This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has been a promising approach for studying the discrete optimization methods. Despite the crucial role of momentum in gradient-based optimization methods, the gap between the original dynamics and the continuous time approximations due to the discretization error has not been comprehensively bridged yet. In this work, we study the HB momentum method in continuous time while putting more focus on the discretization error to provide additional theoretical tools to this area. In particular, we design a first-order piece-wise continuous differential equation, where we add a number of counter terms to account for the discretization error explicitly. As a result, we provide a continuous time model for the HB momentum method that allows the control of discretization error to arbitrary order of the learning rate. As an application, we leverage it to find a new implicit regularization of the directional smoothness and investigate the implicit bias of HB for diagonal linear networks, indicating how our results can be used in deep learning. Our theoretical findings are further supported by numerical experiments.

The Transformer architecture serves as the foundation of modern AI systems, powering recent advances in Large Language Models (LLMs) and Large Multimodal Models (LMMs). Central to these models, attention mechanisms capture contextual dependencies via token interactions. Beyond inference, attention has been widely adopted for interpretability, offering insights into model behavior. Among interpretability techniques, attention flow --- which traces global information transfer across layers --- provides a more comprehensive perspective than single-layer attention maps. However, computing attention flow is computationally intensive due to the high complexity of max-flow algorithms. To address this challenge, we introduce FlowPrune, a novel framework that accelerates attention flow analysis by pruning the attention graph before applying max-flow computations.

Despite the importance of aligning language models with human preferences, crowd-sourced human feedback is often noisy---for example, preferring less desirable responses---posing a fundamental challenge to alignment. A truly robust alignment objective should yield identical model parameters even under severe label noise, a property known as redescending. We prove that no existing alignment methods satisfy this property. To address this, we propose Hölder-DPO, the first principled alignment loss with a provable redescending property, enabling estimation of the clean data distribution from noisy feedback. The aligned model estimates the likelihood of clean data, providing a theoretically grounded metric for dataset valuation that identifies the location and fraction of mislabels. This metric is gradient-free, enabling scalable and automated human feedback valuation without costly manual verification or clean validation dataset. Hölder-DPO achieves state-of-the-art robust alignment performance while accurately detecting mislabels in controlled datasets. Finally, applied to Anthropic HH-RLHF dataset, it reveals substantial noise levels and removing these mislabels significantly improves alignment performance across methods. The code is available at https://github.com/ma921/HolderDPO.

This work addresses the finite-time analysis of nonsmooth nonconvex stochastic optimization under Riemannian manifold constraints. We adapt the notion of Goldstein stationarity to the Riemannian setting as a performance metric for nonsmooth optimization on manifolds. We then propose a Riemannian Online to NonConvex (RO2NC) algorithm, for which we establish the sample complexity of $O(\epsilon^{-3}\delta^{-1})$ in finding ($\delta,\epsilon$)-stationary points. This result is the first-ever finite-time guarantee for fully nonsmooth, nonconvex optimization on manifolds and matches the optimal complexity in the Euclidean setting. When gradient information is unavailable, we develop a zeroth order version of RO2NC algorithm (ZO-RO2NC), for which we establish the same sample complexity. The numerical results support the theory and demonstrate the practical effectiveness of the algorithms.

However, its use of low-degree spherical harmonics limits its ability to capture spatially varying color and view-dependent effects such as specular highlights. Existing works augment Gaussians with either a global texture map, which struggles with complex scenes, or per-Gaussian texture maps, which introduces high storage overhead. We propose Image-Based Gaussian Splatting, an efficient alternative that leverages high-resolution source images for fine details and view-specific color modeling. Specifically, we model each pixel color as a combination of a base color from standard 3DGS rendering and a learned residual inferred from neighboring training images. This promotes accurate surface alignment and enables rendering images of high-frequency details and accurate view-dependent effects. Experiments on standard NVS benchmarks show that our method significantly outperforms prior Gaussian Splatting approaches in rendering quality, without increasing the storage footprint.

