only the pooler object.
Direct comparisons of pooling techniques become possible because all methods return objects with the same structure.
Batched and dense graphs can be pooled in both unbatched and batched modes using the same interface.
Caching and pre-coarsening workflows can be applied uniformly across all supported poolers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

A similar decomposition pattern could standardize other variable GNN operations such as message passing or readout.
Future pooling methods could be designed from the start to map cleanly onto SRCL steps for immediate compatibility.
Benchmarking suites might adopt the library's output format to reduce reimplementation effort across papers.

Load-bearing premise

The SRCL decomposition can represent the core differences among existing pooling methods without forcing awkward adaptations or loss of behavior for any of them.

What would settle it

A well-known pooling method whose node assignment, batch behavior, or output structure cannot be expressed through SRCL steps without changing its original functionality or results.

Figures

Figures reproduced from arXiv: 2512.12642 by Carlo Abate, Filippo Maria Bianchi, Ivan Marisca.

**Figure 2.** Figure 2: Pooling examples with different operators. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Node clustering architecture. The model is trained for up to 2000 epochs using the Adam optimizer [26] with a learning rate of 5 · 10−4 and the ReduceLROnPlateau scheduler2 , with early stopping (patience of 500 epochs). After training, we extract hard cluster assignments via an argmax operation on the matrix S and evaluate quality using the Normalized Mutual Information (NMI). D.2 Node Classification We a… view at source ↗

**Figure 4.** Figure 4: Node classification architecture. sum pooling followed by a 3-layer MLP with a dropout of 0.5. In the deeper GNN architecture with multiple pooling layers presented in Section 4.5, the same [Pool - MP] block has been replicated multiple times. A schematic depiction of the architecture is reported in [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗

**Figure 5.** Figure 5: Architecture for graph-level tasks (graph classification and regression). [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗

**Figure 6.** Figure 6: Architecture for graph-level tasks with pre-coarsening. [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗

read the original abstract

Torch Geometric Pool (tgp) is a pooling library built on top of PyTorch Geometric. Graph pooling methods differ in how they assign nodes to supernodes, how they handle batches, what they return after pooling, and whether they expose auxiliary losses. These differences make it hard to compare methods or reuse the same model code across them. tgp addresses this problem with a common software interface based on the Select-Reduce-Connect-Lift (SRCL) decomposition. The library provides 20 hierarchical poolers, standardized output objects, standalone readout modules, support for dense poolers in batched and unbatched mode, and workflows for caching and pre-coarsening. It is released under the MIT license on GitHub and PyPI, with comprehensive documentation, tutorials, and examples.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a practical software release that unifies 20 existing pooling methods under a shared SRCL interface on top of PyTorch Geometric.

read the letter

This paper releases Torch Geometric Pool, a library that gives a single interface to 20 different graph pooling methods inside PyTorch Geometric. The key move is the Select-Reduce-Connect-Lift breakdown, which lets them standardize node assignment, batch handling, and what gets returned. The library does the basics right: uniform output objects, support for dense and batched modes, caching, and pre-coarsening. It also ships standalone readout modules and solid documentation with examples. That kind of packaging reduces the friction when someone wants to try different poolers in the same model. Nothing here is a new algorithm. The contribution is the common interface and the fact that they made it work across the set of methods. The abstract shows no internal contradictions, and the SRCL approach looks like a reasonable way to factor the differences. A minor question is how well the decomposition holds up once people start using it on less common pooling variants or custom extensions. The paper presents it as covering the main cases without awkward fits. This is useful for anyone doing comparative experiments with graph neural networks. A reader who needs to swap pooling layers without rewriting training loops will find it directly helpful. I would take it to a reading group focused on practical GNN tools. It should go to peer review because the engineering is reproducible and the standardization claim can be checked against the code.

Referee Report

0 major / 2 minor

Summary. The manuscript introduces Torch Geometric Pool (tgp), a PyTorch Geometric library that standardizes graph pooling for GNNs via the Select-Reduce-Connect-Lift (SRCL) decomposition. It supplies a common interface for node assignment, batch handling, return values, and auxiliary losses; implements 20 hierarchical poolers; provides standardized output objects, standalone readout modules, dense/batched support, and caching/pre-coarsening workflows; and releases the code under MIT with documentation and examples.

