Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive problem-solving skills in many tasks and domains, but their ability in mathematical reasoning in visual contexts has not been systematically studied. To bridge this gap, we present MathVista, a benchmark designed to combine challenges from diverse mathematical and visual tasks. It consists of 6,141 examples, derived from 28 existing multimodal datasets involving mathematics and 3 newly created datasets (i.e., IQTest, FunctionQA, and PaperQA). Completing these tasks requires fine-grained, deep visual understanding and compositional reasoning, which all state-of-the-art foundation models find challenging. With MathVista, we have conducted a comprehensive, quantitative evaluation of 12 prominent foundation models. The best-performing GPT-4V model achieves an overall accuracy of 49.9%, substantially outperforming Bard, the second-best performer, by 15.1%. Our in-depth analysis reveals that the superiority of GPT-4V is mainly attributed to its enhanced visual perception and mathematical reasoning. However, GPT-4V still falls short of human performance by 10.4%, as it often struggles to understand complex figures and perform rigorous reasoning. This significant gap underscores the critical role that MathVista will play in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. We further explore the new ability of self-verification, the application of self-consistency, and the interactive chatbot capabilities of GPT-4V, highlighting its promising potential for future research. The project is available at https://mathvista.github.io/.

The generalization of decision-making agents encompasses two fundamental elements: learning from past experiences and reasoning in novel contexts. However, the predominant emphasis in most interactive environments is on learning, often at the expense of complexity in reasoning. In this paper, we introduce CivRealm, an environment inspired by the Civilization game. Civilization's profound alignment with human history and society necessitates sophisticated learning, while its ever-changing situations demand strong reasoning to generalize. Particularly, CivRealm sets up an imperfect-information general-sum game with a changing number of players; it presents a plethora of complex features, challenging the agent to deal with open-ended stochastic environments that require diplomacy and negotiation skills. Within CivRealm, we provide interfaces for two typical agent types: tensor-based agents that focus on learning, and language-based agents that emphasize reasoning. To catalyze further research, we present initial results for both paradigms. The canonical RL-based agents exhibit reasonable performance in mini-games, whereas both RL- and LLM-based agents struggle to make substantial progress in the full game. Overall, CivRealm stands as a unique learning and reasoning challenge for decision-making agents. The code is available at https://github.com/bigai-ai/civrealm.

The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated expansion of nodes corresponding to the same dynamic programming states by querying expansion thresholds cached throughout the search. These thresholds are based on dominance relations between partial solutions previously found and on the pruning inequalities of the filtering techniques introduced by Gillard et al. in 2021. Computational experiments show that the pruning brought by this caching mechanism allows significantly reducing the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams.

We show that it is possible to understand and identify a decision maker's subjective causal judgements by observing her preferences over interventions. Following Pearl [2000], we represent causality using causal models (also called structural equations models), where the world is described by a collection of variables, related by equations. We show that if a preference relation over interventions satisfies certain axioms (related to standard axioms regarding counterfactuals), then we can define (i) a causal model, (ii) a probability capturing the decision-maker's uncertainty regarding the external factors in the world and (iii) a utility on outcomes such that each intervention is associated with an expected utility and such that intervention $A$ is preferred to $B$ iff the expected utility of $A$ is greater than that of $B$. In addition, we characterize when the causal model is unique. Thus, our results allow a modeler to test the hypothesis that a decision maker's preferences are consistent with some causal model and to identify causal judgements from observed behavior.

Knowledge graph (KG) based reasoning has been regarded as an effective means for the analysis of semantic networks and is of great usefulness in areas of information retrieval, recommendation, decision-making, and man-machine interaction. It is widely used in recommendation, decision-making, question-answering, search, and other fields. However, previous studies mainly used low-level knowledge in the KG for reasoning, which may result in insufficient generalization and poor robustness of reasoning. To this end, this paper proposes a new inference approach using a novel knowledge augmentation strategy to improve the generalization capability of KG. This framework extracts high-level pyramidal knowledge from low-level knowledge and applies it to reasoning in a multi-level hierarchical KG, called knowledge pyramid in this paper. We tested some medical data sets using the proposed approach, and the experimental results show that the proposed knowledge pyramid has improved the knowledge inference performance with better generalization. Especially, when there are fewer training samples, the inference accuracy can be significantly improved.

