We propose the first return time distribution (FRTD) of a random walk as an interpretable and mathematically grounded node embedding. The FRTD assigns a probability mass function to each node, allowing us to define a distance between any pair of nodes using standard metrics for discrete distributions. We present several arguments to motivate the FRTD embedding. First, we show that FRTDs are strictly more informative than eigenvalue spectra, yet insufficient for complete graph identification, thus placing FRTD equivalence between cospectrality and isomorphism. Second, we argue that FRTD equivalence between nodes captures structural similarity. Third, we empirically demonstrate that the FRTD embedding outperforms manually designed graph metrics in network alignment tasks. Finally, we show that random networks that approximately match the FRTD of a desired target also preserve other salient features. Together these results demonstrate the FRTD as a simple and mathematically principled embedding for complex networks.

These additional behavior tokens will be augmented to the vocabulary of pretrained Multimodal Language Models. With this encoder, we then pack long-term multimodal interactions involving task instructions, memories, thoughts, observations, textual responses, behavior trajectories, etc .

Large Language Models (LLMs) trained on massive corpora have shown remarkable success in knowledge-intensive tasks. Y et, most of them rely on pre-stored knowledge. Inducing new general knowledge from a specific environment and performing reasoning with the acquired knowledge-- situated inductive reasoning, is crucial and challenging for machine intelligence. In this paper, we design Mars, an interactive environment devised for situated inductive reasoning. It introduces counter-commonsense game mechanisms by modifying terrain, survival setting and task dependency while adhering to certain principles.

Large Language Models (LLMs) trained on massive corpora have shown remarkable success in knowledge-intensive tasks. Y et, most of them rely on pre-stored knowledge. Inducing new general knowledge from a specific environment and performing reasoning with the acquired knowledge-- situated inductive reasoning, is crucial and challenging for machine intelligence. In this paper, we design Mars, an interactive environment devised for situated inductive reasoning. It introduces counter-commonsense game mechanisms by modifying terrain, survival setting and task dependency while adhering to certain principles.

Large language models (LLMs) have shown promise in zero-shot and single step reasoning and decision making problems, but in long horizon sequential planning tasks, their errors compound, often leading to unreliable or inefficient behavior. We introduce LogicGuard, a modular actor-critic architecture in which an LLM actor is guided by a trajectory level LLM critic that communicates through Linear Temporal Logic (LTL). Our setup combines the reasoning strengths of language models with the guarantees of formal logic. The actor selects high-level actions from natural language observations, while the critic analyzes full trajectories and proposes new LTL constraints that shield the actor from future unsafe or inefficient behavior. LogicGuard supports both fixed safety rules and adaptive, learned constraints, and is model-agnostic: any LLM-based planner can serve as the actor, with LogicGuard acting as a logic-generating wrapper. We formalize planning as graph traversal under symbolic constraints, allowing LogicGuard to analyze failed or suboptimal trajectories and generate new temporal logic rules that improve future behavior. To demonstrate generality, we evaluate LogicGuard across two distinct settings: short-horizon general tasks and long-horizon specialist tasks. On the Behavior benchmark of 100 household tasks, LogicGuard increases task completion rates by 25% over a baseline InnerMonologue planner. On the Minecraft diamond-mining task, which is long-horizon and requires multiple interdependent subgoals, LogicGuard improves both efficiency and safety compared to SayCan and InnerMonologue. These results show that enabling LLMs to supervise each other through temporal logic yields more reliable, efficient and safe decision-making for both embodied agents.

Large Language Models (LLMs) demonstrate impressive general capabilities but often struggle with step-by-step reasoning, especially in complex applications such as games. While retrieval-augmented methods like GraphRAG attempt to bridge this gap through cross-document extraction and indexing, their fragmented entity-relation graphs and overly dense local connectivity hinder the construction of coherent reasoning. In this paper, we propose a novel framework based on Goal-Oriented Graphs (GoGs), where each node represents a goal and its associated attributes, and edges encode logical dependencies between goals. This structure enables explicit retrieval of reasoning paths by first identifying high-level goals and recursively retrieving their subgoals, forming coherent reasoning chains to guide LLM prompting. Our method significantly enhances the reasoning ability of LLMs in game-playing tasks, as demonstrated by extensive experiments on the Minecraft testbed, outperforming GraphRAG and other baselines.

