As a comprehensive indicator of mathematical thinking and intelligence, the number sense (Dehaene 2011) bridges the induction of symbolic concepts and the competence of problem-solving. To endow such a crucial cognitive ability to machine intelligence, we propose a dataset, Machine Number Sense (MNS), consisting of visual arithmetic problems automatically generated using a grammar model--And-Or Graph (AOG). These visual arithmetic problems are in the form of geometric figures: each problem has a set of geometric shapes as its context and embedded number symbols. Solving such problems is not trivial; the machine not only has to recognize the number, but also to interpret the number with its contexts, shapes, and relations (e.g., symmetry) together with proper operations. We benchmark the MNS dataset using four predominant neural network models as baselines in this visual reasoning task. Comprehensive experiments show that current neural-network-based models still struggle to understand number concepts and relational operations. We show that a simple brute-force search algorithm could work out some of the problems without context information. Crucially, taking geometric context into account by an additional perception module would provide a sharp performance gain with fewer search steps. Altogether, we call for attention in fusing the classic search-based algorithms with modern neural networks to discover the essential number concepts in future research.
Tel Aviv University（特拉维夫大学）；Facebook AI Research（Facebook人工智能研究院）
We consider the abstract relational reasoning task, which is commonly used as an intelligence test. Since some patterns have spatial rationales, while others are only semantic, we propose a multi-scale architecture that processes each query in multiple resolutions. We show that indeed different rules are solved by different resolutions and a combined multi-scale approach outperforms the existing state of the art in this task on all benchmarks by 5-54%. The success of our method is shown to arise from multiple novelties. First, it searches for relational patterns in multiple resolutions, which …
Analogical reasoning has been a principal focus of various waves of AI research. Analogy is particularly challenging for machines because it requires relational structures to be represented such that they can be flexibly applied across diverse domains of experience. Here, we study how analogical reasoning can be induced in neural networks that learn to perceive and reason about raw visual data. We find that the critical factor for inducing such a capacity is not an elaborate architecture, but rather, careful attention to the choice of data and the manner in which it is presented to the model. …
Learning structured representations of visual scenes is currently a major bottleneck to bridging perception with reasoning. While there has been exciting progress with slot-based models, which learn to segment scenes into sets of objects, learning configurational properties of entire groups of objects is still under-explored. To address this problem, we introduce Constellation, a network that learns relational abstractions of static visual scenes, and generalises these abstractions over sensory particularities, thus offering a potential basis for abstract relational reasoning. We further show …
School of Computing and Augmented Intelligence（计算与增强智能学院）；Arizona State University（亚利桑那州立大学）
Reinforcement learning in problems with symbolic state spaces is challenging due to the need for reasoning over long horizons. This paper presents a new approach that utilizes relational abstractions in conjunction with deep learning to learn a generalizable Q-function for such problems. The learned Q-function can be efficiently transferred to related problems that have different object names and object quantities, and thus, entirely different state spaces. We show that the learned generalized Q-function can be utilized for zero-shot transfer to related problems without an explicit, hand-coded…
The Relational Bottleneck as an Inductive Bias for Efficient Abstraction
University of California, Los Angeles（加州大学洛杉矶分校）；Dartmouth College（达特茅斯学院）；Yale University（耶鲁大学）；Princeton University（普林斯顿大学）；Brown University（布朗大学）；University of California, Davis（加州大学戴维斯分校）
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured and the resulting model-generated sequences may not reflect the kind of systematic reasoning we might expect an expert human to produce. In this paper, we study how to build stronger reasoning capability in language models using the idea of relational abstractions. We introduce new types of sequences that more explicitly provide an abstract characterization …
Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this paper, we expand PIMT to a lifted version that also processes random functions and relations. This enhancement is achieved by adapting Inversion, a method from Lifted First-Order Probabilistic Inference literature, to also be modulo theories. This results in the first algorithm for exact probabilistic inference that efficiently and simultaneously exploits ran…
Artificial Intelligence Research Laboratory（人工智能研究实验室）；College of Information Sciences and Technology（信息科学与技术学院）；Pennsylvania State University（宾夕法尼亚州立大学）