Significance. If the implementation matches the described interface, the library would reduce fragmentation across pooling methods, enabling direct reuse of model code and fairer comparisons. The explicit SRCL decomposition, 20 concrete implementations, and engineering features (batched/dense modes, standardized outputs) constitute a useful contribution to the GNN tooling ecosystem, with the open release and tutorials further supporting reproducibility.

minor comments (2)

[Abstract] Abstract: the phrase '20 hierarchical poolers' would be more informative if accompanied by a short enumerated list or reference to a table in the main text.
[Introduction] The description of SRCL would benefit from a single running example that shows the four steps on a small graph, to make the decomposition immediately concrete for readers unfamiliar with the prior literature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review and the recommendation to accept the manuscript. The assessment accurately captures the library's goals of standardizing hierarchical pooling via the SRCL interface and the practical engineering features that support reproducibility and reuse.

Circularity Check

0 steps flagged

No significant circularity; engineering interface release

full rationale

The manuscript introduces a PyTorch Geometric library that standardizes graph pooling via the SRCL decomposition. No equations, derivations, fitted parameters, or predictions appear in the provided text. The SRCL interface is offered as an engineering abstraction that unifies existing methods' node assignment, batch handling, and return values; it is not derived from or reduced to any internal result by construction. No self-citations function as load-bearing uniqueness theorems or ansatzes. The contribution is self-contained as a software implementation with 20 poolers, standardized outputs, and documentation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The library adds no new mathematical free parameters, axioms, or invented entities; it re-expresses existing pooling algorithms through a common software interface built on PyTorch Geometric.

axioms (1)

domain assumption PyTorch Geometric supplies correct base graph data structures and operations
The library is explicitly built on top of PyTorch Geometric.

pith-pipeline@v0.9.0 · 5431 in / 1122 out tokens · 42959 ms · 2026-05-16T22:45:08.604954+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages · 4 internal anchors

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Abate and F

C. Abate and F. M. Bianchi. Maxcutpool: differentiable feature-aware maxcut for pooling in graph neural networks. InThe Thirteenth International Conference on Learning Representations, 2025. URL https://openreview. net/forum?id=xlbXRJ2XCP

work page 2025

[2] [2]

Bacciu and L

D. Bacciu and L. Di Sotto. A non-negative factorization approach to node pooling in graph convolutional neural networks. InAI* IA 2019–Advances in Artificial Intelligence: XVIIIth International Conference of the Italian Association for Artificial Intelligence, Rende, Italy, November 19–22, 2019, Proceedings 18, pages 294–306. Springer, 2019

work page 2019

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Bacciu, A

D. Bacciu, A. Conte, and F. Landolfi. Graph pooling with maximum-weight k-independent sets. InThirty-Seventh AAAI Conference on Artificial Intelligence, 2023

work page 2023

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F. M. Bianchi. Simplifying clustering with graph neural networks.arXiv preprint arXiv:2207.08779, 2022

work page arXiv 2022

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F. M. Bianchi and V . Lachi. The expressive power of pooling in graph neural networks. InAdvances in Neural Information Processing Systems, volume 36, pages 71603–71618, 2023

work page 2023

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F. M. Bianchi, D. Grattarola, and C. Alippi. Spectral clustering with graph neural networks for graph pooling. In International conference on machine learning, pages 874–883. PMLR, 2020

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F. M. Bianchi, D. Grattarola, L. Livi, and C. Alippi. Hierarchical representation learning in graph neural networks with node decimation pooling.IEEE Transactions on Neural Networks and Learning Systems, 33(5):2195–2207, 2020

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F. M. Bianchi, D. Grattarola, L. Livi, and C. Alippi. Graph neural networks with convolutional arma filters.IEEE transactions on pattern analysis and machine intelligence, 44(7):3496–3507, 2021

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F. M. Bianchi, C. Gallicchio, and A. Micheli. Pyramidal reservoir graph neural network.Neurocomputing, 470: 389–404, 2022. ISSN 0925-2312. doi: https://doi.org/10.1016/j.neucom.2021.04.131. 10

work page doi:10.1016/j.neucom.2021.04.131 2022

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work page internal anchor Pith review Pith/arXiv arXiv 2021

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Castellana and F

D. Castellana and F. M. Bianchi. Bn-pool: a bayesian nonparametric approach to graph pooling, 2025. URL https://arxiv.org/abs/2501.09821

work page arXiv 2025

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Defferrard, L

M. Defferrard, L. Martin, R. Pena, and N. Perraudin. Pygsp: Graph signal processing in python, Oct. 2017. URL https://doi.org/10.5281/zenodo.1003158

