Physical reasoning is a crucial aspect in the development of general AI systems, given that human learning starts with interacting with the physical world before progressing to more complex concepts. Although researchers have studied and assessed the physical reasoning of AI approaches through various specific benchmarks, there is no comprehensive approach to evaluating and measuring progress. Therefore, we aim to offer an overview of existing benchmarks and their solution approaches and propose a unified perspective for measuring the physical reasoning capacity of AI systems. We select benchmarks that are designed to test algorithmic performance in physical reasoning tasks. While each of the selected benchmarks poses a unique challenge, their ensemble provides a comprehensive proving ground for an AI generalist agent with a measurable skill level for various physical reasoning concepts. This gives an advantage to such an ensemble of benchmarks over other holistic benchmarks that aim to simulate the real world by intertwining its complexity and many concepts. We group the presented set of physical reasoning benchmarks into subcategories so that more narrow generalist AI agents can be tested first on these groups.

Large multi-modal models (LMMs) have demonstrated promising intelligence owing to the rapid development of pre-training techniques. However, their fine-grained cross-modal alignment ability is constrained by the coarse alignment in image-text pairs. This limitation hinders awareness of fine-grained concepts, resulting in sub-optimal performance. In this paper, we propose a multi-modal conceptual knowledge base, named M2ConceptBase, which aims to provide fine-grained alignment between images and concepts. Specifically, M2ConceptBase models concepts as nodes, associating each with relevant images and detailed text, thereby enhancing LMMs' cross-modal alignment with rich conceptual knowledge. To collect concept-image and concept-description alignments, we propose a context-aware multi-modal symbol grounding approach that considers context information in existing large-scale image-text pairs with respect to each concept. A cutting-edge large language model supplements descriptions for concepts not grounded via our symbol grounding approach. Finally, our M2ConceptBase contains more than 951K images and 152K concepts, each associating with an average of 6.27 images and a single detailed description. We conduct experiments on the OK-VQA task, demonstrating that our M2ConceptBase facilitates the model in achieving state-of-the-art performance. Moreover, we construct a comprehensive benchmark to evaluate the concept understanding of LMMs and show that M2ConceptBase could effectively improve LMMs' concept understanding and cross-modal alignment abilities.

The rapid progression of Artificial Intelligence (AI) systems, facilitated by the advent of Large Language Models (LLMs), has resulted in their widespread application to provide human assistance across diverse industries. This trend has sparked significant discourse centered around the ever-increasing need for LLM-based AI systems to function among humans as part of human society, sharing human values, especially as these systems are deployed in high-stakes settings (e.g., healthcare, autonomous driving, etc.). Towards this end, neurosymbolic AI systems are attractive due to their potential to enable easy-to-understand and interpretable interfaces for facilitating value-based decision-making, by leveraging explicit representations of shared values. In this paper, we introduce substantial extensions to Khaneman's System one/two framework and propose a neurosymbolic computational framework called Value-Inspired AI (VAI). It outlines the crucial components essential for the robust and practical implementation of VAI systems, aiming to represent and integrate various dimensions of human values. Finally, we further offer insights into the current progress made in this direction and outline potential future directions for the field.

Statistical mechanics of spin glasses is one of the main strands toward a comprehension of information processing by neural networks and learning machines. Tackling this approach, at the fairly standard replica symmetric level of description, recently Hebbian attractor networks with multi-node interactions (often called Dense Associative Memories) have been shown to outperform their classical pairwise counterparts in a number of tasks, from their robustness against adversarial attacks and their capability to work with prohibitively weak signals to their supra-linear storage capacities. Focusing on mathematical techniques more than computational aspects, in this paper we relax the replica symmetric assumption and we derive the one-step broken-replica-symmetry picture of supervised and unsupervised learning protocols for these Dense Associative Memories: a phase diagram in the space of the control parameters is achieved, independently, both via the Parisi's hierarchy within then replica trick as well as via the Guerra's telescope within the broken-replica interpolation. Further, an explicit analytical investigation is provided to deepen both the big-data and ground state limits of these networks as well as a proof that replica symmetry breaking does not alter the thresholds for learning and slightly increases the maximal storage capacity. Finally the De Almeida and Thouless line, depicting the onset of instability of a replica symmetric description, is also analytically derived highlighting how, crossed this boundary, the broken replica description should be preferred.

