QuadFM: Foundational Text-Driven Quadruped Motion Dataset for Generation and Control

Despite significant advances in quadrupedal robotics, a critical gap persists in foundational motion resources that holistically integrate diverse locomotion, emotionally expressive behaviors, and rich language semantics-essential for agile, intuitive human-robot interaction. Current quadruped motion datasets are limited to a few mocap primitives (e.g., walk, trot, sit) and lack diverse behaviors with rich language grounding. To bridge this gap, we introduce Quadruped Foundational Motion (QuadFM) , the first large-scale, ultra-high-fidelity dataset designed for text-to-motion generation and general motion control. QuadFM contains 11,784 curated motion clips spanning locomotion, interactive, and emotion-expressive behaviors (e.g., dancing, stretching, peeing), each with three-layer annotation-fine-grained action labels, interaction scenarios, and natural language commands-totaling 35,352 descriptions to support language-conditioned understanding and command execution. We further propose Gen2Control RL, a unified framework that jointly trains a general motion controller and a text-to-motion generator, enabling efficient end-to-end inference on edge hardware. On a real quadruped robot with an NVIDIA Orin, our system achieves real-time motion synthesis (<500 ms latency). Simulation and real-world results show realistic, diverse motions while maintaining robust physical interaction. The dataset will be released at https://github.com/GaoLii/QuadFM.

CoMaTrack: Competitive Multi-Agent Game-Theoretic Tracking with Vision-Language-Action Models

Embodied Visual Tracking (EVT), a core dynamic task in embodied intelligence, requires an agent to precisely follow a language-specified target. Yet most existing methods rely on single-agent imitation learning, suffering from costly expert data and limited generalization due to static training environments. Inspired by competition-driven capability evolution, we propose CoMaTrack, a competitive game-theoretic multi-agent reinforcement learning framework that trains agents in a dynamic adversarial setting with competitive subtasks, yielding stronger adaptive planning and interference-resilient strategies. We further introduce CoMaTrack-Bench, the first benchmark for competitive EVT, featuring game scenarios between a tracker and adaptive opponents across diverse environments and instructions, enabling standardized robustness evaluation under active adversarial interactions. Experiments show that CoMaTrack achieves state-of-the-art results on both standard benchmarks and CoMaTrack-Bench. Notably, a 3B VLM trained with our framework surpasses previous single-agent imitation learning methods based on 7B models on the challenging EVT-Bench, achieving 92.1% in STT, 74.2% in DT, and 57.5% in AT. The benchmark code will be available at https://github.com/wlqcode/CoMaTrack-Bench

A New Lower Bound for the Random Offerer Mechanism in Bilateral Trade using AI-Guided Evolutionary Search

The celebrated Myerson--Satterthwaite theorem shows that in bilateral trade, no mechanism can be simultaneously fully efficient, Bayesian incentive compatible (BIC), and budget balanced (BB). This naturally raises the question of how closely the gains from trade (GFT) achievable by a BIC and BB mechanism can approximate the first-best (fully efficient) benchmark. The optimal BIC and BB mechanism is typically complex and highly distribution-dependent, making it difficult to characterize directly. Consequently, much of the literature analyzes simpler mechanisms such as the Random-Offerer (RO) mechanism and establishes constant-factor guarantees relative to the first-best GFT. An important open question concerns the worst-case performance of the RO mechanism relative to first-best (FB) efficiency. While it was originally hypothesized that the approximation ratio $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}}$ is bounded by $2$, recent work provided counterexamples to this conjecture: Cai et al. proved that the ratio can be strictly larger than $2$, and Babaioff et al. exhibited an explicit example with ratio approximately $2.02$. In this work, we employ AlphaEvolve, an AI-guided evolutionary search framework, to explore the space of value distributions. We identify a new worst-case instance that yields an improved lower bound of $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}} \ge \textbf{2.0749}$. This establishes a new lower bound on the worst-case performance of the Random-Offerer mechanism, demonstrating a wider efficiency gap than previously known.

