Kaicheng Zhang

Kaicheng Zhang, David N. Reynolds, Piero Deidda et al.

Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau Graph Neural Network (SLGNN), a novel architecture grounded in Stuart-Landau oscillator dynamics. Stuart-Landau oscillators are canonical models of limit-cycle behavior near Hopf bifurcations, which are fundamental to synchronization theory and are widely used in e.g. neuroscience for mesoscopic brain modeling. Unlike harmonic oscillators and phase-only Kuramoto models, Stuart-Landau oscillators retain both amplitude and phase dynamics, enabling rich phenomena such as amplitude regulation and multistable synchronization. The proposed SLGNN generalizes existing phase-centric Kuramoto-based OGNNs by allowing node feature amplitudes to evolve dynamically according to Stuart-Landau dynamics, with explicit tunable hyperparameters (such as the Hopf-parameter and the coupling strength) providing additional control over the interplay between feature amplitudes and network structure. We conduct extensive experiments across node classification, graph classification, and graph regression tasks, demonstrating that SLGNN outperforms existing OGNNs and establishes a novel, expressive, and theoretically grounded framework for deep oscillatory architectures on graphs.

Kaicheng Zhang, Wen Ge, Lei Jiang et al.

Although large language model agents are increasingly applied to quantitative-finance workflows, their evaluation remains fragmented across isolated tasks, while the financial relevance of benchmark tasks is often overlooked. Yet financial workflows are inherently multi-stage, spanning interdependent tasks such as forecasting, strategy construction, risk management, and trading. Existing platforms typically focus on a single task, and can therefore overstate agent competence and fail to reveal weaknesses in generalization, real-market interaction, and financially meaningful decision-making. We introduce OpenFinGym, a unified gym environment for quantitative-finance agent development that covers forecasting, market generation, real-time trading, and fraud detection under a single execution and verification interface. OpenFinGym additionally provides an automated task-construction pipeline that turns quantitative finance publications into executable task packages; a containerised runtime with a host-side verifier service that supports scalable agent rollouts and prevents runtime train-test leakage; a paper trading engine with a low-latency data-stream design; deferred-resolution support for long-horizon and event-market forecasts; and integration for SFT and RL post-training

Kaicheng Zhang, Piero Deidda, Desmond Higham et al.

Oversmoothing is a fundamental challenge in graph neural networks (GNNs): as the number of layers increases, node embeddings become increasingly similar, and model performance drops sharply. Traditionally, oversmoothing has been quantified using metrics that measure the similarity of neighbouring node features, such as the Dirichlet energy. While these metrics are related to oversmoothing, we argue they have critical limitations and fail to reliably capture oversmoothing in realistic scenarios. For instance, they provide meaningful insights only for very deep networks and under somewhat strict conditions on the norm of network weights and feature representations. As an alternative, we propose measuring oversmoothing by examining the numerical or effective rank of the feature representations. We provide theoretical support for this approach, demonstrating that the numerical rank of feature representations converges to one for a broad family of nonlinear activation functions under the assumption of nonnegative trained weights. To the best of our knowledge, this is the first result that proves the occurrence of oversmoothing in the nonlinear setting without assumptions on the boundedness of the weight matrices. Along with the theoretical findings, we provide extensive numerical evaluation across diverse graph architectures. Our results show that rank-based metrics consistently capture oversmoothing, whereas energy-based metrics often fail. Notably, we reveal that a significant drop in the rank aligns closely with performance degradation, even in scenarios where energy metrics remain unchanged.