Title: HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell data
Venue: NeurIPS 2025
Accepted: yes
Keywords: Geometric Deep Learning

Point Clouds

Multi-View Learning

High-Dimensional Data Analysis

Single-Cell Data
Abstract: In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for every patient), necessitating models that can process large, high-dimensional point-clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric and topological information. In contrast,  HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We  show that geometric and topological information is preserved in this framework both theoretically and empirically.  We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a methodology, HiPoNet, for analysing high-dimensional point clouds. This proceeds by constructing several different Vietoris-Rips complexes that capture different aspects of the data, then vectorising these simplicial complexes using simplicial wavelets. The vectorisations of the simplicial complexes are then concatenated and used as input to a multilayer perceptron, with the entire stack being trained (end-to-end) on the appropriate classification problem for that point cloud.\n\nThe authors then apply their methodology to three datasets of medical data that feature large numbers of datapoints per patient, with each datapoint being information about a cell from that patient.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n* The empirical performance of HiPoNet described in Section 5 is the strongest part of the paper\n\n## Weaknesses\n\n* The theoretical justifications presented throughout the paper are weak, and basic definitions are often either confusing or confused. See the questions below for some examples.\n\n* The choice to apply the absolute value to all of the wavelet transforms, just after equation 4, lacks conceptual justification.\n\n* The theoretical analysis in Section 4 lacks detail and precision -- it is vague and sketchy --  and is all about heat flow on simplicial complexes whereas the algorithm presented does not involve heat flow at all. The purported justification for analysing heat flow is that the algorithm uses random walks, which are proxies for the diffusion of heat, but given the way the \"random walks\" are calculated (see below), it is not clear, at least to me, that this link is valid.\n\n* In the definition of \"random walk matrices\" $P_k$  just below equation 3, the authors choose to ignore all signs, even in the oriented case. This is likely to make a very big difference, and requires analysis and/or conceptual justification.\n\nQUESTIONS:\nIs your definition of upper adjacent neighbours correct? The definition in words does not match the definition in mathematical symbols unless every pair of k-simplices that meets along a (k-1)-simplex together span a (k+1)-simplex, which is quite close to the notion of the simplicial complex being a Kan complex. (Also (k+1)-simplices have k+2 vertices, so there is a typo in the formula there.)\n\nCan you analyse or give a conceptual justification for the definition of $P_k$ in the oriented case, just below equation 3? Also, in the non-oriented case, are you working with integer coefficients or with coefficients in the integers modulo 2? The latter would be more conventional, as otherwise e.g. the boundary operator won't square to zero in general.\n\nIn algorithm 1, on lines 7 and 8, you construct features by successively applying boundary operators. But doesn't the boundary operator square to zero? That is: why isn't $B_k^T B_{k-1}^T$ zero?\n\nIn the section, \"Interpretability of Learned Features\", currently your logic goes the wrong way around: you identify that known-meaningful biomarkers have high importance across views. Are there other features that have high importance across views? Can you determine whether or not these are known to be meaningful?\n\nLIMITATIONS:\nThere is no limitations section. I assume that this is in the Appendices, which were not provided.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-26"}

comments: SUMMARY:
The paper introduces a novel neural network architecture specifically designed for analyzing high-dimensional point clouds, particularly from single-cell and spatial transcriptomics data. Contributions include: 1. HiPoNet learns multiple weighted views of high-dimensional data. 2. HiPoNet uses higher-order simplicial complexes to model data.

STRENGTHS AND WEAKNESSES:
Strengths:
1. It models high-dimensional point clouds using simplicial complexes rather than standard graphs.
2. The learnable feature reweighting mechanism allows the model to generate multiple views of the data.
3. This paper outperform other methods across different real-world datasets. 

Weaknesses:
1. The architecture becomes computationally intensive when processing multiple learned views.
2. The model is heavily specialized to biological data, which may not be suitable for other types of data.

QUESTIONS:
1. Can authors explain computational bottlenecks of HiPoNet in terms of memory and runtime for large-scale datasets, especially when using multiple views and higher-order simplices?
2. Can authors explain how robust is HiPoNet to changes in the Vietoris–Rips threshold, kernel bandwidth, and number of views?
3. Can authors explain the possibility of applying this method to non-biological high-dimensional point clouds?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

comments: SUMMARY:
Authors propose HiPoNet, an end to end differentiable neural net for regression, classification, and representation learning on higher dimensional point clouds. The key to their approach lies in modeling the data as a simplicial complex instead of a graph to capture higher-order relationships between cells. The authors showcase its applicability by modeling three different single-cell datasets (biological point clouds). Quantitative results showcase strong performance of the proposed approach.

