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Computer Vision · 3D Rendering & Reconstruction

Dominic Maggio, Hyungtae Lim, Luca Carlone

We present VGGT-SLAM, a dense RGB SLAM 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-degrees-of-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 VGGT-SLAM achieves improved map quality using long video sequences that are infeasible for VGGT due to its high GPU requirements. Our code is available at https://github.com/MIT-SPARK/VGGT-SLAM.

Theory · Learning Theory

YuQing Xie, Tess Smidt

Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In particular, recent works have found small training benefits from relaxing equivariance constraints. This raises the question: do equivariance constraints introduce fundamental obstacles to optimization? Or do they simply require different hyperparameter tuning? In this work, we investigate this question through a theoretical analysis of the loss landscape geometry. We focus on networks built using permutation representations, which we can view as a subset of unconstrained MLPs. Importantly, we show that the parameter symmetries of the unconstrained model has nontrivial effects on the loss landscape of the equivariant subspace and under certain conditions can provably prevent learning of the global minima. Further, we empirically demonstrate in such cases, relaxing to an unconstrained MLP can sometimes solve the issue. Interestingly, the weights eventually found via relaxation corresponds to a different choice of group representation in the hidden layer. From this, we draw 3 key takeaways. (1) By viewing the unconstrained version of an architecture, we can uncover hidden parameter symmetries which were broken by choice of constraint enforcement (2) Hidden symmetries give important insights on loss landscapes and can induce critical points and even minima (3) Hidden symmetry induced minima can sometimes be escaped by constraint relaxation and we observe the network jumps to a different choice of constraint enforcement. Effective equivariance relaxation may require rethinking the fixed choice of group representation in the hidden layers.

Optimization · Stochastic & Convex Optimization

Gokul Rajaraman, Debasish Chatterjee

The problem of optimally covering a given compact subset of $\mathbb{R}^N$ with a preassigned number $n$ of Euclidean metric balls has a long-standing history and it is well-recognized to be computationally hard. This article establishes a numerically viable algorithm for obtaining optimal covers of compact sets via two key contributions. The first is a foundational result establishing Lipschitz continuity of the marginal function of a certain parametric non-convex maximization problem in the optimal covering problem, and it provides the substrate for numerical gradient algorithms to be employed in this context. The second is an adaptation of a stochastically smoothed numerical gradient-based (zeroth-order) algorithm for a non-convex minimization problem, that, equipped with randomized restarts, spurs global convergence to an optimal cover. Several numerical experiments with complicated nonconvex compact sets demonstrate the excellent performance of our techniques.

Reinforcement Learning · Deep RL

Lang Feng, Zhenghai Xue, Tingcong Liu, Bo An

Recent advances in group-based reinforcement learning (RL) have driven frontier large language models (LLMs) in single-turn tasks like mathematical reasoning. However, their scalability to multi-turn LLM agent training remains limited. Unlike static tasks, agent-environment interactions unfold over many steps and often yield sparse or delayed rewards, making credit assignment across individual steps significantly more challenging. In this work, we propose Group-in-Group Policy Optimization (GiGPO), a novel RL algorithm that achieves fine-grained credit assignment for LLM agents while preserving the appealing properties of group-based RL: critic-free, low memory, and stable convergence. GiGPO introduces a two-level structure for estimating relative advantage: (i) At the episode-level, GiGPO computes macro relative advantages based on groups of complete trajectories; (ii) At the step-level, GiGPO introduces an anchor state grouping mechanism that retroactively constructs step-level groups by identifying repeated environment states across trajectories. Actions stemming from the same state are grouped together, enabling micro relative advantage estimation. This hierarchical structure effectively captures both global trajectory quality and local step effectiveness without relying on auxiliary models or additional rollouts. We evaluate GiGPO on challenging agent benchmarks, including ALFWorld and WebShop, as well as tool-integrated reasoning on search-augmented QA tasks, using Qwen2.5-1.5B/3B/7B-Instruct. Crucially, GiGPO delivers fine-grained per-step credit signals, achieves performance gains of > 12\% on ALFWorld and > 9\% on WebShop over GRPO, and obtains superior performance on QA tasks (42.1\% on 3B and 47.2\% on 7B): all while maintaining the same GPU memory overhead, identical LLM rollout, and incurring little to no additional time cost.

