Driving on Registers

We present DrivoR, a simple and efficient transformer-based architecture for end-to-end autonomous driving. Our approach builds on pretrained Vision Transformers (ViTs) and introduces camera-aware register tokens that compress multi-camera features into a compact scene representation, significantly reducing downstream computation without sacrificing accuracy. These tokens drive two lightweight transformer decoders that generate and then score candidate trajectories. The scoring decoder learns to mimic an oracle and predicts interpretable sub-scores representing aspects such as safety, comfort, and efficiency, enabling behavior-conditioned driving at inference. Despite its minimal design, DrivoR outperforms or matches strong contemporary baselines across NAVSIM-v1, NAVSIM-v2, and the photorealistic closed-loop HUGSIM benchmark. Our results show that a pure-transformer architecture, combined with targeted token compression, is sufficient for accurate, efficient, and adaptive end-to-end driving. Code and checkpoints will be made available via the project page.

Not All Steps are Informative: On the Linearity of LLMs' RLVR Training

Reinforcement learning with verifiable rewards (RLVR) has become a central component of large language model (LLM) post-training. Unlike supervised fine-tuning (SFT), RLVR lets an LLM generate multiple candidate solutions and reinforces those that lead to a verifiably correct final answer. However, in practice, RLVR often requires thousands of training steps to reach strong performance, incurring substantial computation largely attributed to prolonged exploration. In this work, we make a surprising observation: during RLVR, LLMs evolve in a strongly linear manner. Specifically, both model weights and model output log-probabilities exhibit strong linear correlations with RL training steps. This suggests that RLVR predominantly amplifies trends that emerge early in training, rather than continuously discovering new behaviors throughout the entire optimization trajectory. Motivated by this linearity, we investigate whether future model states can be predicted from intermediate checkpoints via extrapolation, avoiding continued expensive training. We show that Weight Extrapolation produces models with performance comparable to standard RL training while requiring significantly less computation. Moreover, Logits Extrapolation consistently outperforms continued RL training on all four benchmarks by extrapolating beyond the step range where RL training remains stable.

UniDrive-WM: Unified Understanding, Planning and Generation World Model For Autonomous Driving

World models have become central to autonomous driving, where accurate scene understanding and future prediction are crucial for safe control. Recent work has explored using vision-language models (VLMs) for planning, yet existing approaches typically treat perception, prediction, and planning as separate modules. We propose UniDrive-WM, a unified VLM-based world model that jointly performs driving-scene understanding, trajectory planning, and trajectory-conditioned future image generation within a single architecture. UniDrive-WM's trajectory planner predicts a future trajectory, which conditions a VLM-based image generator to produce plausible future frames. These predictions provide additional supervisory signals that enhance scene understanding and iteratively refine trajectory generation. We further compare discrete and continuous output representations for future image prediction, analyzing their influence on downstream driving performance. Experiments on the challenging Bench2Drive benchmark show that UniDrive-WM produces high-fidelity future images and improves planning performance by 5.9% in L2 trajectory error and 9.2% in collision rate over the previous best method. These results demonstrate the advantages of tightly integrating VLM-driven reasoning, planning, and generative world modeling for autonomous driving. The project page is available at https://unidrive-wm.github.io/UniDrive-WM .

Predictable Gradient Manifolds in Deep Learning: Temporal Path-Length and Intrinsic Rank as a Complexity Regime

Deep learning optimization exhibits structure that is not captured by worst-case gradient bounds. Empirically, gradients along training trajectories are often temporally predictable and evolve within a low-dimensional subspace. In this work we formalize this observation through a measurable framework for predictable gradient manifolds. We introduce two computable quantities: a prediction-based path length that measures how well gradients can be forecast from past information, and a predictable rank that quantifies the intrinsic temporal dimension of gradient increments. We show how classical online and nonconvex optimization guarantees can be restated so that convergence and regret depend explicitly on these quantities, rather than on worst-case variation. Across convolutional networks, vision transformers, language models, and synthetic control tasks, we find that gradient trajectories are locally predictable and exhibit strong low-rank structure over time. These properties are stable across architectures and optimizers, and can be diagnosed directly from logged gradients using lightweight random projections. Our results provide a unifying lens for understanding optimization dynamics in modern deep learning, reframing standard training as operating in a low-complexity temporal regime. This perspective suggests new directions for adaptive optimizers, rank-aware tracking, and prediction-based algorithm design grounded in measurable properties of real training runs.

