Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and a Tight Univariate Rate

In high-dimensional online prediction, the best predictor may depend on only a few features, so regret should scale with sparsity rather than the ambient dimension. Feature priming pursues this goal by estimating feature weights from past data and refitting a minimum-norm predictor on the rescaled design. Warmuth and Amid asked at COLT 2023 whether any of three such rules admits a competitive online regret guarantee. Using the natural Moore--Penrose protocol based only on past data, we give a negative answer to the sparse-logarithmic form of this COLT open problem. Our analysis identifies a common obstruction: cheap nuisance interpolation causes the refit to underweight the truly predictive coordinate. An exact target-mass identity and a two-sign argument turn this effect into clipped prediction loss. Hadamard constructions force $Ω(\min\{T,\sqrt{d}\})$ regret for all three rules against a zero-loss one-sparse comparator, with extensions to fixed prime powers and selectors among the rules. Conversely, regret is controlled by data rank, and a Euclidean-normalized triangular construction matches this dependence for powered univariate priming, even under nonnegative second-stage ridge regularization; a paired ridge construction also covers all three powered rules. Exploratory diagnostics on frozen language-model activations exhibit the same relation among nuisance interpolation, target weight, and loss. The exact multivariate and Pearson frontiers remain open.

ACE-Brain-0.5: A Unified Embodied Foundational Model for Physical Agentic AI

Embodied AI is moving from isolated perception or action modules toward physical agents that understand, plan under goals, act through robot bodies, monitor progress, and improve from experience. Existing systems address this loop only in parts: end-to-end policies generate actions but often lack spatial reasoning, planning, and execution assessment, while robot-agent systems orchestrate tools or specialists but do not learn a shared representation. This fragmentation limits general Physical Agentic AI. We present ACE-Brain-0.5, a unified embodied foundation model that organizes robot intelligence into five coupled functions: spatial perception, decision making, embodied interaction, self-monitoring, and self-improvement. Built on ACE-Brain-0, which established spatial intelligence as a shared scaffold across robot platforms, ACE-Brain-0.5 extends an understanding-centric model into a closed-loop foundation model. A single 8B backbone instantiates the first four functions: grounding objects and affordances, reasoning over 3D and egocentric spatial relations, decomposing instructions into subgoals, generating navigation and manipulation actions, and estimating progress for verification and recovery. To unify these capabilities without cross-task interference, we introduce SSR+, which extends Scaffold-Specialize-Reconcile with a Reactivate stage after task-vector merging. The fifth function, self-improvement, is realized by a companion framework that updates external execution state, including task schemas, spatial memory, and failure-recovery cases, from rollouts. Across fifteen benchmarks, ACE-Brain-0.5 improves over ACE-Brain-0 on 14 of 18 spatial perception and grounding benchmarks, achieves competitive navigation and manipulation performance, and provides strong progress estimation in ID and OOD settings. Together, these results mark an early step toward general Physical Agentic AI.

Kairos: A Native World Model Stack for Physical AI

World models are transitioning from passive visual generators to foundational, operational infrastructure for Physical AI: they must natively acquire world knowledge from heterogeneous experience, maintain persistent states over long horizons, and execute efficiently within real deployment constraints. We introduce Kairos, a native world model stack designed around these requirements. (1) Kairos learns the world by pioneering a Native Pre-training Paradigm governed by a Cross-Embodiment Data Curriculum, which organizes open-world videos, human behavioral data, and robot interactions into a progressive developmental pathway. (2) Kairos maintains the world by unified world understanding, generation, and prediction within a Native Unified Architecture equipped with Hybrid Linear Temporal Attention, where sliding-window attention captures local dynamics, dilated sliding windows capture mid-range dependencies, and gated linear attention maintains persistent global memory. We establish formal theoretical bounds demonstrating that this temporal factorization strictly limits error accumulation, mathematically guaranteeing state propagation across extended horizons. (3) Kairos runs the world by incorporating a Deployment-Aware System Co-Design to support low-latency rollout generation on server and consumer-grade hardware for real-world observation-action-feedback loops. Experiments on embodied world-model, long-horizon, and action-policy benchmarks show that Kairos achieves top level performance while offering a strong efficiency-capability trade-off. Together, these results position Kairos as a cohesive operational foundation for future self-evolving physical intelligence.

