Y. Sungtaek Ju

Y. Sungtaek Ju

Kolmogorov-Arnold Networks have emerged as interpretable alternatives to traditional multi-layer perceptrons. However, standard implementations lack principled uncertainty quantification capabilities essential for many scientific applications. We present a framework integrating sparse variational Gaussian process inference with the Kolmogorov-Arnold topology, enabling scalable Bayesian inference with computational complexity quasi-linear in sample size. Through analytic moment matching, we propagate uncertainty through deep additive structures while maintaining interpretability. We use three example studies to demonstrate the framework's ability to distinguish aleatoric from epistemic uncertainty: calibration of heteroscedastic measurement noise in fluid flow reconstruction, quantification of prediction confidence degradation in multi-step forecasting of advection-diffusion dynamics, and out-of-distribution detection in convolutional autoencoders. These results suggest Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KANs) is a promising architecture for uncertainty-aware learning in scientific machine learning.

Yongyuan Liang, Xiyao Wang, Yuanchen Ju et al.

Scaling large multimodal models (LMMs) to 3D understanding poses unique challenges: point cloud data is sparse and irregular, existing models rely on fragmented architectures with modality-specific encoders, and training pipelines often suffer from instability and poor scalability. We introduce Lemon, a unified transformer architecture that addresses these challenges by jointly processing 3D point cloud patches and language tokens as a single sequence. Unlike prior work that relies on modality-specific encoders and cross-modal alignment modules, this design enables early spatial-linguistic fusion, eliminates redundant encoders, improves parameter efficiency, and supports more effective model scaling. To handle the complexity of 3D data, we develop a structured patchification and tokenization scheme that preserves spatial context, and a three-stage training curriculum that progressively builds capabilities from object-level recognition to scene-level spatial reasoning. Lemon establishes new state-of-the-art performance across comprehensive 3D understanding and reasoning tasks, from object recognition and captioning to spatial reasoning in 3D scenes, while demonstrating robust scaling properties as model size and training data increase. Our work provides a unified foundation for advancing 3D spatial intelligence in real-world applications.