Developing intelligent agents for long-term cooperation in dynamic open-world scenarios is a major challenge in multi-agent systems. Traditional Multi-agent Reinforcement Learning (MARL) frameworks like centralized training decentralized execution (CTDE) struggle with scalability and flexibility. They require centralized long-term planning, which is difficult without custom reward functions, and face challenges in processing multi-modal data. CTDE approaches also assume fixed cooperation strategies, making them impractical in dynamic environments where agents need to adapt and plan independently. To address decentralized multi-agent cooperation, we propose Decentralized Adaptive Knowledge Graph Memory and Structured Communication System (DAMCS) in a novel Multi-agent Crafter environment. Our generative agents, powered by Large Language Models (LLMs), are more scalable than traditional MARL agents by leveraging external knowledge and language for long-term planning and reasoning. Instead of fully sharing information from all past experiences, DAMCS introduces a multi-modal memory system organized as a hierarchical knowledge graph and a structured communication protocol to optimize agent cooperation. This allows agents to reason from past interactions and share relevant information efficiently. Experiments on novel multi-agent open-world tasks show that DAMCS outperforms both MARL and LLM baselines in task efficiency and collaboration. Compared to single-agent scenarios, the two-agent scenario achieves the same goal with 63% fewer steps, and the six-agent scenario with 74% fewer steps, highlighting the importance of adaptive memory and structured communication in achieving long-term goals. We publicly release our project at: https://happyeureka.github.io/damcs.

Large Language Models (LLMs) trained on massive corpora have shown remarkable success in knowledge-intensive tasks. Yet, most of them rely on pre-stored knowledge. Inducing new general knowledge from a specific environment and performing reasoning with the acquired knowledge -- \textit{situated inductive reasoning}, is crucial and challenging for machine intelligence. In this paper, we design Mars, an interactive environment devised for situated inductive reasoning. It introduces counter-commonsense game mechanisms by modifying terrain, survival setting and task dependency while adhering to certain principles. In Mars, agents need to actively interact with their surroundings, derive useful rules and perform decision-making tasks in specific contexts. We conduct experiments on various RL-based and LLM-based methods, finding that they all struggle on this challenging situated inductive reasoning benchmark. Furthermore, we explore \textit{Induction from Reflection}, where we instruct agents to perform inductive reasoning from history trajectory. The superior performance underscores the importance of inductive reasoning in Mars. Through Mars, we aim to galvanize advancements in situated inductive reasoning and set the stage for developing the next generation of AI systems that can reason in an adaptive and context-sensitive way.

We present OmniJARVIS, a novel Vision-Language-Action (VLA) model for open-world instruction-following agents in open-world Minecraft. Compared to prior works that either emit textual goals to separate controllers or produce the control command directly, OmniJARVIS seeks a different path to ensure both strong reasoning and efficient decision-making capabilities via unified tokenization of multimodal interaction data. First, we introduce a self-supervised approach to learn a behavior encoder that produces discretized tokens for behavior trajectories $\tau$ = {$o_0$, $a_0$, $\dots$} and an imitation learning (IL) policy decoder conditioned on these tokens. These additional behavior tokens will be augmented to the vocabulary of pretrained Multimodal Language Models (MLMs). With this encoder, we then pack long-term multimodal interactions involving task instructions, memories, thoughts, observations, textual responses, behavior trajectories, etc. into unified token sequences and model them with autoregressive transformers. Thanks to the semantically meaningful behavior tokens, the resulting VLA model, OmniJARVIS, can reason (by producing chain-of-thoughts), plan, answer questions, and act (by producing behavior tokens for the IL policy decoder). OmniJARVIS demonstrates excellent performances on a comprehensive collection of atomic, programmatic, and open-ended tasks in open-world Minecraft. Our analysis further unveils the crucial design principles in interaction data formation, unified tokenization, and its scaling potentials.