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.

With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose a new technique named Common randOm REconstruction(CORE), which can be used to compress the information transmitted between machines in order to reduce communication complexity without other strict conditions. Especially, our technique CORE projects the vector-valued information to a low-dimensional one through common random vectors and reconstructs the information with the same random noises after communication. We apply CORE to two distributed tasks, respectively convex optimization on linear models and generic non-convex optimization, and design new distributed algorithms, which achieve provably lower communication complexities. For example, we show for linear models CORE-based algorithm can encode the gradient vector to $\mathcal{O}(1)$-bits (against $\mathcal{O}(d)$), with the convergence rate not worse, preceding the existing results.

This paper proposes a parsing algorithm for scene understanding which includes four aspects: computing 3D scene layout, detecting 3D objects (e.g. furniture), detecting 2D faces (windows, doors etc.), and segmenting background. In contrast to previous scene labeling work that applied discriminative classifiers to pixels (or super-pixels), we use a generative Stochastic Scene Grammar (SSG). This grammar represents the compositional structures of visual entities from scene categories, 3D foreground/background, 2D faces, to 1D lines. The grammar includes three types of production rules and two types of contextual relations. Production rules: (i) AND rules represent the decomposition of an entity into sub-parts; (ii) OR rules represent the switching among sub-types of an entity; (iii) SET rules rep- resent an ensemble of visual entities. Contextual relations: (i) Cooperative “+” relations represent positive links between binding entities, such as hinged faces of a object or aligned boxes; (ii) Competitive “-” relations represents negative links between competing entities, such as mutually exclusive boxes. We design an efficient MCMC inference algorithm, namely Hierarchical cluster sampling, to search in the large solution space of scene configurations. The algorithm has two stages: (i) Clustering: It forms all possible higher-level structures (clusters) from lower-level entities by production rules and contextual relations. (ii) Sampling: It jumps between alternative structures (clusters) in each layer of the hierarchy to find the most probable configuration (represented by a parse tree). In our experiment, we demonstrate the superiority of our algorithm over existing methods on public dataset. In addition, our approach achieves richer structures in the parse tree.