We present VGGT-SLAM, a dense RGBSLAM system constructed by incrementally and globally aligning submaps created from the feed-forward scene reconstruction approach VGGT using only uncalibrated monocular cameras. While related works align submaps using similarity transforms (i.e., translation, rotation, and scale), we show that such approaches are inadequate in the case of uncalibrated cameras. In particular, we revisit the idea of reconstruction ambiguity, where given a set of uncalibrated cameras with no assumption on the camera motion or scene structure, the scene can only be reconstructed up to a 15-degreesof-freedom projective transformation of the true geometry. This inspires us to recover a consistent scene reconstruction across submaps by optimizing over the SL(4) manifold, thus estimating 15-degrees-of-freedom homography transforms between sequential submaps while accounting for potential loop closure constraints. As verified by extensive experiments, we demonstrate that VGGTSLAM achieves improved map quality using long video sequences that are infeasible for VGGT due to its high GPU requirements.

In real-world environments, a well-designed model must be capable of handling dynamically evolving distributions, where both in-distribution (ID) and out-ofdistribution (OOD) samples appear unpredictably and individually, making realtime adaptation particularly challenging. While open-set test-time adaptation has demonstrated effectiveness in adjusting to distribution shifts, existing methods often rely on batch processing and struggle to manage single-sample data stream in open-set environments.

We propose GAM-Agent, a game-theoretic multi-agent framework for enhancing vision-language reasoning. Unlike prior single-agent or monolithic models, GAM-Agent formulates the reasoning process as a non-zero-sum game between base agents--each specializing in visual perception subtasks--and a critical agent that verifies logic consistency and factual correctness. Agents communicate via structured claims, evidence, and uncertainty estimates. The framework introduces an uncertainty-aware controller to dynamically adjust agent collaboration, triggering multi-round debates when disagreement or ambiguity is detected.

This leaks pose and scale cues that networks may exploit to memorize absolute positions rather than inferring intrinsic geometry. When such alignment is absent in real data, performance collapses. We argue that robust generalization demands architectural equivariance to the similarity group, SIM(3), so the model remains agnostic to pose and scale. Following this principle, we introduce the first SIM(3)-equivariant shape completion network, whose modular layers successively canonicalize features, reason over similarity-invariant geometry, and restore the original frame. Under a de-biased evaluation protocol that removes the hidden cues, our model outperforms both equivariant and augmentation baselines on the PCN benchmark. It also sets new cross-domain records on real driving and indoor scans, lowering minimal matching distance on KITTI by 17%and Chamfer distance ℓ1on OmniObject3D by 14%. Perhaps surprisingly, ours under the stricter protocol still outperforms competitors under their biased settings. These results establish full SIM(3) equivariance as an effective route to truly generalizable shape completion.

Attention mechanisms have made significant strides in graph learning, yet they still exhibit notable limitations: local attention faces challenges in capturing long-range information due to the inherent problems of the message-passing scheme, while global attention cannot reflect the hierarchical neighborhood structure and fails to capture fine-grained local information. In this paper, we propose a novel multihop graph attention mechanism, named Subtree Attention (STA), to address the aforementioned issues. STA seamlessly bridges the fully-attentional structure and the rooted subtree, with theoretical proof that STA approximates the global attention under extreme settings.

The transformer architecture [52], which underlies present-day Large Language Models, has been one of the main drivers of recent advances in machine learning and artificial intelligence. At each layer, the hidden state of the network is updated by sequentially applying two distinct operations: attention modules [3], which capture long-range interactions in the input sequence, and classical MultiLayer Perceptrons (MLPs), acting separately on each element of that sequence. Despite their empirical success, the mechanisms governing information propagation through depth, and the way attention and MLP blocks jointly shape internal representations, remain only partially understood from a theoretical viewpoint. Recent progress has come from viewing transformers in suitable scaling limits as deterministic mean-field interacting particle systems modeling the evolution of N tokens1 through the layers of the neural network architecture (the so-called residual stream dynamics), see, among others, [46, 26, 27, 45]. In these descriptions, depth plays the role of a continuous time variable, and, in the large-context regime (N), the evolution of token representations is encoded by a PDE for their empirical distribution. This viewpoint is closely connected to the literature on scaling laws, where the effect of various scaling exponents controlling the relative size of the network's hyperparameters (e.g., depth, width, context length) on the effective dynamics of the model

A.1 Molecule Design We present more examples of generated molecules by our method and the CNN baseline liGAN. We select 6 molecules with highest binding affinity for each method and each binding site. The 3 additional binding sites are selected randomly from the testing set. By comparing the samples from two methods, we can find that the 3D molecules generated by our method are generally more realistic, while molecules generated by the baseline have more erroneous structures, such as bonds that are too short and angles that are too sharp. Besides, molecules generated by our method are more diverse, while the 3D atom configurations generated by the baseline are often similar.

The InfoNCE loss in contrastive learning depends critically on a temperature parameter, yet its dynamics under fixed versus annealed schedules remain poorly understood. We provide a theoretical analysis by modeling embedding evolution under Langevin dynamics on a compact Riemannian manifold. Under mild smoothness and energy-barrier assumptions, we show that classical simulated annealing guarantees extend to this setting: slow logarithmic inverse-temperature schedules ensure convergence in probability to a set of globally optimal representations, while faster schedules risk becoming trapped in suboptimal minima. Our results establish a link between contrastive learning and simulated annealing, providing a principled basis for understanding and tuning temperature schedules.