Computer Vision · Vision Models & Multimodal

Philip Schroeder, Ondrej Biza, Thomas Weng, Hongyin Luo, Jim Glass

Vision-language models (VLMs) have exhibited impressive capabilities across diverse image understanding tasks, but still struggle in settings that require reasoning over extended sequences of camera frames from a video. This limits their utility in embodied settings, which require reasoning over long frame sequences from a continuous stream of visual input at each moment of a task attempt. To address this limitation, we propose ROVER (Reasoning Over VidEo Recursively), a framework that enables the model to recursively decompose long-horizon video trajectories into segments corresponding to shorter subtasks within the trajectory. In doing so, ROVER facilitates more focused and accurate reasoning over temporally localized frame sequences without losing global context. We evaluate ROVER, implemented using an in-context learning approach, on diverse OpenX Embodiment videos and on a new dataset derived from RoboCasa that consists of 543 videos showing both expert and perturbed non-expert trajectories across 27 manipulation tasks. ROVER outperforms strong baselines across three video reasoning tasks: task progress estimation, frame-level natural language reasoning, and video question answering. We observe that, by reducing the number of frames the model reasons over at each timestep, ROVER mitigates model hallucinations, especially during unexpected or non-optimal moments of a trajectory. In addition, by enabling the implementation of a subtask-specific sliding context window, ROVER's time complexity scales linearly with video length, an asymptotic improvement over baselines.

Optimization · Large Scale, Parallel and Distributed

TaeHo Yoon, Sayantan Choudhury, Nicolas Loizou

Traditional Federated Learning (FL) approaches assume collaborative clients with aligned objectives working towards a shared global model. However, in many real-world scenarios, clients act as rational players with individual objectives and strategic behaviors, a concept that existing FL frameworks are not equipped to adequately address. To bridge this gap, we introduce *Multiplayer Federated Learning (MpFL)*, a novel framework that models the clients in the FL environment as players in a game-theoretic context, aiming to reach an equilibrium. In this scenario, each player tries to optimize their own utility function, which may not align with the collective goal. Within MpFL, we propose *Per-Player Local Stochastic Gradient Descent (PEARL-SGD)*, an algorithm in which each player/client performs local updates independently and periodically communicates with other players. We theoretically analyze PEARL-SGD and prove that it reaches a neighborhood of equilibrium with less communication in the stochastic setup compared to its non-local counterpart. Finally, we verify our theoretical findings through numerical experiments.

Computer Vision · 3D Rendering & Reconstruction

qigeng duan, Benyun ZHAO, Mingqiao Han, Yijun Huang, Ben Chen

Scene understanding based on 3D Gaussian Splatting (3DGS) has recently achieved notable advances. Although 3DGS related methods have efficient rendering capabilities, they fail to address the inherent contradiction between the anisotropic color representation of gaussian primitives and the isotropic requirements of semantic features, leading to insufficient cross-view feature consistency. To overcome the limitation, we proposes FHGS (Feature-Homogenized Gaussian Splatting), a novel 3D feature distillation framework inspired by physical models, which freezes and distills 2D pre-trained features into 3D representations while preserving the real-time rendering efficiency of 3DGS. Specifically, our FHGS introduces the following innovations: Firstly, a universal feature fusion architecture is proposed, enabling robust embedding of large-scale pre-trained models' semantic features (e.g., SAM, CLIP) into sparse 3D structures. Secondly, a non-differentiable feature fusion mechanism is introduced, which enables semantic features to exhibit viewpoint independent isotropic distributions. This fundamentally balances the anisotropic rendering of gaussian primitives and the isotropic expression of features; Thirdly, a dual-driven optimization strategy inspired by electric potential fields is proposed, which combines external supervision from semantic feature fields with internal primitive clustering guidance. This mechanism enables synergistic optimization of global semantic alignment and local structural consistency. Extensive comparison experiments with other state-of-the-art methods on benchmark datasets demonstrate that our FHGS exhibits superior reconstruction performance in feature fusion, noise suppression, and geometric precision, while maintaining a significantly lower training time. This work establishes a novel Gaussian Splatting data structure, offering practical advancements for real-time semantic mapping, 3D stylization, and Vision-Language Navigation (VLN). Our code and additional results are available on our project page:https://fhgs.cuastro.org/.

