A fundamental challenge in artificial intelligence is the transformation of observations into explicit symbolic representations suitable for abstraction, interpretation, and reasoning. While modern AI systems achieve remarkable perceptual capabilities through large-scale statistical learning, the resulting knowledge is typically encoded within latent parameters that are difficult to inspect or manipulate analytically. Inspired by Neuro-Symbolic AI and theories of human abstraction, this paper investigates the formation of symbolic mathematical representations from geometric observations. We propose NeuSOGA (Neuro-Symbolic Geometric Abstraction), a framework that progressively transforms observations into topological abstractions, geometric abstractions, and ultimately symbolic mathematical representations. The architecture combines topology-guided structural discovery using Euclidean Distance Transforms, foundation-model perception using Segment Anything, adaptive multi-scale geometric abstraction, and symbolic synthesis through Implicit Area Splines. The resulting representation is an analytical implicit model supporting arbitrary-order smoothness, additive composition, and closed-form evaluation. Unlike neural latent encodings, the generated representation remains interpretable, editable, and mathematically explicit. Experiments on ModelNet40 point clouds, arbitrary-view projections, and segmented optical observations demonstrate that NeuSOGA transforms diverse observations into compact symbolic representations while preserving essential geometric and topological structure across sensing modalities and viewing directions. NeuSOGA provides an interpretable and explainable pathway from observation to symbol and establishes
We present a real-time human-centric world model for upper-body interactive generation, aiming to synthesize coherent local world dynamics centered on a person, where coordinated body, hand, and facial motions evolve jointly with controllable human-object discrete interaction. To this end, we adopt a continuous-discrete joint control scheme with two complementary components: a continuous human state and a discrete interaction state. For continuous human-state control, we introduce a unified implicit representation based on multi-scale motion encoding, in which motion latents from the upper body, hands, and face are fused into a shared latent space. This multi-scale design improves expressiveness across different spatial scales, captures fine-grained human dynamics more effectively, and enables direct control without explicit retargeting. For discrete object interaction-state control, we represent object contact using a small set of language-encoded discrete interaction states, where text serves as an explicit interaction-state command, such as \emph{no contact} or \emph{grasp}, rather than an open-ended generation prompt, and we further construct a dedicated rendering pipeline for human-object interaction data to supervise such discrete interaction states. By combining continuous implicit human-state control with discrete interaction-state control, our model enables precise modeling of how a person moves and interacts with the local environment, including controllable changes to nearby scene states. Finally, we distill the model for efficient streaming real-time inference, achieving 25 FPS on two H100 GPUs. Experiments demonstrate improved fine-grained motion fidelity, more realistic hand-object coordination, and effective real-time interaction, establishing a practical step beyond motion reproduction toward real-time human-centric world modeling.
Single image dehazing continues to be hindered by the loss of high-frequency details and the difficulty of accurate physical scattering modeling. To address these issues, we propose Fi-Gaussian, a frequency-aware implicit Gaussian splatting network for single image dehazing. Unlike explicit rendering methods that rely on 3D point clouds, our method employs implicit Gaussian splatting to adaptively model the underlying distribution of clear images as a continuous representation in 2D feature space. The core of the network is a frequency-aware implicit Gaussian splatting module, which decouples low-frequency structural information and high-frequency texture information in the frequency domain and then performs adaptive Gaussian aggregation with complex-valued weights to recover fine details. In addition, a physics-driven scattering renormalization mechanism is introduced to estimate the transmission map and atmospheric light under the guidance of implicit Gaussian priors. Extensive experiments on multiple benchmark datasets demonstrate that Fi-Gaussian achieves state-of-the-art quantitative performance and produces visually superior dehazed results, validating the effectiveness of implicit Gaussian splatting for low-level vision tasks.