ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.

DBHP: Trajectory Imputation in Multi-Agent Sports Using Derivative-Based Hybrid Prediction

Many spatiotemporal domains handle multi-agent trajectory data, but in real-world scenarios, collected trajectory data are often partially missing due to various reasons. While existing approaches demonstrate good performance in trajectory imputation, they face challenges in capturing the complex dynamics and interactions between agents due to a lack of physical constraints that govern realistic trajectories, leading to suboptimal results. To address this issue, the paper proposes a Derivative-Based Hybrid Prediction (DBHP) framework that can effectively impute multiple agents' missing trajectories. First, a neural network equipped with Set Transformers produces a naive prediction of missing trajectories while satisfying the permutation-equivariance in terms of the order of input agents. Then, the framework makes alternative predictions leveraging velocity and acceleration information and combines all the predictions with properly determined weights to provide final imputed trajectories. In this way, our proposed framework not only accurately predicts position, velocity, and acceleration values but also enforces the physical relationship between them, eventually improving both the accuracy and naturalness of the predicted trajectories. Accordingly, the experiment results about imputing player trajectories in team sports show that our framework significantly outperforms existing imputation baselines.

Discrete Dictionary-based Decomposition Layer for Structured Representation Learning

Neuro-symbolic neural networks have been extensively studied to integrate symbolic operations with neural networks, thereby improving systematic generalization. Specifically, Tensor Product Representation (TPR) framework enables neural networks to perform differentiable symbolic operations by encoding the symbolic structure of data within vector spaces. However, TPR-based neural networks often struggle to decompose unseen data into structured TPR representations, undermining their symbolic operations. To address this decomposition problem, we propose a Discrete Dictionary-based Decomposition (D3) layer designed to enhance the decomposition capabilities of TPR-based models. D3 employs discrete, learnable key-value dictionaries trained to capture symbolic features essential for decomposition operations. It leverages the prior knowledge acquired during training to generate structured TPR representations by mapping input data to pre-learned symbolic features within these dictionaries. D3 is a straightforward drop-in layer that can be seamlessly integrated into any TPR-based model without modifications. Our experimental results demonstrate that D3 significantly improves the systematic generalization of various TPR-based models while requiring fewer additional parameters. Notably, D3 outperforms baseline models on the synthetic task that demands the systematic decomposition of unseen combinatorial data.

Attention-based Iterative Decomposition for Tensor Product Representation

In recent research, Tensor Product Representation (TPR) is applied for the systematic generalization task of deep neural networks by learning the compositional structure of data. However, such prior works show limited performance in discovering and representing the symbolic structure from unseen test data because their decomposition to the structural representations was incomplete. In this work, we propose an Attention-based Iterative Decomposition (AID) module designed to enhance the decomposition operations for the structured representations encoded from the sequential input data with TPR. Our AID can be easily adapted to any TPR-based model and provides enhanced systematic decomposition through a competitive attention mechanism between input features and structured representations. In our experiments, AID shows effectiveness by significantly improving the performance of TPR-based prior works on the series of systematic generalization tasks. Moreover, in the quantitative and qualitative evaluations, AID produces more compositional and well-bound structural representations than other works.

Punctuation Restoration Improves Structure Understanding without Supervision

Unsupervised learning objectives like language modeling and de-noising constitute a significant part in producing pre-trained models that perform various downstream applications from natural language understanding to conversational tasks. However, despite impressive generative capabilities of recent large language models, their abilities to capture syntactic or semantic structure within text lag behind. We hypothesize that the mismatch between linguistic performance and competence in machines is attributable to insufficient transfer of linguistic structure knowledge to computational systems with currently popular pre-training objectives. We show that punctuation restoration as a learning objective improves in- and out-of-distribution performance on structure-related tasks like named entity recognition, open information extraction, chunking, and part-of-speech tagging. Punctuation restoration is an effective learning objective that can improve structure understanding and yield a more robust structure-aware representations of natural language.

Structured Language Generation Model for Robust Structure Prediction

Previous work in structured prediction (e.g. NER, information extraction) using single model make use of explicit dataset information, which helps boost in-distribution performance but is orthogonal to robust generalization in real-world situations. To overcome this limitation, we propose the Structured Language Generation Model (SLGM), a framework that reduces sequence-to-sequence problems to classification problems via methodologies in loss calibration and decoding method. Our experimental results show that SLGM is able to maintain performance without explicit dataset information, follow and potentially replace dataset-specific fine-tuning.