Reinforcement Learning (RL) can mitigate the causal confusion and distribution shift inherent to imitation learning (IL). However, applying RL to end-to-end autonomous driving (E2E-AD) remains an open problem for its training difficulty, and IL is still the mainstream paradigm in both academia and industry. Recently Model-based Reinforcement Learning (MBRL) have demonstrated promising results in neural planning; however, these methods typically require privileged information as input rather than raw sensor data. We fill this gap by designing Raw2Drive, a dual-stream MBRL approach. Initially, we efficiently train an auxiliary privileged world model paired with a neural planner that uses privileged information as input. Subsequently, we introduce a raw sensor world model trained via our proposed Guidance Mechanism, which ensures consistency between the raw sensor world model and the privileged world model during rollouts. Finally, the raw sensor world model combines the prior knowledge embedded in the heads of the privileged world model to effectively guide the training of the raw sensor policy. Raw2Drive is so far the only RL based end-to-end method on CARLA Leaderboard 2.0, and Bench2Drive and it achieves state-of-the-art performance.

Online planning has proven effective in reinforcement learning (RL) for improving sample efficiency and final performance. However, using planning for environment interaction inevitably introduces a divergence between the collected data and the policy's actual behaviors, degrading both model learning and policy improvement. To address this, we propose BOOM (Bootstrap Off-policy with WOrld Model), a framework that tightly integrates planning and off-policy learning through a bootstrap loop: the policy initializes the planner, and the planner refines actions to bootstrap the policy through behavior alignment. This loop is supported by a jointly learned world model, which enables the planner to simulate future trajectories and provides value targets to facilitate policy improvement. The core of BOOM is a likelihood-free alignment loss that bootstraps the policy using the planner's non-parametric action distribution, combined with a soft value-weighted mechanism that prioritizes high-return behaviors and mitigates variability in the planner's action quality within the replay buffer. Experiments on the high-dimensional DeepMind Control Suite and Humanoid-Bench show that BOOM achieves state-of-the-art results in both training stability and final performance.

Determining the precise geographic location of an image at a global scale remains an unsolved challenge. Standard image retrieval techniques are inefficient due to the sheer volume of images (>100M) and fail when coverage is insufficient. Scalable solutions, however, involve a trade-off: global classification typically yields coarse results (10+ kilometers), while cross-view retrieval between ground and aerial imagery suffers from a domain gap and has been primarily studied on smaller regions. This paper introduces a hybrid approach that achieves fine-grained geo-localization across a large geographic expanse the size of a continent. We leverage a proxy classification task during training to learn rich feature representations that implicitly encode precise location information. We combine these learned prototypes with embeddings of aerial imagery to increase robustness to the sparsity of ground-level data. This enables direct, fine-grained retrieval over areas spanning multiple countries. Our extensive evaluation demonstrates that our approach can localize within 200m more than 68\% of queries of a dataset covering a large part of Europe. The code is publicly available at scaling-geoloc.github.io .

Applying Transformers to irregular time-series typically requires specializations to their baseline architecture, which can result in additional computational overhead and increased method complexity. We present the Rotary Masked Autoencoder (RoMAE), which utilizes the popular Rotary Positional Embedding (RoPE) method for continuous positions. RoMAE is an extension to the Masked Autoencoder (MAE) that enables interpolation and representation learning with multidimensional continuous positional information while avoiding any time-series-specific architectural specializations.

Decision-making across various fields, such as medicine, heavily relies on conditional average treatment effects (CATEs). Practitioners commonly make decisions by checking whether the estimated CATE is positive, even though the decision-making performance of modern CATE estimators is poorly understood from a theoretical perspective. In this paper, we study optimal decision-making based on two-stage CATE estimators (e.g., DR-learner), which are considered state-of-the-art and widely used in practice. We prove that, while such estimators may be optimal for estimating CATE, they can be suboptimal when used for decision-making. Intuitively, this occurs because such estimators prioritize CATE accuracy in regions far away from the decision boundary, which is ultimately irrelevant to decision-making. As a remedy, we propose a novel two-stage learning objective that retargets the CATE to balance CATE estimation error and decision performance. We then propose a neural method that optimizes an adaptively-smoothed approximation of our learning objective. Finally, we confirm the effectiveness of our method both empirically and theoretically. In sum, our work is the first to show how state-of-the-art CATE estimators can be adapted for optimal decision-making.