WMAttack: Automated Attack Search for Adversarial Evaluation of World-Model Agents

Despite the growing use of world models as decision-making agents, their adversarial robustness remains underexplored due to the lack of dedicated automated evaluation methods. A key obstacle is that attack evaluation must be both accurate and efficient: weak manually tuned attacks can overestimate robustness, while exhaustive hyperparameter search is prohibitively expensive because each candidate requires closed-loop rollouts through learned latent dynamics. We introduce WMAttack, an automated attack-search framework for adversarial evaluation of world-model agents. WMAttack formulates robustness evaluation as a finite-budget search over attack configurations, including attack families, perturbation budgets, optimization steps, restarts, and allocation rules. To improve search accuracy, Self-Correcting Attack Search (SCAS) refines the attack proposal distribution using feedback from reward degradation, action instability, runtime cost, and rollout variability. To improve search efficiency, Representation-Guided Attack Retrieval (RGAR) retrieves effective historical configurations from representation-similar tasks, providing a warm start for unseen environments. We provide a theoretical explanation showing that proposal refinement improves finite-budget search when it shifts probability mass toward high-utility attacks. Across Atari and DeepMind Control tasks, WMAttack consistently discovers stronger attacks than the evaluated baselines, improving normalized reward drop from 0.497 to 1.034 on DreamerV3 Atari and from 0.319 to 0.682 on DMC. Ablations further show that RGAR improves initial candidate quality and SCAS improves final attack utility under fixed evaluation budgets.

ACE-Brain-0: Spatial Intelligence as a Shared Scaffold for Universal Embodiments

Universal embodied intelligence demands robust generalization across heterogeneous embodiments, such as autonomous driving, robotics, and unmanned aerial vehicles (UAVs). However, existing embodied brain in training a unified model over diverse embodiments frequently triggers long-tail data, gradient interference, and catastrophic forgetting, making it notoriously difficult to balance universal generalization with domain-specific proficiency. In this report, we introduce ACE-Brain-0, a generalist foundation brain that unifies spatial reasoning, autonomous driving, and embodied manipulation within a single multimodal large language model~(MLLM). Our key insight is that spatial intelligence serves as a universal scaffold across diverse physical embodiments: although vehicles, robots, and UAVs differ drastically in morphology, they share a common need for modeling 3D mental space, making spatial cognition a natural, domain-agnostic foundation for cross-embodiment transfer. Building on this insight, we propose the Scaffold-Specialize-Reconcile~(SSR) paradigm, which first establishes a shared spatial foundation, then cultivates domain-specialized experts, and finally harmonizes them through data-free model merging. Furthermore, we adopt Group Relative Policy Optimization~(GRPO) to strengthen the model's comprehensive capability. Extensive experiments demonstrate that ACE-Brain-0 achieves competitive and even state-of-the-art performance across 24 spatial and embodiment-related benchmarks.

Why Self-Rewarding Works: Theoretical Guarantees for Iterative Alignment of Language Models

Self-Rewarding Language Models (SRLMs) achieve notable success in iteratively improving alignment without external feedback. Yet, despite their striking empirical progress, the core mechanisms driving their capabilities remain unelucidated, leaving a critical gap in theoretical understanding. This paper provides the first rigorous theoretical guarantees for SRLMs. We first establish a lower bound that characterizes the fundamental limits of a single update step, revealing a critical dependence on the quality of the initial model. We then derive finite-sample error bounds for the full iterative paradigm, showing that performance improves at a rate of $\widetilde{\mathcal{O}}\left(1/\sqrt{n}\right)$ with sample size $n$. Crucially, our analysis reveals that the dependence on the initial model decays exponentially with the number of iterations $T$. This provides a formal explanation for why self-rewarding succeeds: it robustly overcomes poor initialization by steering the dynamics toward internal stability and consistency. Finally, we instantiate our theoretical framework for the linear softmax model class, yielding tailored guarantees that connect our high-level insights to practical model architectures.

