Position Paper: Challenges and Opportunities in Topological Deep Learning

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

Out-of-Distribution Detection and Data Drift Monitoring using Statistical Process Control

Background: Machine learning (ML) methods often fail with data that deviates from their training distribution. This is a significant concern for ML-enabled devices in clinical settings, where data drift may cause unexpected performance that jeopardizes patient safety. Method: We propose a ML-enabled Statistical Process Control (SPC) framework for out-of-distribution (OOD) detection and drift monitoring. SPC is advantageous as it visually and statistically highlights deviations from the expected distribution. To demonstrate the utility of the proposed framework for monitoring data drift in radiological images, we investigated different design choices, including methods for extracting feature representations, drift quantification, and SPC parameter selection. Results: We demonstrate the effectiveness of our framework for two tasks: 1) differentiating axial vs. non-axial computed tomography (CT) images and 2) separating chest x-ray (CXR) from other modalities. For both tasks, we achieved high accuracy in detecting OOD inputs, with 0.913 in CT and 0.995 in CXR, and sensitivity of 0.980 in CT and 0.984 in CXR. Our framework was also adept at monitoring data streams and identifying the time a drift occurred. In a simulation with 100 daily CXR cases, we detected a drift in OOD input percentage from 0-1% to 3-5% within two days, maintaining a low false-positive rate. Through additional experimental results, we demonstrate the framework's data-agnostic nature and independence from the underlying model's structure. Conclusion: We propose a framework for OOD detection and drift monitoring that is agnostic to data, modality, and model. The framework is customizable and can be adapted for specific applications.

TopoX: A Suite of Python Packages for Machine Learning on Topological Domains

We introduce topox, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. topox consists of three packages: toponetx facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; topoembedx provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; topomodelx is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of topox is available under MIT license at https://github.com/pyt-team.

Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphs

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize \emph{different} types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type and hierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks.

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Uncovering the effects of model initialization on deep model generalization: A study with adult and pediatric Chest X-ray images

Model initialization techniques are vital for improving the performance and reliability of deep learning models in medical computer vision applications. While much literature exists on non-medical images, the impacts on medical images, particularly chest X-rays (CXRs) are less understood. Addressing this gap, our study explores three deep model initialization techniques: Cold-start, Warm-start, and Shrink and Perturb start, focusing on adult and pediatric populations. We specifically focus on scenarios with periodically arriving data for training, thereby embracing the real-world scenarios of ongoing data influx and the need for model updates. We evaluate these models for generalizability against external adult and pediatric CXR datasets. We also propose novel ensemble methods: F-score-weighted Sequential Least-Squares Quadratic Programming (F-SLSQP) and Attention-Guided Ensembles with Learnable Fuzzy Softmax to aggregate weight parameters from multiple models to capitalize on their collective knowledge and complementary representations. We perform statistical significance tests with 95% confidence intervals and p-values to analyze model performance. Our evaluations indicate models initialized with ImageNet-pre-trained weights demonstrate superior generalizability over randomly initialized counterparts, contradicting some findings for non-medical images. Notably, ImageNet-pretrained models exhibit consistent performance during internal and external testing across different training scenarios. Weight-level ensembles of these models show significantly higher recall (p<0.05) during testing compared to individual models. Thus, our study accentuates the benefits of ImageNet-pretrained weight initialization, especially when used with weight-level ensembles, for creating robust and generalizable deep learning solutions.

Semantically Redundant Training Data Removal and Deep Model Classification Performance: A Study with Chest X-rays

Deep learning (DL) has demonstrated its innate capacity to independently learn hierarchical features from complex and multi-dimensional data. A common understanding is that its performance scales up with the amount of training data. Another data attribute is the inherent variety. It follows, therefore, that semantic redundancy, which is the presence of similar or repetitive information, would tend to lower performance and limit generalizability to unseen data. In medical imaging data, semantic redundancy can occur due to the presence of multiple images that have highly similar presentations for the disease of interest. Further, the common use of augmentation methods to generate variety in DL training may be limiting performance when applied to semantically redundant data. We propose an entropy-based sample scoring approach to identify and remove semantically redundant training data. We demonstrate using the publicly available NIH chest X-ray dataset that the model trained on the resulting informative subset of training data significantly outperforms the model trained on the full training set, during both internal (recall: 0.7164 vs 0.6597, p<0.05) and external testing (recall: 0.3185 vs 0.2589, p<0.05). Our findings emphasize the importance of information-oriented training sample selection as opposed to the conventional practice of using all available training data.

Does image resolution impact chest X-ray based fine-grained Tuberculosis-consistent lesion segmentation?

Deep learning (DL) models are becoming state-of-the-art in segmenting anatomical and disease regions of interest (ROIs) in medical images, particularly chest X-rays (CXRs). However, these models are reportedly trained on reduced image resolutions citing reasons for the lack of computational resources. Literature is sparse considering identifying the optimal image resolution to train these models for the task under study, particularly considering segmentation of Tuberculosis (TB)-consistent lesions in CXRs. In this study, we used the (i) Shenzhen TB CXR dataset, investigated performance gains achieved through training an Inception-V3-based UNet model using various image/mask resolutions with/without lung ROI cropping and aspect ratio adjustments, and (ii) identified the optimal image resolution through extensive empirical evaluations to improve TB-consistent lesion segmentation performance. We proposed a combinatorial approach consisting of storing model snapshots, optimizing test-time augmentation (TTA) methods, and selecting the optimal segmentation threshold to further improve performance at the optimal resolution. We emphasize that (i) higher image resolutions are not always necessary and (ii) identifying the optimal image resolution is indispensable to achieve superior performance for the task under study.

Generalizability of Deep Adult Lung Segmentation Models to the Pediatric Population: A Retrospective Study

Lung segmentation in chest X-rays (CXRs) is an important prerequisite for improving the specificity of diagnoses of cardiopulmonary diseases in a clinical decision support system. Current deep learning (DL) models for lung segmentation are trained and evaluated on CXR datasets in which the radiographic projections are captured predominantly from the adult population. However, the shape of the lungs is reported to be significantly different for pediatrics across the developmental stages from infancy to adulthood. This might result in age-related data domain shifts that would adversely impact lung segmentation performance when the models trained on the adult population are deployed for pediatric lung segmentation. In this work, our goal is to analyze the generalizability of deep adult lung segmentation models to the pediatric population and improve performance through a systematic combinatorial approach consisting of CXR modality-specific weight initializations, stacked generalization, and an ensemble of the stacked generalization models. Novel evaluation metrics consisting of Mean Lung Contour Distance and Average Hash Score are proposed in addition to the Multi-scale Structural Similarity Index Measure, Intersection of Union, and Dice metrics to evaluate segmentation performance. We observed a significant improvement (p < 0.05) in cross-domain generalization through our combinatorial approach. This study could serve as a paradigm to analyze the cross-domain generalizability of deep segmentation models for other medical imaging modalities and applications.