Optimization

Lachlan MacDonald, Hancheng Min, Leandro Palma, Salma Tarmoun, Ziqing Xu, Rene Vidal

Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or "stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large step size regime called the "edge of stability", in which the objective decreases non-monotonically with an observed implicit bias towards flat minima. In this paper, we take a step toward quantifying this phenomenon by providing convergence rates for gradient descent with large learning rates in an overparametrised least squares setting. The key insight behind our analysis is that, as a consequence of overparametrisation, the set of global minimisers forms a Riemannian manifold $M$, which enables the decomposition of the GD dynamics into components parallel and orthogonal to $M$. The parallel component corresponds to Riemannian gradient descent on the objective sharpness, while the orthogonal component corresponds to a quadratic dynamical system. This insight allows us to derive convergence rates in three regimes characterised by the learning rate size: the subcritical regime, in which transient instability is overcome in finite time before linear convergence to a suboptimally flat global minimum; the critical regime, in which instability persists for all time with a power-law convergence toward the optimally flat global minimum; the supercritical regime, in which instability persists for all time with linear convergence to an oscillation of period two centred on the optimally flat global minimum.

Theory · Everything Else

Hancheng Min, Zhihui Zhu, Rene Vidal

Among many mysteries behind the success of deep networks lies the exceptional discriminative power of their learned representations as manifested by the intriguing Neural Collapse (NC) phenomenon, where simple feature structures emerge at the last layer of a trained neural network. Prior works on the theoretical understandings of NC have focused on analyzing the optimization landscape of matrix-factorization-like problems by considering the last-layer features as unconstrained free optimization variables and showing that their global minima exhibit NC. In this paper, we show that gradient flow on a two-layer ReLU network for classifying orthogonally separable data provably exhibits NC, thereby advancing prior results in two ways: First, we relax the assumption of unconstrained features, showing the effect of data structure and nonlinear activations on NC characterizations. Second, we reveal the role of the implicit bias of the training dynamics in facilitating the emergence of NC.

Deep Learning · Theory

Jingfeng Wu, Pierre Marion, Peter Bartlett

We study *gradient descent* (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective, achieving exponential convergence in $\widetilde{\mathcal{O}}(\kappa)$ steps with $\kappa$ being the condition number. Surprisingly, we show that this can be *accelerated* to $\widetilde{\mathcal{O}}(\sqrt{\kappa})$ by simply using a large stepsize---for which the objective evolves *nonmonotonically*. The acceleration brought by large stepsizes extends to minimizing the population risk for separable distributions, improving on the best-known upper bounds on the number of steps to reach a near-optimum. Finally, we characterize the largest stepsize for the local convergence of GD, which also determines the global convergence in special scenarios. Our results extend the analysis of Wu et al. (2024) from convex settings with minimizers at infinity to strongly convex cases with finite minimizers.