Distribution-Guided and Constrained Quantum Machine Unlearning

Machine unlearning aims to remove the influence of specific training data from a learned model without full retraining. While recent work has begun to explore unlearning in quantum machine learning, existing approaches largely rely on fixed, uniform target distributions and do not explicitly control the trade-off between forgetting and retained model behaviour. In this work, we propose a distribution-guided framework for class-level quantum machine unlearning that treats unlearning as a constrained optimization problem. Our method introduces a tunable target distribution derived from model similarity statistics, decoupling the suppression of forgotten-class confidence from assumptions about redistribution among retained classes. We further incorporate an anchor-based preservation constraint that explicitly maintains predictive behaviour on selected retained data, yielding a controlled optimization trajectory that limits deviation from the original model. We evaluate the approach on variational quantum classifiers trained on the Iris and Covertype datasets. Results demonstrate sharp suppression of forgotten-class confidence, minimal degradation of retained-class performance, and closer alignment with the gold retrained model baselines compared to uniform-target unlearning. These findings highlight the importance of target design and constraint-based formulations for reliable and interpretable quantum machine unlearning.

LinkD: AutoRegressive Diffusion Model for Mechanical Linkage Synthesis

Designing mechanical linkages to achieve target end-effector trajectories presents a fundamental challenge due to the intricate coupling between continuous node placements, discrete topological configurations, and nonlinear kinematic constraints. The highly nonlinear motion-to-configuration relationship means small perturbations in joint positions drastically alter trajectories, while the combinatorially expanding design space renders conventional optimization and heuristic methods computationally intractable. We introduce an autoregressive diffusion framework that exploits the dyadic nature of linkage assembly by representing mechanisms as sequentially constructed graphs, where nodes correspond to joints and edges to rigid links. Our approach combines a causal transformer with a Denoising Diffusion Probabilistic Model (DDPM), both conditioned on target trajectories encoded via a transformer encoder. The causal transformer autoregressively predicts discrete topology node-by-node, while the DDPM refines each node's spatial coordinates and edge connectivity to previously generated nodes. This sequential generation enables adaptive trial-and-error synthesis where problematic nodes exhibiting kinematic locking or collisions can be selectively regenerated, allowing autonomous correction of degenerate configurations during design. Our graph-based, data-driven methodology surpasses traditional optimization approaches, enabling scalable inverse design that generalizes to mechanisms with arbitrary node counts. We demonstrate successful synthesis of linkage systems containing up to 20 nodes with extensibility to N-node architectures. This work advances autoregressive graph generation methodologies and computational kinematic synthesis, establishing new paradigms for scalable inverse design of complex mechanical systems.

PointWorld: Scaling 3D World Models for In-The-Wild Robotic Manipulation

Humans anticipate, from a glance and a contemplated action of their bodies, how the 3D world will respond, a capability that is equally vital for robotic manipulation. We introduce PointWorld, a large pre-trained 3D world model that unifies state and action in a shared 3D space as 3D point flows: given one or few RGB-D images and a sequence of low-level robot action commands, PointWorld forecasts per-pixel displacements in 3D that respond to the given actions. By representing actions as 3D point flows instead of embodiment-specific action spaces (e.g., joint positions), this formulation directly conditions on physical geometries of robots while seamlessly integrating learning across embodiments. To train our 3D world model, we curate a large-scale dataset spanning real and simulated robotic manipulation in open-world environments, enabled by recent advances in 3D vision and simulated environments, totaling about 2M trajectories and 500 hours across a single-arm Franka and a bimanual humanoid. Through rigorous, large-scale empirical studies of backbones, action representations, learning objectives, partial observability, data mixtures, domain transfers, and scaling, we distill design principles for large-scale 3D world modeling. With a real-time (0.1s) inference speed, PointWorld can be efficiently integrated in the model-predictive control (MPC) framework for manipulation. We demonstrate that a single pre-trained checkpoint enables a real-world Franka robot to perform rigid-body pushing, deformable and articulated object manipulation, and tool use, without requiring any demonstrations or post-training and all from a single image captured in-the-wild. Project website at https://point-world.github.io/.