Graph Neural Networks (GNNs) have paved its way for being a cornerstone in graph related learning tasks. From a theoretical perspective, the expressive power of GNNs is primarily characterised according to their ability to distinguish non-isomorphic graphs. It is a well-known fact that most of the conventional GNNs are upper-bounded by Weisfeiler-Lehman graph isomorphism test (1-WL). In this work, we study the expressive power of graph neural networks through the lens of graph partitioning. This follows from our observation that permutation invariant graph partitioning enables a powerful way of exploring structural interactions among vertex sets and subgraphs, and can help uplifting the expressive power of GNNs efficiently. Based on this, we first establish a theoretical connection between graph partitioning and graph isomorphism. Then we introduce a novel GNN architecture, namely Graph Partitioning Neural Networks (GPNNs). We theoretically analyse how a graph partitioning scheme and different kinds of structural interactions relate to the k-WL hierarchy. Empirically, we demonstrate its superior performance over existing GNN models in a variety of graph benchmark tasks.

While recent model-free Reinforcement Learning (RL) methods have demonstrated human-level effectiveness in gaming environments, their success in everyday tasks like visual navigation has been limited, particularly under significant appearance variations. This limitation arises from (i) poor sample efficiency and (ii) over-fitting to training scenarios. To address these challenges, we present a world model that learns invariant features using (i) contrastive unsupervised learning and (ii) an intervention-invariant regularizer. Learning an explicit representation of the world dynamics i.e. a world model, improves sample efficiency while contrastive learning implicitly enforces learning of invariant features, which improves generalization. However, the naive integration of contrastive loss to world models fails due to a lack of supervisory signals to the visual encoder, as world-model-based RL methods independently optimize representation learning and agent policy. To overcome this issue, we propose an intervention-invariant regularizer in the form of an auxiliary task such as depth prediction, image denoising, etc., that explicitly enforces invariance to style-interventions. Our method outperforms current state-of-the-art model-based and model-free RL methods and significantly on out-of-distribution point navigation task evaluated on the iGibson benchmark. We further demonstrate that our approach, with only visual observations, outperforms recent language-guided foundation models for point navigation, which is essential for deployment on robots with limited computation capabilities. Finally, we demonstrate that our proposed model excels at the sim-to-real transfer of its perception module on Gibson benchmark.

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.

While question answering over knowledge bases (KBQA) has shown progress in addressing factoid questions, KBQA with numerical reasoning remains relatively unexplored. In this paper, we focus on the complex numerical reasoning in KBQA and propose a new task, NR-KBQA, which necessitates the ability to perform both multi-hop reasoning and numerical reasoning. We design a logic form in Python format called PyQL to represent the reasoning process of numerical reasoning questions. To facilitate the development of NR-KBQA, we present a large dataset called MarkQA, which is automatically constructed from a small set of seeds. Each question in MarkQA is equipped with its corresponding SPARQL query, alongside the step-by-step reasoning process in the QDMR format and PyQL program. Experimental results of some state-of-the-art QA methods on the MarkQA show that complex numerical reasoning in KBQA faces great challenges.

Knowledge-grounded dialogue is a task of generating an informative response based on both the dialogue history and external knowledge source. In general, there are two forms of knowledge: manually annotated knowledge graphs and knowledge text from website. From various evaluation viewpoints, each type of knowledge has advantages and downsides. To further distinguish the principles and determinants from the intricate factors, we conduct a thorough experiment and study on the task to answer three essential questions. The questions involve the choice of appropriate knowledge form, the degree of mutual effects between knowledge and the model selection, and the few-shot performance of knowledge. Supported by statistical shreds of evidence, we offer conclusive solutions and sensible suggestions for directions and standards of future research.

Sequential planning in large state space and action space quickly becomes intractable due to combinatorial explosion of the search space. Heuristic methods, like monte-carlo tree search, though effective for large state space, but struggle if action space is large. Pure reinforcement learning methods, relying only on reward signals, needs prohibitively large interactions with the environment to device a viable plan. If the state space, observations and actions can be represented in natural language then Large Language models (LLM) can be used to generate action plans. Recently several such goal-directed agents like Reflexion, CLIN, SayCan were able to surpass the performance of other state-of-the-art methods with minimum or no task specific training. But they still struggle with exploration and get stuck in local optima. Their planning capabilities are limited by the limited reasoning capability of the foundational LLMs on text data. We propose a hybrid agent "neoplanner", that synergizes both state space search with queries to foundational LLM to get the best action plan. The reward signals are quantitatively used to drive the search. A balance of exploration and exploitation is maintained by maximizing upper confidence bounds of values of states. In places where random exploration is needed, the LLM is queried to generate an action plan. Learnings from each trial are stored as entity relationships in text format. Those are used in future queries to the LLM for continual improvement. Experiments in the Scienceworld environment reveals a 124% improvement from the current best method in terms of average reward gained across multiple tasks.