Computer Vision · 3D Rendering & Reconstruction

Xiaoshan Wu, Yifei Yu, Xiaoyang Lyu, Yihua Huang, Bo Wang, Baoheng Zhang, Zhongrui Wang, Xiaojuan Qi

Robust 3D geometry estimation from videos is critical for applications such as autonomous navigation, SLAM, and 3D scene reconstruction. Recent methods like DUSt3R demonstrate that regressing dense pointmaps from image pairs enables accurate and efficient pose-free reconstruction. However, existing RGB-only approaches struggle under real-world conditions involving dynamic objects and extreme illumination, due to the inherent limitations of conventional cameras. In this paper, we propose \textbf{EAG3R}, a novel geometry estimation framework that augments pointmap-based reconstruction with asynchronous event streams. Built upon the MonST3R backbone, EAG3R introduces two key innovations: (1) a retinex-inspired image enhancement module and a lightweight event adapter with SNR-aware fusion mechanism that adaptively combines RGB and event features based on local reliability; and (2) a novel event-based photometric consistency loss that reinforces spatiotemporal coherence during global optimization. Our method enables robust geometry estimation in challenging dynamic low-light scenes without requiring retraining on night-time data. Extensive experiments demonstrate that EAG3R significantly outperforms state-of-the-art RGB-only baselines across monocular depth estimation, camera pose tracking, and dynamic reconstruction tasks.

Theory · Learning Theory

Paul Liautaud, Pierre Gaillard, Olivier Wintenberger

We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular competitor functions,% prediction rules, modeled by Besov spaces $B_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s > \tfrac{d}{p}$. We introduce an adaptive wavelet-based algorithm that performs sequential prediction without prior knowledge of $(s,p,q)$, and establish minimax-optimal regret bounds against any comparator in $B_{pq}^s$. We further design a locally adaptive extension capable of sequentially adapting to spatially inhomogeneous smoothness. This adaptive mechanism adjusts the resolution of the predictions over both time and space, yielding refined regret bounds in terms of local regularity. Consequently, in heterogeneous environments, our adaptive guarantees can significantly surpass those obtained by standard global methods.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Seanie Lee, Sangwoo Park, Dong Bok Lee, Dominik Wagner, Haebin Seong, Tobias Bocklet, Juho Lee, Sung Ju Hwang

Low-Rank Adaptation (LoRA), which introduces a product of two trainable low-rank matrices into frozen pre-trained weights, is widely used for efficient fine-tuning of language models in federated learning (FL). However, when combined with differentially private stochastic gradient descent (DP-SGD), LoRA faces substantial noise amplification: DP-SGD perturbs per-sample gradients, and the matrix multiplication of the LoRA update ($BA$) intensifies this effect. Freezing one matrix (*e.g.*, $A$) reduces the noise but restricts model expressiveness, often resulting in suboptimal adaptation. To address this, we propose $\texttt{FedSVD}$, a simple yet effective method that introduces a global reparameterization based on singular value decomposition (SVD). In our approach, each client optimizes only the $B$ matrix and transmits it to the server. The server aggregates the $B$ matrices, computes the product $BA$ using the previous $A$, and refactorizes the result via SVD. This yields a new adaptive $A$ composed of the orthonormal right singular vectors of $BA$, and an updated $B$ containing the remaining SVD components. This reparameterization avoids quadratic noise amplification, while allowing $A$ to better capture the principal directions of the aggregate updates. Moreover, the orthonormal structure of $A$ bounds the gradient norms of $B$ and preserves more signal under DP-SGD, as confirmed by our theoretical analysis. As a result, $\texttt{FedSVD}$ consistently improves stability and performance across a variety of privacy settings and benchmarks, outperforming relevant baselines under both private and non-private regimes.

