NeurIPS 2026 Papers

Recent advances in 3D object generation have enabled the creation of high-fidelity 3D assets from 2D images. This *2D-to-3D* capability offers a promising path for alleviating 3D data scarcity, which remains a key bottleneck for scalable simulation in robotics and AR/VR applications. However, existing 3D generation methods primarily emphasize visual plausibility and geometric fidelity, with limited consideration of object-level interaction and structural understanding that are critical for downstream embodied AI tasks. To bridge this gap, we introduce **EmbodiedObject**, a unified framework for embodied 3D object understanding built upon latent representations produced by modern *2D-to-3D* generative models such as SAM3D. We first systematically analyze the part-level locality of these latent representations against existing unified 3D point encoders and show that they naturally preserve rich structural semantics suitable for object understanding. Motivated by this observation, we then design a unified DiT-style decoder that operates directly on the latent representation and supports multiple object-level tasks, including open-vocabulary 3D affordance prediction, 3D part segmentation, and 3D articulation estimation. Given a real-world 2D image containing an object of interest, **EmbodiedObject** extends *2D-to-3D* generation beyond visual reconstruction by jointly reasoning about affordance, articulation, and part semantics. This transforms generated 3D assets into actionable object representations suitable for downstream embodied AI applications. Our source-code will be open-sourced.

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM training, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

Multimodal Large Language Models (MLLMs) have demonstrated substantial promise in spatial understanding. Existing works typically incorporate prior knowledge extracted from a pre-trained foundation model to further enhance the spatial awareness of MLLMs. In this paper, we first reveal that when integrating diverse foundation models into MLLMs, each model provides complementary spatial priors that benefit different tasks. Motivated by this, we propose $\textbf{ViPS}$, a novel multi-model prior framework designed to fully unleash the potential of incorporating multiple $\textbf{Vi}$sual $\textbf{P}$riors from diverse models into MLLMs for $\textbf{S}$patial understanding. Specifically, ViPS introduces an Efficient Prior Proxy to generate multiple foundational priors with minimal inference overhead, and a Dynamic Prior Fusion mechanism to achieve harmonious and context-aware prior fusion and injection from the prior proxies. Extensive experiments demonstrate that ViPS successfully harmonizes diverse visual priors, establishing new state-of-the-art performance across multiple complex spatial reasoning and 3D spatial understanding benchmarks.

Graph Neural Networks (GNNs) perform computations on graphs by routing the signal between graph regions using a graph shift operator or a message passing scheme. Often, the propagation of the signal leads to a loss of information, where the signal tends to diffuse across the graph instead of being deliberately routed between regions of interest. Two notions that depict this phenomenon are oversmoothing and oversquashing. In this paper, we propose an alternative approach for modeling signal propagation, inspired by quantum mechanics, using the notion of observables. Specifically, we model the place in the graph where the signal lies, how much the signal is concentrated there, and how much of the signal is propagated towards a location of interest when applying a GNN. Using these new concepts, we prove that standard spectral GNNs have poor signal propagation capabilities. We then propose a new type of spectral GNN, termed Schrödinger GNN, which we show has a superior capacity to route the signal across the graph.