ABot-N0: Technical Report on the VLA Foundation Model for Versatile Embodied Navigation

Embodied navigation has long been fragmented by task-specific architectures. We introduce ABot-N0, a unified Vision-Language-Action (VLA) foundation model that achieves a ``Grand Unification'' across 5 core tasks: Point-Goal, Object-Goal, Instruction-Following, POI-Goal, and Person-Following. ABot-N0 utilizes a hierarchical ``Brain-Action'' architecture, pairing an LLM-based Cognitive Brain for semantic reasoning with a Flow Matching-based Action Expert for precise, continuous trajectory generation. To support large-scale learning, we developed the ABot-N0 Data Engine, curating 16.9M expert trajectories and 5.0M reasoning samples across 7,802 high-fidelity 3D scenes (10.7 $\text{km}^2$). ABot-N0 achieves new SOTA performance across 7 benchmarks, significantly outperforming specialized models. Furthermore, our Agentic Navigation System integrates a planner with hierarchical topological memory, enabling robust, long-horizon missions in dynamic real-world environments.

Is Online Linear Optimization Sufficient for Strategic Robustness?

We consider bidding in repeated Bayesian first-price auctions. Bidding algorithms that achieve optimal regret have been extensively studied, but their strategic robustness to the seller's manipulation remains relatively underexplored. Bidding algorithms based on no-swap-regret algorithms achieve both desirable properties, but are suboptimal in terms of statistical and computational efficiency. In contrast, online gradient ascent is the only algorithm that achieves $O(\sqrt{TK})$ regret and strategic robustness [KSS24], where $T$ denotes the number of auctions and $K$ the number of bids. In this paper, we explore whether simple online linear optimization (OLO) algorithms suffice for bidding algorithms with both desirable properties. Our main result shows that sublinear linearized regret is sufficient for strategic robustness. Specifically, we construct simple black-box reductions that convert any OLO algorithm into a strategically robust no-regret bidding algorithm, in both known and unknown value distribution settings. For the known value distribution case, our reduction yields a bidding algorithm that achieves $O(\sqrt{T \log K})$ regret and strategic robustness (with exponential improvement on the $K$-dependence compared to [KSS24]). For the unknown value distribution case, our reduction gives a bidding algorithm with high-probability $O(\sqrt{T (\log K+\log(T/δ)})$ regret and strategic robustness, while removing the bounded density assumption made in [KSS24].

Asymptotic Universal Alignment: A New Alignment Framework via Test-Time Scaling

Aligning large language models (LLMs) to serve users with heterogeneous and potentially conflicting preferences is a central challenge for personalized and trustworthy AI. We formalize an ideal notion of universal alignment through test-time scaling: for each prompt, the model produces $k\ge 1$ candidate responses and a user selects their preferred one. We introduce $(k,f(k))$-robust alignment, which requires the $k$-output model to have win rate $f(k)$ against any other single-output model, and asymptotic universal alignment (U-alignment), which requires $f(k)\to 1$ as $k\to\infty$. Our main result characterizes the optimal convergence rate: there exists a family of single-output policies whose $k$-sample product policies achieve U-alignment at rate $f(k)=\frac{k}{k+1}$, and no method can achieve a faster rate in general. We show that popular post-training methods, including Nash learning from human feedback (NLHF), can fundamentally underutilize the benefits of test-time scaling. Even though NLHF is optimal for $k=1$, sampling from the resulting (often deterministic) policy cannot guarantee win rates above $\tfrac{1}{2}$ except for an arbitrarily small slack. This stems from a lack of output diversity: existing alignment methods can collapse to a single majority-preferred response, making additional samples redundant. In contrast, our approach preserves output diversity and achieves the optimal test-time scaling rate. In particular, we propose a family of symmetric multi-player alignment games and prove that any symmetric Nash equilibrium policy of the $(k+1)$-player alignment game achieves the optimal $(k,\frac{k}{k+1})$-robust alignment. Finally, we provide theoretical convergence guarantees for self-play learning dynamics in these games and extend the framework to opponents that also generate multiple responses.

Smooth Operator: Smooth Verifiable Reward Activates Spatial Reasoning Ability of Vision-Language Model

Vision-Language Models (VLMs) face a critical bottleneck in achieving precise numerical prediction for 3D scene understanding. Traditional reinforcement learning (RL) approaches, primarily based on relative ranking, often suffer from severe reward sparsity and gradient instability, failing to effectively exploit the verifiable signals provided by 3D physical constraints. Notably, in standard GRPO frameworks, relative normalization causes "near-miss" samples (characterized by small but non-zero errors) to suffer from advantage collapse. This leads to a severe data utilization bottleneck where valuable boundary samples are discarded during optimization. To address this, we introduce the Smooth Numerical Reward Activation (SNRA) operator and the Absolute-Preserving GRPO (AP-GRPO) framework. SNRA employs a dynamically parameterized Sigmoid function to transform raw feedback into a dense, continuous reward continuum. Concurrently, AP-GRPO integrates absolute scalar gradients to mitigate the numerical information loss inherent in conventional relative-ranking mechanisms. By leveraging this approach, we constructed Numerical3D-50k, a dataset comprising 50,000 verifiable 3D subtasks. Empirical results indicate that AP-GRPO achieves performance parity with large-scale supervised methods while maintaining higher data efficiency, effectively activating latent 3D reasoning in VLMs without requiring architectural modifications.

