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Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

MLLM-powered embodied agents deployed in real-world environments encounter physical hazards. However, existing approaches lack explicit mechanisms for identifying hazards and reasoning about action-conditioned risks, leading agents to either miss risky interactions or over-identify risks. To address this, we propose EMBGuard, the first MLLM-based safety guardrail for embodied agents designed to decouple physical risk reasoning from agent policy. By evaluating a (visual observation, action) pair, EMBGuard identifies hazardous configurations and provides natural language explanations of potential risks. Alongside EMBGuard, we contribute EMBHazard, a training dataset of 15.1K action-conditioned pairs, and EMBGuardTest, a benchmark of 329 manually curated real-world scenarios spanning seven physical risk categories. Through compositional variation of hazards and actions, we generate diverse risky and benign scenarios that agents may encounter during planning. Despite its compact size (2B, 4B), EMBGuard achieves performance competitive with proprietary MLLMs (e.g., GPT-5.1, Gemini-2.5-Pro) while significantly reducing the false-positive rates that hinder real-time deployment. We make the code, data, and models publicly available at https://github.com/dongwxxkchoi/EMBGuard.

We study stochastic minimum-cost reach-avoid reinforcement learning, where an agent must satisfy a reach-avoid specification with probability at least $p$ while minimizing expected cumulative costs in stochastic environments. Existing safe and constrained reinforcement learning methods typically fail to jointly enforce probabilistic reach-avoid constraints and optimize cost in the learning setting in stochastic environments. To address this challenge, we introduce reach-avoid probability certificates (RAPCs), which identify states from which stochastic reach-avoid constraints are satisfiable. Building on RAPCs, we develop a contraction-based Bellman formulation that serves as a principled surrogate for integrating reach-avoid considerations into reinforcement learning, enabling cost optimization under probabilistic constraints. We establish almost sure convergence of the proposed algorithms to locally optimal policies with respect to the resulting objective. Experiments in the MuJoCo simulator demonstrate improved cost performance and consistently higher reach-avoid satisfaction rates.

Transformers have shown inconsistent success in AI planning tasks, and theoretical understanding of when generalization should be expected has been limited. We take important steps towards addressing this gap by analyzing the ability of decoder-only models to verify whether a given plan correctly solves a given planning instance. To analyse the general setting where the number of objects -- and thus the effective input alphabet -- grows at test time, we introduce C*-RASP, an extension of C-RASP designed to establish length generalization guarantees for transformers under the simultaneous growth in sequence length and vocabulary size. Our results identify a large class of classical planning domains for which transformers can provably learn to verify long plans, and structural properties that significantly affects the learnability of length generalizable solutions. Empirical experiments corroborate our theory.

This paper studies the theoretical foundations of guidance mechanisms in continuous-time score-based diffusion models. We adopt Doob’s h-transform as a principled framework for characterizing ideal guided diffusion processes and analyze the discrepancy between ideal and approximate guidance. Our analysis provides explicit error bounds and yields probabilistic guarantees on satisfying prescribed constraints, which are particularly important for safety-critical planning. We further show that the Doob-based formulation induces a stochastic optimal control problem, enabling practical guidance design without additional model training. We demonstrate the effectiveness of the proposed framework on robotic navigation tasks, including language-conditioned planning.

Meta reinforcement learning (RL) allows agents to leverage experience across a distribution of tasks on which the agent can train at will, enabling faster learning of optimal policies on new test tasks. Despite its success in improving sample complexity on test tasks, many real-world applications, such as robotics and healthcare, impose safety constraints during testing. Constrained meta RL provides a promising framework for integrating safety into meta RL. An open question in constrained meta RL is how to ensure safety of the policy on the real-world test task, while reducing the sample complexity and thus, enabling faster learning of optimal policies. To address this gap, we propose an algorithm that refines policies learned during training, with provable safety and sample complexity guarantees for learning a near optimal policy on the test tasks. We further derive a matching lower bound, showing that this sample complexity is tight.

Bayesian experimental design (BED) is a principled framework for data-efficient design of sequential experiments. However, existing BED methods are unable to adapt to dynamic constraints inherent in real-world tasks due to budget limitations, varying costs, or physical constraints that restrict how designs evolve over time. In this paper, we introduce a novel approach to BED that enables constrained optimization of experimental designs by combining offline pre-training of an amortized policy and a posterior network with online multi-step lookahead planning using scenario trees. We empirically demonstrate that our method yields substantially more informative design sequences than existing methods across a range of constrained BED tasks, while incurring only a modest additional computational overhead.

Optimizing maintenance strategies for large-scale infrastructure is a critical sequential decision-making problem. While Reinforcement Learning (RL) offers a theoretical framework for such problems, practical deployment necessitates offline constrained RL—learning policies solely from static historical datasets under rigid budgetary limits without dangerous on-policy exploration. However, current research is hindered by benchmarks that fail to capture the confluence of distributional shift and hard constraints typical of real-world assets. We introduce InfraRL, a high-fidelity benchmark that uses bridge maintenance as a rigorous testbed for general infrastructure asset management challenges. Constructed from the U.S. National Bridge Inventory, InfraRL defines a rigorous offline task for optimizing maintenance strategies under hard budgetary constraints. We benchmark a diverse suite of baselines, ranging from industry-standard heuristics to single-agent, multi-agent, planning-based, and constrained offline RL methods. Through a comprehensive evaluation protocol, we analyze performance across structural utility, constraint adherence, and behavioral fidelity, revealing critical trade-offs between safety and long-term efficiency. Our code and data are available at https://github.com/BriSky-2021/InfraRL.