URDF-Anything+: Autoregressive Articulated 3D Models Generation for Physical Simulation

Articulated objects are fundamental for robotics, simulation of physics, and interactive virtual environments. However, reconstructing them from visual input remains challenging, as it requires jointly inferring both part geometry and kinematic structure. We present, an end-to-end autoregressive framework that directly generates executable articulated object models from visual observations. Given image and object-level 3D cues, our method sequentially produces part geometries and their associated joint parameters, resulting in complete URDF models without reliance on multi-stage pipelines. The generation proceeds until the model determines that all parts have been produced, automatically inferring complete geometry and kinematics. Building on this capability, we enable a new Real-Follow-Sim paradigm, where high-fidelity digital twins constructed from visual observations allow policies trained and tested purely in simulation to transfer to real robots without online adaptation. Experiments on large-scale articulated object benchmarks and real-world robotic tasks demonstrate that outperforms prior methods in geometric reconstruction quality, joint parameter accuracy, and physical executability.

Generalizable Geometric Image Caption Synthesis

Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack of high-quality image-text pair datasets for understanding geometric images. Furthermore, most template-based data synthesis pipelines typically fail to generalize to questions beyond their predefined templates. In this paper, we bridge this gap by introducing a complementary process of Reinforcement Learning with Verifiable Rewards (RLVR) into the data generation pipeline. By adopting RLVR to refine captions for geometric images synthesized from 50 basic geometric relations and using reward signals derived from mathematical problem-solving tasks, our pipeline successfully captures the key features of geometry problem-solving. This enables better task generalization and yields non-trivial improvements. Furthermore, even in out-of-distribution scenarios, the generated dataset enhances the general reasoning capabilities of multimodal large language models, yielding accuracy improvements of $2.8\%\text{-}4.8\%$ in statistics, arithmetic, algebraic, and numerical tasks with non-geometric input images of MathVista and MathVerse, along with $2.4\%\text{-}3.9\%$ improvements in Art, Design, Tech, and Engineering tasks in MMMU.

Towards the Dynamics of a DNN Learning Symbolic Interactions

This study proves the two-phase dynamics of a deep neural network (DNN) learning interactions. Despite the long disappointing view of the faithfulness of post-hoc explanation of a DNN, in recent years, a series of theorems have been proven to show that given an input sample, a small number of interactions between input variables can be considered as primitive inference patterns, which can faithfully represent every detailed inference logic of the DNN on this sample. Particularly, it has been observed that various DNNs all learn interactions of different complexities with two-phase dynamics, and this well explains how a DNN's generalization power changes from under-fitting to over-fitting. Therefore, in this study, we prove the dynamics of a DNN gradually encoding interactions of different complexities, which provides a theoretically grounded mechanism for the over-fitting of a DNN. Experiments show that our theory well predicts the real learning dynamics of various DNNs on different tasks.

Mix-GENEO: A flexible filtration for multiparameter persistent homology detects digital images

Two important problems in the field of Topological Data Analysis are defining practical multifiltrations on objects and showing ability of TDA to detect the geometry. Motivated by the problems, we constuct three multifiltrations named multi-GENEO, multi-DGENEO and mix-GENEO, and prove the stability of both the interleaving distance and multiparameter persistence landscape of multi-GENEO with respect to the pseudometric of the subspace of bounded functions. We also give the estimations of upper bound for multi-DGENEO and mix-GENEO. Finally, we provide experiment results on MNIST dataset to demonstrate our bifiltrations have ability to detect geometric and topological differences of digital images.

Why Adversarial Training of ReLU Networks Is Difficult?

This paper mathematically derives an analytic solution of the adversarial perturbation on a ReLU network, and theoretically explains the difficulty of adversarial training. Specifically, we formulate the dynamics of the adversarial perturbation generated by the multi-step attack, which shows that the adversarial perturbation tends to strengthen eigenvectors corresponding to a few top-ranked eigenvalues of the Hessian matrix of the loss w.r.t. the input. We also prove that adversarial training tends to strengthen the influence of unconfident input samples with large gradient norms in an exponential manner. Besides, we find that adversarial training strengthens the influence of the Hessian matrix of the loss w.r.t. network parameters, which makes the adversarial training more likely to oscillate along directions of a few samples, and boosts the difficulty of adversarial training. Crucially, our proofs provide a unified explanation for previous findings in understanding adversarial training.