A Theoretical Perspective: How to Prevent Model Collapse in Self-consuming Training Loops

High-quality data is essential for training large generative models, yet the vast reservoir of real data available online has become nearly depleted. Consequently, models increasingly generate their own data for further training, forming Self-consuming Training Loops (STLs). However, the empirical results have been strikingly inconsistent: some models degrade or even collapse, while others successfully avoid these failures, leaving a significant gap in theoretical understanding to explain this discrepancy. This paper introduces the intriguing notion of recursive stability and presents the first theoretical generalization analysis, revealing how both model architecture and the proportion between real and synthetic data influence the success of STLs. We further extend this analysis to transformers in in-context learning, showing that even a constant-sized proportion of real data ensures convergence, while also providing insights into optimal synthetic data sizing.

HRP: High-Rank Preheating for Superior LoRA Initialization

This paper studies the crucial impact of initialization on the convergence properties of Low-Rank Adaptation (LoRA). We theoretically demonstrate that random initialization, a widely used schema, will likely lead LoRA to random low-rank results, rather than the best low-rank result. While this issue can be mitigated by adjusting initialization towards a well-informed direction, it relies on prior knowledge of the target, which is typically unknown in real-world scenarios. To approximate this well-informed initial direction, we propose High-Rank Preheating (HRP), which fine-tunes high-rank LoRA for a few steps and uses the singular value decomposition of the preheated result as a superior initialization. HRP initialization is theory-supported to combine the convergence strengths of high-rank LoRA and the generalization strengths of low-rank LoRA. Extensive experiments demonstrate that HRP significantly enhances LoRA's effectiveness across various models and tasks, achieving performance comparable to full-parameter fine-tuning and outperforming other initialization strategies.

On Championing Foundation Models: From Explainability to Interpretability

Understanding the inner mechanisms of black-box foundation models (FMs) is essential yet challenging in artificial intelligence and its applications. Over the last decade, the long-running focus has been on their explainability, leading to the development of post-hoc explainable methods to rationalize the specific decisions already made by black-box FMs. However, these explainable methods have certain limitations in terms of faithfulness, detail capture and resource requirement. Consequently, in response to these issues, a new class of interpretable methods should be considered to unveil the underlying mechanisms in an accurate, comprehensive, heuristic and resource-light way. This survey aims to review interpretable methods that comply with the aforementioned principles and have been successfully applied to FMs. These methods are deeply rooted in machine learning theory, covering the analysis of generalization performance, expressive capability, and dynamic behavior. They provide a thorough interpretation of the entire workflow of FMs, ranging from the inference capability and training dynamics to their ethical implications. Ultimately, drawing upon these interpretations, this review identifies the next frontier research directions for FMs.

Towards Theoretical Understandings of Self-Consuming Generative Models

This paper tackles the emerging challenge of training generative models within a self-consuming loop, wherein successive generations of models are recursively trained on mixtures of real and synthetic data from previous generations. We construct a theoretical framework to rigorously evaluate how this training regimen impacts the data distributions learned by future models. Specifically, we derive bounds on the total variation (TV) distance between the synthetic data distributions produced by future models and the original real data distribution under various mixed training scenarios. Our analysis demonstrates that this distance can be effectively controlled under the condition that mixed training dataset sizes or proportions of real data are large enough. Interestingly, we further unveil a phase transition induced by expanding synthetic data amounts, proving theoretically that while the TV distance exhibits an initial ascent, it declines beyond a threshold point. Finally, we specialize our general results to diffusion models, delivering nuanced insights such as the efficacy of optimal early stopping within the self-consuming loop.