Artefact descriptions are the primary carriers of engineering design knowledge that is both an outcome and a driver of the design process. While an artefact could be described in different connotations, the design process requires a description to embody engineering design knowledge, which is expressed in the text through intricate placement of entities and relationships. As large-language models learn from all kinds of text merely as a sequence of characters/tokens, these are yet to generate text that embodies explicit engineering design facts. Existing ontological design theories are less likely to guide the large-language models whose applications are currently limited to ideation and learning purposes. In this article, we explicate engineering design knowledge as knowledge graphs from a large sample of 33,881 patent documents. We examine the constituents of these knowledge graphs to understand the linguistic and structural basis of engineering design knowledge. In terms of linguistic basis, we observe that entities and relationships could be generalised to 64 and 24 linguistic syntaxes. While relationships mainly capture attributes ('of'), structure ('in', 'with'), purpose ('to', 'for'), hierarchy ('include'), exemplification ('such as'), and behaviour ('to', 'from'), the hierarchical relationships could specifically be identified using 75 unique syntaxes. To understand the structural basis, we draw inspiration from various studies on biological/ecological networks and discover motifs from patent knowledge graphs. We identify four 3-node and four 4-node patterns that could further be converged and simplified into sequence [->...->], aggregation [->...<-], and hierarchy [<-...->]. Expected to guide large-language model based design tools, we propose few regulatory precepts for concretising abstract entities and relationships within subgraphs, while explicating hierarchical structures.

Learning world models can teach an agent how the world works in an unsupervised manner. Even though it can be viewed as a special case of sequence modeling, progress for scaling world models on robotic applications such as autonomous driving has been somewhat less rapid than scaling language models with Generative Pre-trained Transformers (GPT). We identify two reasons as major bottlenecks: dealing with complex and unstructured observation space, and having a scalable generative model. Consequently, we propose a novel world modeling approach that first tokenizes sensor observations with VQVAE, then predicts the future via discrete diffusion. When applied to learning world models on point cloud observations, our model reduces prior SOTA Chamfer distance by more than 65% for 1s prediction, and more than 50% for 3s prediction, across NuScenes, KITTI Odometry, and Argoverse2 datasets. Our results demonstrate that discrete diffusion on tokenized agent experience can unlock the power of GPT-like unsupervised learning for robotic agents. Figure 1: Our unsupervised world model can produce accurate near-term 1s predictions and diverse multi-future 3s predictions directly on the level of point cloud observations. World models explicitly represent the knowledge of an autonomous agent about its environment. They are defined as a generative model that predicts the next observation in an environment given past observations and the current action. Such a generative model can learn from any unlabeled agent experience, and can be used for both learning and planning in the model-based reinforcement learning framework (Sutton, 1991). This approach has excelled in domains such as Atari (Kaiser et al., 2019), robotic manipulation (Nagabandi et al., 2020), and Minecraft (Hafner et al., 2023). Learning world models can be viewed as a special case of sequence modeling on agent experience. While Generative Pre-trained Transformers (GPT) (Brown et al., 2020) have enabled rapid progress Prediction systems in autonomous driving still require supervised learning, either on the level of bounding boxes (Luo et al., 2018), semantic segmentation (Sadat et al., 2020), or instance segmentation (Hu et al., 2021). However, just as GPT learns to understand language via next token prediction, if a world model can predict unlabeled future observations really well, it must have developed a general understanding of the scene including geometry and dynamics.

Predicting the future location of mobile objects reinforces location-aware services with proactive intelligence and helps businesses and decision-makers with better planning and near real-time scheduling in different applications such as traffic congestion control, location-aware advertisements, and monitoring public health and well-being. The recent developments in the smartphone and location sensors technology and the prevalence of using location-based social networks alongside the improvements in artificial intelligence and machine learning techniques provide an excellent opportunity to exploit massive amounts of historical and real-time contextual information to recognise mobility patterns and achieve more accurate and intelligent predictions. This survey provides a comprehensive overview of the next useful location prediction problem with context-awareness. First, we explain the concepts of context and context-awareness and define the next location prediction problem. Then we analyse nearly thirty studies in this field concerning the prediction method, the challenges addressed, the datasets and metrics used for training and evaluating the model, and the types of context incorporated. Finally, we discuss the advantages and disadvantages of different approaches, focusing on the usefulness of the predicted location and identifying the open challenges and future work on this subject by introducing two potential use cases of next location prediction in the automotive industry.

The potential of Vision-Language Models (\textsc{vlm}s) often remains underutilized in handling complex text-based problems, particularly when these problems could benefit from visual representation. Resonating with humans' ability to solve complex text-based problems by (1) creating a visual diagram from the problem and (2) deducing what steps they need to take to solve it, we propose \textsc{Self-Imagine}. We leverage a single Vision-Language Model (\textsc{vlm}) to generate a structured representation of the question using HTML, then render the HTML as an image, and finally use the same \vlm to answer the question using both the question and the image. Our approach does not require any additional training data or training. We evaluate our approach in three mathematics tasks and nine general-purpose reasoning tasks using state-of-the-art \textsc{vlm}. Our approach boosts the performance of \textsc{vlm} on all math tasks (\gsm: +4.62\%; \asdiv: +4.49\%; \svamp: +9.30\%) and the majority of the general-purpose reasoning tasks by 0.4\% to 13.20\% while achieving comparable performance in other tasks. Code and data at https://github.com/snat1505027/self-imagine .