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F. Diehl. Edge contraction pooling for graph neural networks.arXiv preprint arXiv:1905.10990, 2019

work page internal anchor Pith review Pith/arXiv arXiv 1905

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A. Duval and F. Malliaros. Higher-order clustering and pooling for graph neural networks. InProceedings of the 31st ACM international conference on information & knowledge management, pages 426–435, 2022

work page 2022

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V . P. Dwivedi, L. Rampášek, M. Galkin, A. Parviz, G. Wolf, A. T. Luu, and D. Beaini. Long range graph benchmark.Advances in Neural Information Processing Systems, 35:22326–22340, 2022

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M. Fey and J. E. Lenssen. Fast graph representation learning with PyTorch Geometric. InICLR Workshop on Representation Learning on Graphs and Manifolds, 2019

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X. Fu, J. Zhang, Z. Meng, and I. King. Magnn: Metapath aggregated graph neural network for heterogeneous graph embedding. InProceedings of the web conference 2020, pages 2331–2341, 2020

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E. Gal, M. Eliasof, C.-B. Schönlieb, I. I. Kyrchei, E. Haber, and E. Treister. Towards efficient training of graph neural networks: A multiscale approach.arXiv preprint arXiv:2503.19666, 2025

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Gao and S

H. Gao and S. Ji. Graph u-nets. Ininternational conference on machine learning, pages 2083–2092. PMLR, 2019

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M. Gori, G. Monfardini, and F. Scarselli. A new model for learning in graph domains. InProceedings. 2005 IEEE international joint conference on neural networks, 2005., volume 2, pages 729–734. IEEE, 2005. doi: 10.1109/IJCNN.2005.1555942

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Grattarola, D

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J. B. Hansen and F. M. Bianchi. Total variation graph neural networks. InInternational Conference on Machine Learning, pages 12445–12468. PMLR, 2023

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W. Hu, M. Fey, M. Zitnik, Y . Dong, H. Ren, B. Liu, M. Catasta, and J. Leskovec. Open graph benchmark: Datasets for machine learning on graphs.Advances in neural information processing systems, 33:22118–22133, 2020

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F. Landolfi. Revisiting edge pooling in graph neural networks. InESANN, 2022

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D. Lim, F. Hohne, X. Li, S. L. Huang, V . Gupta, O. Bhalerao, and S. N. Lim. Large scale learning on non- homophilous graphs: New benchmarks and strong simple methods.Advances in Neural Information Processing Systems, 34:20887–20902, 2021

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C. Morris, N. M. Kriege, F. Bause, K. Kersting, P. Mutzel, and M. Neumann. Tudataset: A collection of benchmark datasets for learning with graphs. InICML 2020 Workshop on Graph Representation Learning and Beyond (GRL+ 2020), 2020

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E. Noutahi, D. Beaini, J. Horwood, S. Giguère, and P. Tossou. Towards interpretable sparse graph representation learning with laplacian pooling.arXiv preprint arXiv:1905.11577, 2019

work page arXiv 1905

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O. Platonov, D. Kuznedelev, M. Diskin, A. Babenko, and L. Prokhorenkova. A critical look at the evaluation of GNNs under heterophily: Are we really making progress? InThe Eleventh International Conference on Learning Representations, 2023. 11

work page 2023

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Ranjan, S

E. Ranjan, S. Sanyal, and P. Talukdar. Asap: Adaptive structure aware pooling for learning hierarchical graph representations. InProceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 5470–5477, 2020

work page 2020

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Scarselli, M

F. Scarselli, M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini. The graph neural network model.IEEE transactions on neural networks, 20(1):61–80, 2008

work page 2008

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Tsitsulin, J

A. Tsitsulin, J. Palowitch, B. Perozzi, and E. Müller. Graph clustering with graph neural networks.J. Mach. Learn. Res., 24:127:1–127:21, 2023

work page 2023

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M. Wang, D. Zheng, Z. Ye, Q. Gan, M. Li, X. Song, J. Zhou, C. Ma, L. Yu, Y . Gai, et al. Deep graph library: A graph-centric, highly-performant package for graph neural networks.arXiv preprint arXiv:1909.01315, 2019

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