Optimizing Control-Friendly Trajectories with Self-Supervised Residual Learning

Real-world physics can only be analytically modeled with a certain level of precision for modern intricate robotic systems. As a result, tracking aggressive trajectories accurately could be challenging due to the existence of residual physics during controller synthesis. This paper presents a self-supervised residual learning and trajectory optimization framework to address the aforementioned challenges. At first, unknown dynamic effects on the closed-loop model are learned and treated as residuals of the nominal dynamics, jointly forming a hybrid model. We show that learning with analytic gradients can be achieved using only trajectory-level data while enjoying accurate long-horizon prediction with an arbitrary integration step size. Subsequently, a trajectory optimizer is developed to compute the optimal reference trajectory with the residual physics along it minimized. It ends up with trajectories that are friendly to the following control level. The agile flight of quadrotors illustrates that by utilizing the hybrid dynamics, the proposed optimizer outputs aggressive motions that can be precisely tracked.

From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in LLMs

Recent studies reveal that large language models (LLMs) exhibit limited logical reasoning abilities in mathematical problem-solving, instead often relying on pattern-matching and memorization. We systematically analyze this limitation, focusing on logical relationship understanding, which is a core capability underlying genuine logical reasoning, and reveal that errors related to this capability account for over 90\% of incorrect predictions, with Chain-of-Thought Supervised Fine-Tuning (CoT-SFT) failing to substantially reduce these errors. To address this bottleneck, we propose First-Step Logical Reasoning (FSLR), a lightweight training framework targeting logical relationship understanding. Our key insight is that the first planning step-identifying which variables to use and which operation to apply-encourages the model to derive logical relationships directly from the problem statement. By training models on this isolated step, FSLR provides explicit supervision for logical relationship understanding, unlike CoT-SFT which implicitly embeds such relationships within complete solution trajectories. Extensive experiments across multiple models and datasets demonstrate that FSLR consistently outperforms CoT-SFT under both in-distribution and out-of-distribution settings, with average improvements of 3.2\% and 4.6\%, respectively. Moreover, FSLR achieves 4-6x faster training and reduces training token consumption by over 80\%.

MFC-RFNet: A Multi-scale Guided Rectified Flow Network for Radar Sequence Prediction

Accurate and high-resolution precipitation nowcasting from radar echo sequences is crucial for disaster mitigation and economic planning, yet it remains a significant challenge. Key difficulties include modeling complex multi-scale evolution, correcting inter-frame feature misalignment caused by displacement, and efficiently capturing long-range spatiotemporal context without sacrificing spatial fidelity. To address these issues, we present the Multi-scale Feature Communication Rectified Flow (RF) Network (MFC-RFNet), a generative framework that integrates multi-scale communication with guided feature fusion. To enhance multi-scale fusion while retaining fine detail, a Wavelet-Guided Skip Connection (WGSC) preserves high-frequency components, and a Feature Communication Module (FCM) promotes bidirectional cross-scale interaction. To correct inter-frame displacement, a Condition-Guided Spatial Transform Fusion (CGSTF) learns spatial transforms from conditioning echoes to align shallow features. The backbone adopts rectified flow training to learn near-linear probability-flow trajectories, enabling few-step sampling with stable fidelity. Additionally, lightweight Vision-RWKV (RWKV) blocks are placed at the encoder tail, the bottleneck, and the first decoder layer to capture long-range spatiotemporal dependencies at low spatial resolutions with moderate compute. Evaluations on four public datasets (SEVIR, MeteoNet, Shanghai, and CIKM) demonstrate consistent improvements over strong baselines, yielding clearer echo morphology at higher rain-rate thresholds and sustained skill at longer lead times. These results suggest that the proposed synergy of RF training with scale-aware communication, spatial alignment, and frequency-aware fusion presents an effective and robust approach for radar-based nowcasting.