Maier et al. (2010) introduced the relational causal model (RCM) for representing and inferring causal relationships in relational data. A lifted representation, called abstract ground graph (AGG), plays a central role in reasoning with and learning of RCM. The correctness of the algorithm proposed by Maier et al. (2013a) for learning RCM from data relies on the soundness and completeness of AGG for relational d-separation to reduce the learning of an RCM to learning of an AGG. We revisit the definition of AGG and show that AGG, as defined in Maier et al. (2013b), does not correctly abstract a…
Causal reasoning in relational domains is fundamental to studying real-world social phenomena in which individual units can influence each other's traits and behavior. Dynamics between interconnected units can be represented as an instantiation of a relational causal model; however, causal reasoning over such instantiation requires additional templating assumptions that capture feedback loops of influence. Previous research has developed lifted representations to address the relational nature of such dynamics but has strictly required that the representation has no cycles. To facilitate cycles…
Deep neural networks have become the dominant approach in natural language processing (NLP). However, in recent years, it has become apparent that there are shortcomings in systematicity that limit the performance and data efficiency of deep learning in NLP. These shortcomings can be clearly shown in lower-level artificial tasks, mostly on synthetic data. Abstract patterns are the best known examples of a hard problem for neural networks in terms of generalisation to unseen data. They are defined by relations between items, such as equality, rather than their values. It has been argued that th…
Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the value iteration algorithm. However, exact versions of more complex algorithms, including policy iteration, have not been developed or analyzed. The paper investigates this potential and makes several contributions. First we observe two anomalies for relational representations showing that the value of some policies is not well defined or cannot be calculated…
Markov decision processes capture sequential decision making under uncertainty, where an agent must choose actions so as to optimize long term reward. The paper studies efficient reasoning mechanisms for Relational Markov Decision Processes (RMDP) where world states have an internal relational structure that can be naturally described in terms of objects and relations among them. Two contributions are presented. First, the paper develops First Order Decision Diagrams (FODD), a new compact representation for functions over relational structures, together with a set of operators to combine FODDs…
Current deep learning approaches have shown good in-distribution generalization performance, but struggle with out-of-distribution generalization. This is especially true in the case of tasks involving abstract relations like recognizing rules in sequences, as we find in many intelligence tests. Recent work has explored how forcing relational representations to remain distinct from sensory representations, as it seems to be the case in the brain, can help artificial systems. Building on this work, we further explore and formalize the advantages afforded by 'partitioned' representations of rela…
Swiss AI Lab IDSIA, USI, SUPSI（瑞士IDSIA人工智能实验室，瑞士意大利语区大学，瑞士应用科学与艺术大学（SUPSI））
Common-sense physical reasoning in the real world requires learning about the interactions of objects and their dynamics. The notion of an abstract object, however, encompasses a wide variety of physical objects that differ greatly in terms of the complex behaviors they support. To address this, we propose a novel approach to physical reasoning that models objects as hierarchies of parts that may locally behave separately, but also act more globally as a single whole. Unlike prior approaches, our method learns in an unsupervised fashion directly from raw visual images to discover objects, part…
Several goal-oriented problems in the real-world can be naturally expressed as Stochastic Shortest Path Problems (SSPs). However, the computational complexity of solving SSPs makes finding solutions to even moderately sized problems intractable. Currently, existing state-of-the-art planners and heuristics often fail to exploit knowledge learned from solving other instances. This paper presents an approach for learning \emph{Generalized Policy Automata} (GPA): non-deterministic partial policies that can be used to catalyze the solution process. GPAs are learned using relational, feature-based a…
Humans have a rich representation of the entities in their environment. Entities are described by their attributes, and entities that share attributes are often semantically related. For example, if two books have "Natural Language Processing" as the value of their `title' attribute, we can expect that their `topic' attribute will also be equal, namely, "NLP". Humans tend to generalize such observations, and infer sufficient conditions under which the `topic' attribute of any entity is "NLP". If robots need to interact successfully with humans, they need to represent entities, attributes, and …
Oregon State University（俄勒冈州立大学）；Tufts University（塔夫茨大学）