DiffVL: Diffusion-Based Visual Localization on 2D Maps via BEV-Conditioned GPS Denoising

Accurate visual localization is crucial for autonomous driving, yet existing methods face a fundamental dilemma: While high-definition (HD) maps provide high-precision localization references, their costly construction and maintenance hinder scalability, which drives research toward standard-definition (SD) maps like OpenStreetMap. Current SD-map-based approaches primarily focus on Bird's-Eye View (BEV) matching between images and maps, overlooking a ubiquitous signal-noisy GPS. Although GPS is readily available, it suffers from multipath errors in urban environments. We propose DiffVL, the first framework to reformulate visual localization as a GPS denoising task using diffusion models. Our key insight is that noisy GPS trajectory, when conditioned on visual BEV features and SD maps, implicitly encode the true pose distribution, which can be recovered through iterative diffusion refinement. DiffVL, unlike prior BEV-matching methods (e.g., OrienterNet) or transformer-based registration approaches, learns to reverse GPS noise perturbations by jointly modeling GPS, SD map, and visual signals, achieving sub-meter accuracy without relying on HD maps. Experiments on multiple datasets demonstrate that our method achieves state-of-the-art accuracy compared to BEV-matching baselines. Crucially, our work proves that diffusion models can enable scalable localization by treating noisy GPS as a generative prior-making a paradigm shift from traditional matching-based methods.

What Makes Treatment Effects Identifiable? Characterizations and Estimators Beyond Unconfoundedness

Most of the widely used estimators of the average treatment effect (ATE) in causal inference rely on the assumptions of unconfoundedness and overlap. Unconfoundedness requires that the observed covariates account for all correlations between the outcome and treatment. Overlap requires the existence of randomness in treatment decisions for all individuals. Nevertheless, many types of studies frequently violate unconfoundedness or overlap, for instance, observational studies with deterministic treatment decisions -- popularly known as Regression Discontinuity designs -- violate overlap. In this paper, we initiate the study of general conditions that enable the identification of the average treatment effect, extending beyond unconfoundedness and overlap. In particular, following the paradigm of statistical learning theory, we provide an interpretable condition that is sufficient and nearly necessary for the identification of ATE. Moreover, this condition characterizes the identification of the average treatment effect on the treated (ATT) and can be used to characterize other treatment effects as well. To illustrate the utility of our condition, we present several well-studied scenarios where our condition is satisfied and, hence, we prove that ATE can be identified in regimes that prior works could not capture. For example, under mild assumptions on the data distributions, this holds for the models proposed by Tan (2006) and Rosenbaum (2002), and the Regression Discontinuity design model introduced by Thistlethwaite and Campbell (1960). For each of these scenarios, we also show that, under natural additional assumptions, ATE can be estimated from finite samples. We believe these findings open new avenues for bridging learning-theoretic insights and causal inference methodologies, particularly in observational studies with complex treatment mechanisms.

On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate Convergence of Learning in Games

Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic Multiplicative Weights Update (OMWU), can exhibit arbitrarily slow last-iterate convergence even in simple $2 \times 2$ matrix games, despite many of these dynamics being known to converge asymptotically in the last iterate. It remains unclear, however, whether these algorithms achieve fast non-ergodic convergence under weaker criteria, such as best-iterate convergence. We show that for $2\times 2$ matrix games, OMWU achieves an $O(T^{-1/6})$ best-iterate convergence rate, in stark contrast to its slow last-iterate convergence in the same class of games. Furthermore, we establish a lower bound showing that OMWU does not achieve any polynomial random-iterate convergence rate, measured by the expected duality gaps across all iterates. This result challenges the conventional wisdom that random-iterate convergence is essentially equivalent to best-iterate convergence, with the former often used as a proxy for establishing the latter. Our analysis uncovers a new connection to dynamic regret and presents a novel two-phase approach to best-iterate convergence, which could be of independent interest.