Applications · Time Series

Jie Yang, Kexin Zhang, Guibin Zhang, Philip S Yu, Kaize Ding

Time Series Imputation (TSI), which aims to recover missing values in temporal data, remains a fundamental challenge due to the complex and often high-rate missingness in real-world scenarios. Existing models typically optimize the point-wise reconstruction loss, focusing on recovering numerical values (local information). However, we observe that under high missing rates, these models still perform well in the training phase yet produce poor imputations and distorted latent representation distributions (global information) in the inference phase. This reveals a critical optimization dilemma: current objectives lack global guidance, leading models to overfit local noise and fail to capture global information of the data. To address this issue, we propose a new training paradigm, **Glocal** **I**nformation **B**ottleneck (**Glocal-IB**). Glocal-IB is model-agnostic and extends the standard IB framework by introducing a Global Alignment loss, derived from a tractable mutual information approximation. This loss aligns the latent representations of masked inputs with those of their originally observed counterparts. It helps the model retain global structure and local details while suppressing noise caused by missing values, giving rise to better generalization under high missingness. Extensive experiments on nine datasets confirm that Glocal-IB leads to consistently improved performance and aligned latent representations under missingness. Our code implementation is available in [https://github.com/Muyiiiii/NeurIPS-25-Glocal-IB](https://github.com/Muyiiiii/NeurIPS-25-Glocal-IB).

Social Aspects · Privacy-preserving Statistics and Machine Learning

Hrad Ghoukasian, Bonwoo Lee, Shahab Asoodeh

We study the problem of sampling from a distribution under local differential privacy (LDP). Given a private distribution $P \in \mathcal{P}$, the goal is to generate a single sample from a distribution that remains close to $P$ in $f$-divergence while satisfying the constraints of LDP. This task captures the fundamental challenge of producing realistic-looking data under strong privacy guarantees. While prior work by Park et al. (NeurIPS'24) focuses on global minimax-optimality across a class of distributions, we take a local perspective. Specifically, we examine the minimax error in a neighborhood around a fixed distribution $P_0$, and characterize its exact value, which depends on both $P_0$ and the privacy level. Our main result shows that the local minimax error is determined by the global minimax error when the distribution class $\mathcal{P}$ is restricted to a neighborhood around $P_0$. To establish this, we (1) extend previous work from pure LDP to the more general functional LDP framework, and (2) prove that the globally optimal functional LDP sampler yields the optimal local sampler when constrained to distributions near $P_0$. Building on this, we also derive a simple closed-form expression for the locally minimax-optimal samplers which does not depend on the choice of $f$-divergence. We further argue that this local framework naturally models private sampling with public data, where the public data distribution is represented by $P_0$. In this setting, we empirically compare our locally optimal sampler to existing global methods, and demonstrate that it consistently outperforms global minimax samplers.

Deep Learning · Graph Neural Networks

Jin Li, Zezhong Ding, Xike Xie

Knowledge graphs (KGs) are vital for enabling knowledge reasoning across various domains. Recent KG reasoning methods that integrate both global and local information have achieved promising results. However, existing methods often suffer from score over-smoothing, which blurs the distinction between correct and incorrect answers and hinders reasoning effectiveness. To address this, we propose DuetGraph, a **coarse-to-fine** KG reasoning mechanism with **dual-pathway** global-local fusion. DuetGraph tackles over-smoothing by segregating—rather than stacking—the processing of local (via message passing) and global (via attention) information into two distinct pathways, preventing mutual interference and preserving representational discrimination. In addition, DuetGraph introduces a **coarse-to-fine** optimization, which partitions entities into high- and low-score subsets. This strategy narrows the candidate space and sharpens the score gap between the two subsets, which alleviates over-smoothing and enhances inference quality. Extensive experiments on various datasets demonstrate that DuetGraph achieves state-of-the-art (SOTA) performance, with up to an **8.7\%** improvement in reasoning quality and a **1.8$\times$** acceleration in training efficiency.

Theory · Learning Theory

Shunta Akiyama

In this paper, we consider a block coordinate descent (BCD) algorithm for training deep neural networks and provide a new global convergence guarantee under strictly monotonically increasing activation functions. While existing works demonstrate convergence to stationary points for BCD in neural networks, our contribution is the first to prove convergence to global minima, ensuring arbitrarily small loss. We show that the loss with respect to the output layer decreases exponentially while the loss with respect to the hidden layers remains well-controlled. Additionally, we derive generalization bounds using the Rademacher complexity framework, demonstrating that BCD not only achieves strong optimization guarantees but also provides favorable generalization performance. Moreover, we propose a modified BCD algorithm with skip connections and non-negative projection, extending our convergence guarantees to ReLU activation, which are not strictly monotonic. Empirical experiments confirm our theoretical findings, showing that the BCD algorithm achieves a small loss for strictly monotonic and ReLU activations.