Dynamic programming algorithms have been successfully applied to propositional stochastic planning problems by using compact representations, in particular algebraic decision diagrams, to capture domain dynamics and value functions. Work on symbolic dynamic programming lifted these ideas to first order logic using several representation schemes. Recent work introduced a first order variant of decision diagrams (FODD) and developed a value iteration algorithm for this representation. This paper develops several improvements to the FODD algorithm that make the approach practical. These include, …
Raven's Progressive Matrices have been widely used for measuring abstract reasoning and intelligence in humans. However for artificial learning systems, abstract reasoning remains a challenging problem. In this paper we investigate how neural networks augmented with biologically inspired spiking modules gain a significant advantage in solving this problem. To illustrate this, we first investigate the performance of our networks with supervised learning, then with unsupervised learning. Experiments on the RAVEN dataset show that the overall accuracy of our supervised networks surpass human-leve…
Research in analogical reasoning suggests that higher-order cognitive functions such as abstract reasoning, far transfer, and creativity are founded on recognizing structural similarities among relational systems. Here we integrate theories of analogy with the computational framework of reinforcement learning (RL). We propose a psychology theory that is a computational synergy between analogy and RL, in which analogical comparison provides the RL learning algorithm with a measure of relational similarity, and RL provides feedback signals that can drive analogical learning. Simulation results s…
In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which capture the relations among inputs. In many cases, more than two maps are strongly related, so it is wise to make multiplicative unit learn relations among more input maps, in other words, to find the optimal relational-order of each unit. In order to enable our machine to learn relational order, we developed a reinforcement-learning method whose optimality is…
Beyond Abstract Compliance: Operationalising trust in AI as a moral relationship
Boehringer Ingelheim Pharma GmbH \& Co. KG Birkendorfer Str. 65 Biberach an der Riss Germany 88400；Carnegie Mellon University Pittsburgh, PA USA；Rhodes University Makhanda South Africa；International University of Management Namibia；Charles Darwin University Australia；Boehringer Ingelheim Pharma GmbH \& Co. KG；Carnegie Mellon University；Rhodes University；International University of Management；Charles Darwin University
UCLA Center for Vision, Cognition, Learning and Autonomy（加州大学洛杉矶分校视觉、认知、学习与自主性中心）；International Center for AI and Robot Autonomy (CARA)（人工智能与机器人自主性国际中心（CARA））
Dramatic progress has been witnessed in basic vision tasks involving low-level perception, such as object recognition, detection, and tracking. Unfortunately, there is still an enormous performance gap between artificial vision systems and human intelligence in terms of higher-level vision problems, especially ones involving reasoning. Earlier attempts in equipping machines with high-level reasoning have hovered around Visual Question Answering (VQA), one typical task associating vision and language understanding. In this work, we propose a new dataset, built in the context of Raven's Progress…
The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We f…
We demonstrate a declarative differentiable programming framework based on the language of Lifted Relational Neural Networks, where small parameterized logic programs are used to encode relational learning scenarios. When presented with relational data, such as various forms of graphs, the program interpreter dynamically unfolds differentiable computational graphs to be used for the program parameter optimization by standard means. Following from the used declarative Datalog abstraction, this results into compact and elegant learning programs, in contrast with the existing procedural approache…
Computing goal-directed behavior is essential to designing efficient AI systems. Due to the computational complexity of planning, current approaches rely primarily upon hand-coded symbolic action models and hand-coded heuristic-function generators for efficiency. Learned heuristics for such problems have been of limited utility as they are difficult to apply to problems with objects and object quantities that are significantly different from those in the training data. This paper develops a new approach for learning generalized heuristics in the absence of symbolic action models using deep neu…
Visual relations form the basis of understanding our compositional world, as relationships between visual objects capture key information in a scene. It is then advantageous to learn relations automatically from the data, as learning with predefined labels cannot capture all possible relations. However, current relation learning methods typically require supervision, and are not designed to generalize to scenes with more complicated relational structures than those seen during training. Here, we introduce ViRel, a method for unsupervised discovery and learning of Visual Relations with graph-le…
