Shreyas N. Samaga

Cheng Xin, Soham Mukherjee, Shreyas N. Samaga et al.

$1$-parameter persistent homology, a cornerstone in Topological Data Analysis (TDA), studies the evolution of topological features such as connected components and cycles hidden in data. It has been applied to enhance the representation power of deep learning models, such as Graph Neural Networks (GNNs). To enrich the representations of topological features, here we propose to study $2$-parameter persistence modules induced by bi-filtration functions. In order to incorporate these representations into machine learning models, we introduce a novel vector representation called Generalized Rank Invariant Landscape (GRIL) for $2$-parameter persistence modules. We show that this vector representation is $1$-Lipschitz stable and differentiable with respect to underlying filtration functions and can be easily integrated into machine learning models to augment encoding topological features. We present an algorithm to compute the vector representation efficiently. We also test our methods on synthetic and benchmark graph datasets, and compare the results with previous vector representations of $1$-parameter and $2$-parameter persistence modules. Further, we augment GNNs with GRIL features and observe an increase in performance indicating that GRIL can capture additional features enriching GNNs. We make the complete code for the proposed method available at https://github.com/soham0209/mpml-graph.

Mathilde Papillon, Mustafa Hajij, Helen Jenne et al.

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.

Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou et al.

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications.

Mustafa Hajij, Mathilde Papillon, Florian Frantzen et al.

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://pyt-team.github.io/}{https://pyt-team.github.io/.

Tamal K. Dey, Shreyas N. Samaga

In this paper, we propose Quasi Zigzag Persistent Homology (QZPH) as a framework for analyzing time-varying data by integrating multiparameter persistence and zigzag persistence. To this end, we introduce a stable topological invariant that captures both static and dynamic features at different scales. We present an algorithm to compute this invariant efficiently. We show that it enhances the machine learning models when applied to tasks such as sleep-stage detection, demonstrating its effectiveness in capturing the evolving patterns in time-varying datasets.

Shreyas N. Samaga, Gilberto Gonzalez Arroyo, Tamal K. Dey

The factual reliability of Large Language Models (LLMs) remains a critical barrier to their adoption in high-stakes domains due to their propensity to hallucinate. Current detection methods often rely on surface-level signals from the model's output, overlooking the failures that occur within the model's internal reasoning process. In this paper, we introduce a new paradigm for hallucination detection by analyzing the dynamic topology of the evolution of model's layer-wise attention. We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence, a tool from Topological Data Analysis, to extract a topological signature. Our core hypothesis is that factual and hallucinated generations exhibit distinct topological signatures. We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines. Furthermore, our analysis reveals that these topological signatures are generalizable across different models and hallucination detection is possible only using structural signatures from partial network depth.

Soham Mukherjee, Shreyas N. Samaga, Cheng Xin et al.

End-to-end topological learning using 1-parameter persistence is well-known. We show that the framework can be enhanced using 2-parameter persistence by adopting a recently introduced 2-parameter persistence based vectorization technique called GRIL. We establish a theoretical foundation of differentiating GRIL producing D-GRIL. We show that D-GRIL can be used to learn a bifiltration function on standard benchmark graph datasets. Further, we exhibit that this framework can be applied in the context of bio-activity prediction in drug discovery.

Yukti Makhija, Samarth Bhatia, Shalendra Singh et al.

Many countries are now experiencing the third wave of the COVID-19 pandemic straining the healthcare resources with an acute shortage of hospital beds and ventilators for the critically ill patients. This situation is especially worse in India with the second largest load of COVID-19 cases and a relatively resource-scarce medical infrastructure. Therefore, it becomes essential to triage the patients based on the severity of their disease and devote resources towards critically ill patients. Yan et al. 1 have published a very pertinent research that uses Machine learning (ML) methods to predict the outcome of COVID-19 patients based on their clinical parameters at the day of admission. They used the XGBoost algorithm, a type of ensemble model, to build the mortality prediction model. The final classifier is built through the sequential addition of multiple weak classifiers. The clinically operable decision rule was obtained from a 'single-tree XGBoost' and used lactic dehydrogenase (LDH), lymphocyte and high-sensitivity C-reactive protein (hs-CRP) values. This decision tree achieved a 100% survival prediction and 81% mortality prediction. However, these models have several technical challenges and do not provide an out of the box solution that can be deployed for other populations as has been reported in the "Matters Arising" section of Yan et al. Here, we show the limitations of this model by deploying it on one of the largest datasets of COVID-19 patients containing detailed clinical parameters collected from India.