Topology-Informed Graph Transformer

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.

A Gated MLP Architecture for Learning Topological Dependencies in Spatio-Temporal Graphs

Graph Neural Networks (GNNs) and Transformer have been increasingly adopted to learn the complex vector representations of spatio-temporal graphs, capturing intricate spatio-temporal dependencies crucial for applications such as traffic datasets. Although many existing methods utilize multi-head attention mechanisms and message-passing neural networks (MPNNs) to capture both spatial and temporal relations, these approaches encode temporal and spatial relations independently, and reflect the graph's topological characteristics in a limited manner. In this work, we introduce the Cycle to Mixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial invariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP). The Cy2Mixer is composed of three blocks based on MLPs: A message-passing block for encapsulating spatial information, a cycle message-passing block for enriching topological information through cyclic subgraphs, and a temporal block for capturing temporal properties. We bolster the effectiveness of Cy2Mixer with mathematical evidence emphasizing that our cycle message-passing block is capable of offering differentiated information to the deep learning model compared to the message-passing block. Furthermore, empirical evaluations substantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art performances across various traffic benchmark datasets.

Model-Free Reconstruction of Capacity Degradation Trajectory of Lithium-Ion Batteries Using Early Cycle Data

Early degradation prediction of lithium-ion batteries is crucial for ensuring safety and preventing unexpected failure in manufacturing and diagnostic processes. Long-term capacity trajectory predictions can fail due to cumulative errors and noise. To address this issue, this study proposes a data-centric method that uses early single-cycle data to predict the capacity degradation trajectory of lithium-ion cells. The method involves predicting a few knots at specific retention levels using a deep learning-based model and interpolating them to reconstruct the trajectory. Two approaches are used to identify the retention levels of two to four knots: uniformly dividing the retention up to the end of life and finding optimal locations using Bayesian optimization. The proposed model is validated with experimental data from 169 cells using five-fold cross-validation. The results show that mean absolute percentage errors in trajectory prediction are less than 1.60% for all cases of knots. By predicting only the cycle numbers of at least two knots based on early single-cycle charge and discharge data, the model can directly estimate the overall capacity degradation trajectory. Further experiments suggest using three-cycle input data to achieve robust and efficient predictions, even in the presence of noise. The method is then applied to predict various shapes of capacity degradation patterns using additional experimental data from 82 cells. The study demonstrates that collecting only the cycle information of a few knots during model training and a few early cycle data points for predictions is sufficient for predicting capacity degradation. This can help establish appropriate warranties or replacement cycles in battery manufacturing and diagnosis processes.

Biomedical image analysis competitions: The state of current participation practice

The number of international benchmarking competitions is steadily increasing in various fields of machine learning (ML) research and practice. So far, however, little is known about the common practice as well as bottlenecks faced by the community in tackling the research questions posed. To shed light on the status quo of algorithm development in the specific field of biomedical imaging analysis, we designed an international survey that was issued to all participants of challenges conducted in conjunction with the IEEE ISBI 2021 and MICCAI 2021 conferences (80 competitions in total). The survey covered participants' expertise and working environments, their chosen strategies, as well as algorithm characteristics. A median of 72% challenge participants took part in the survey. According to our results, knowledge exchange was the primary incentive (70%) for participation, while the reception of prize money played only a minor role (16%). While a median of 80 working hours was spent on method development, a large portion of participants stated that they did not have enough time for method development (32%). 25% perceived the infrastructure to be a bottleneck. Overall, 94% of all solutions were deep learning-based. Of these, 84% were based on standard architectures. 43% of the respondents reported that the data samples (e.g., images) were too large to be processed at once. This was most commonly addressed by patch-based training (69%), downsampling (37%), and solving 3D analysis tasks as a series of 2D tasks. K-fold cross-validation on the training set was performed by only 37% of the participants and only 50% of the participants performed ensembling based on multiple identical models (61%) or heterogeneous models (39%). 48% of the respondents applied postprocessing steps.