Optimization · Large Scale, Parallel and Distributed

Maximilian Egger, Rawad Bitar, Antonia Wachter-Zeh, Nir Weinberger, Deniz Gunduz

Federated Learning (FL) incurs high communication costs in both uplink and downlink. The literature largely focuses on lossy compression of model updates in deterministic FL. In contrast, stochastic (Bayesian) FL considers distributions over parameters, enabling uncertainty quantification, better generalization, and, crucially, inherent communication-regularized training through a mirror-descent structure. In this paper, we consider both uplink and downlink communication in stochastic FL, and propose a communication framework based on remote source generation. Employing Minimal Random Coding (MRC) for remote generation, we allow the server and the clients to sample from local and global posteriors (sources), respectively, rather than transmitting locally sampled updates. The framework encompasses communication-regularized local optimization and principled compression of model updates, leveraging gradually updated prior distributions as side information. Through extensive simulations, we show that our method achieves $5-32\times$ reduction in total communication cost while preserving accuracy. We further analyze the communication cost, refining existing MRC bounds and enabling precise quantification of uplink and downlink trade-offs. We also extend our method to conventional FL via stochastic quantization and prove a contraction property for the biased MRC compressor to facilitate convergence analysis.

Computer Vision · 3D Rendering & Reconstruction

Yuheng Yuan, Qiuhong Shen, Shizun Wang, Xingyi Yang, Xinchao Wang

Dense matching methods like DUSt3R regress pairwise pointmaps for 3D reconstruction. However, the reliance on pairwise prediction and the limited generalization capability inherently restrict the global geometric consistency. In this work, we introduce \textbf{Test3R}, a surprisingly simple test-time learning technique that significantly boosts geometric accuracy. Using image triplets ($I_1,I_2,I_3$), Test3R generates reconstructions from pairs ($I_1,I_2$) and ($I_1,I_3$). The core idea is to optimize the network at test time via a self-supervised objective: maximizing the geometric consistency between these two reconstructions relative to the common image $I_1$. This ensures the model produces cross-pair consistent outputs, regardless of the inputs. Extensive experiments demonstrate that our technique significantly outperforms previous state-of-the-art methods on the 3D reconstruction and multi-view depth estimation tasks. Moreover, it is universally applicable and nearly cost-free, making it easily applied to other models and implemented with minimal test-time training overhead and parameter footprint. Code is available at https://github.com/nopQAQ/Test3R.

Computer Vision · Classification and Understanding

Jiahang Zhang, Lilang Lin, Shuai Yang, Jiaying Liu

3D human motion-text retrieval is essential for accurate motion understanding, targeted at cross-modal alignment learning. Existing methods typically align the global motion-text concepts directly, suffering from sub-optimal generalization due to the uncertainty of correspondence learning between multiple motion concepts coupled in a single motion/text sequence. Therefore, we study the explicit fine-grained concept decomposition for alignment learning and present a novel framework, Structural Generative Augmentation for 3D Human Motion Retrieval (SGAR), to enable generation-augmented retrieval. Specifically, relying on the strong priors of existing large language model (LLM) assets, we effectively decompose human motions structurally into subtler semantic units, \ie, body parts, for fine-grained motion modeling. Based on this, we develop part-mixture learning to better decouple the local motion concept learning, boosting part-level alignment. Moreover, a directional relation alignment strategy exploiting the correspondence between full-body and part motions is incorporated to regularize feature manifold for better consistency. Extensive experiments on three benchmarks, including motion-text retrieval as well as recognition and generation applications, demonstrate the superior performance and promising transferability of our method.