arXiv subjects

Haoxiang Huang

Publications and source records attributed to Haoxiang Huang.

7 recordsLinked to original sources

arXiv2026

GeoCo-SAVi: Geometry-Consistent Slot Attention for Explicitly Editable Object Representations

Object-centric video models represent scenes with slots, yet exposed geometry can vary in meaning with appearance. In Invariant Slot Attention (ISA), explicit position and scale can disagree with the decoded center and extent; edits can yield unexpected motion or resizing, and replacing appearance can shift geometry. GeoCo-SAVi promotes geometric authority and semantic alignment. Its spatially equivariant, object-wise decoder makes position and scale effective commands: changing them moves or resizes the rendered support. Factual position alignment ties position to the decoded center, and normalized attention overlap discourages duplicate allocation. Appearance transplantation aligns geometry semantics across objects, so recipient geometry governs layout while donor appearance supplies shape. A temporal initializer propagates calibrated slots across frames. On Obj3D, GeoCo-SAVi matches ISA reconstruction, reduces p-centroid error by over 80%, and cuts appearance-induced size variation by over 50% while producing the expected translation and scale responses. On 250 MOVi-C videos, it also improves reconstruction, instance grouping, and fixed-identity geometry control over two same-protocol references. GeoCo-SAVi transforms explicit geometry into compositional control, making both position and scale more readable and editable.

cs.CV↗

arXiv2026

MOSH-WM: Mask-Grounded Soft-Hamiltonian Dynamics for Object-Centric World Models

Object-centric world models forecast future videos by evolving a set of entity slots, but the variables receiving dynamics supervision are often unconstrained visual features. We introduce \method{}, a mask-grounded soft-Hamiltonian world model that makes its position-like state explicitly depend on slot-owned image support. A frozen video-slot encoder produces slots and masks; spatial moments of mask-owned support form a canonical state $Q$, temporal differences form $P$, and a learned energy supplies a soft directional bias to a bounded learned increment. Decoder-relevant appearance and identity are stored separately in a causal visual context. A gated composer and bounded residual then combine this context with the propagated phase state to reconstruct decoder-compatible slots. On OBJ3D, given six observed frames and evaluated over the following 30 frames, \method{} reduces LPIPS by 25.0\% and spatial MSE by 33.7\% relative to the strongest object-centric baseline. On CLEVRER, given six observed frames and evaluated over the following ten frames, the corresponding reductions are 14.5\% and 18.7\%. Horizon-resolved visual and object-state measurements show that the complete model accumulates error more slowly throughout the 30-frame closed-loop rollout. Project page:https://github.com/moshwm-anon/-moshwm-anon.github.io.

cs.LG↗

arXiv2023

Neural Network with Local Converging Input (NNLCI) for Supersonic Flow Problems with Unstructured Grids

In recent years, surrogate models based on deep neural networks (DNN) have been widely used to solve partial differential equations, which were traditionally handled by means of numerical simulations. This kind of surrogate models, however, focuses on global interpolation of the training dataset, and thus requires a large network structure. The process is both time consuming and computationally costly, thereby restricting their use for high-fidelity prediction of complex physical problems. In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data. The framework utilizes the local domain of dependence with converging coarse solutions as input, which greatly reduces computational resource and training time. As a validation case, the NNLCI method is applied to study inviscid supersonic flows in channels with bumps. Different bump geometries and locations are considered to benchmark the effectiveness and versability of the proposed approach. Detailed flow structures, including shock-wave interactions, are examined systematically.

math.NA↗

arXiv2023

Perturbation Analysis of Neural Collapse

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

cs.LG↗

arXiv2022

Deep Probability Estimation

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

cs.LG↗

arXiv2022

Neural Networks with Local Converging Inputs (NNLCI) for Solving Conservation Laws, Part II: 2D Problems

In our prior work [arXiv:2109.09316], neural network methods with inputs based on domain of dependence and a converging sequence were introduced for solving one dimensional conservation laws, in particular the Euler systems. To predict a high-fidelity solution at a given space-time location, two solutions of a conservation law from a converging sequence, computed from low-cost numerical schemes, and in a local domain of dependence of the space-time location, serve as the input of a neural network. In the present work, we extend the methods to two dimensional Euler systems and introduce variations. Numerical results demonstrate that the methods not only work very well in one dimension [arXiv:2109.09316], but also perform well in two dimensions. Despite smeared local input data, the neural network methods are able to predict shocks, contacts, and smooth regions of the solution accurately. The neural network methods are efficient and relatively easy to train because they are local solvers.

math.NA↗

arXiv2021

Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear problems, e.g. the Burger's equation, heat conduction equations, Allen-Cahn and other reaction-diffusion equations, and Navier-Stokes equation. Meanwhile, researchers apply automatic differentiation in physics-informed neural network (PINN) to solve nonlinear hyperbolic systems based on conservation laws with highly discontinuous transition, such as Riemann problem, by inverse problem formulation in data-driven approach. However, it remains a challenge for forward methods using DNNs without knowing part of the solution to resolve discontinuities in nonlinear conservation laws. In this study, we incorporate 1st order numerical schemes into DNNs to set up the loss functional approximator instead of auto-differentiation from traditional deep learning framework, e.g. TensorFlow package, which improves the effectiveness of capturing discontinuities in Riemann problems. In particular, the 2-Coarse-Grid neural network (2CGNN) and 2-Diffusion-Coefficient neural network (2DCNN) are introduced in this work. We use 2 solutions of a conservation law from a converging sequence, computed from a low-cost numerical scheme, and in a domain of dependence of a space-time grid point as the input for a neural network to predict its high-fidelity solution at the grid point. Despite smeared input solutions, they output sharp approximations to solutions containing shocks and contacts and are efficient to use once trained.

math.NA↗