STRENGTHS AND WEAKNESSES:
strengths:
- combination of using multi-view reweighting, simplicial complex and wavelets is novel and opens up applications for other areas like surface reconstruction
- comprehensive baseline comparisons and ablation studies


weaknesses:
- simplicial complex computation is compute heavy
- dataset is limited to biological data and makes it harder to judge the generalizability aspect of HiPoNet
- background information about the differentiable Vietoris-Rips complex is scarce

QUESTIONS:
1. Have the authors tried a simple clustering-based approach as a baseline? What about a simple linear regression baseline?
2. How did you decide the optimal number of views for feature weighting?
3. From the ablation studies it seems that the methods requires careful tuning of number of views, and epsilon threshold. How do you suggest these parameters will change when a completely new dataset is used? What about kernel bandwidth?
4. Can you elaborate on your custom differentiable Vietoris-Rips implementation? I'm trying to understand your end-to-end differentiable claim

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work presents HiPoNet, a method to model point cloud data using higher-order simplicial complexes. The method can represent the data using multiple views, learn interactions between these views through simplicial complexes, and aggregate features using multiscale wavelets. The approach is evaluated across a broad set of tasks, including classification of spatial transcriptomics data, demonstrating strong performance.\n\nWhile I found the biological motivation and empirical results compelling, I must acknowledge that I do not fully grasp the mathematical foundations behind simplicial complexes and wavelet transforms. My evaluation therefore focuses on the modeling motivation, empirical performance, and clarity of presentation.\n\nSTRENGTHS AND WEAKNESSES:\n**Strenghts**\n\n* The intuition of using multiple views of the data is compelling, e.g., scRNA-seq provides a high resolution picture of the active biological processes in each single-cell, and so having multiple views may allow the model to decouple multiple relevant processes for the task at hand. This is in contrast to existing dimensionality reduction algorithms such as tSNE and UMAP, which operate on a single view of the entire transcriptome in a task-independent way and so some features may therefore be convoluted and partially irrelevant for the given task.\n* The benchmark is fairly comprehensive and demonstrated results are impressive, i.e. HiPoNet seems to outperform existing methods across a broad range of tasks. In particular, I was surprised by the large margin demonstrated in the spatial transcriptomics tasks, which have direct clinical relevance. For example, HiPoNet seems to outperform the next best performing baseline by ~20% AUC ROC on the Melanoma response task. Nonetheless, the benchmark could be more transparent in terms of task description, data splits, and class imbalances (see Weaknesses).\n* The ablation results are compelling and help illustrate the contribution of key components, e.g. using multiple views.\n\n\n\n**Weaknesses**\n\n* In terms of the evaluation of the method, the data splits are unclear and, for some of the tasks (e.g. inferring patient recurrence) the total number of patients is fairly low (e.g. 54 melanoma patients). How was the data split and what are the class distributions? For the PDO task, i.e. inferring treatment administered to patient-derived organoids, the total number of patients is 12, while the total number of cultures is 1,678. What are the sampling units in this task (patients or cultures?) Was each culture treated in a different way? What are the treatments that the model is tasked to distinguish? Overall, could the authors show that the evaluation scores reflect improved generalization performance rather than overfitting? In summary, it is difficult to fully interpret the reported results without more transparency around dataset splits, class distributions, and evaluation units. A clear table summarizing each task (dataset, input modality, sample size, number of classes, class imbalance, and split strategy) would greatly improve clarity and interpretability.\n* This is not a weakness per se, but a request out of curiosity. The authors motivate the use of simplicial wavelet transforms arguing that more standard approaches like message-passing neural networks suffer from oversmoothing and oversquashing effects. Could this modelling choice be empirically demonstrated?\n\nQUESTIONS:\n* Please double-check the Appendix references, e.g. L318: \"Detailed descriptions of this data is provided in Appendix F\". This should point to Appendix G instead. Similar for other appendices (e.g. Appendix I does not point to the limitations)\n\nLIMITATIONS:\nThe limitations are presented in Appendix L", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-10"}