Raven's Progressive Matrices (RPM) have been widely used for Intelligence Quotient (IQ) test of humans. In this paper, we aim to solve RPM with neural networks in both supervised and unsupervised manners. First, we investigate strategies to reduce over-fitting in supervised learning. We suggest the use of a neural network with deep layers and pre-training on large-scale datasets to improve model generalization. Experiments on the RAVEN dataset show that the overall accuracy of our supervised approach surpasses human-level performance. Second, as an intelligent agent requires to automatically learn new skills to solve new problems, we propose the first unsupervised method, Multilabel Classification with Pseudo Target (MCPT), for RPM problems. Based on the design of the pseudo target, MCPT converts the unsupervised learning problem to a supervised task. Experiments show that MCPT doubles the testing accuracy of random guessing e.g. 28.50% vs. 12.5%. Finally, we discuss the problem of solving RPM with unsupervised and explainable strategies in the future.
Raven's Progressive Matrices (RPMs) are frequently used in testing human's visual reasoning ability. Recent advances of RPM-like datasets and solution models partially address the challenges of visually understanding the RPM questions and logically reasoning the missing answers. In view of the poor generalization performance due to insufficient samples in RPM datasets, we propose an effective scheme, namely Candidate Answer Morphological Mixup (CAM-Mix). CAM-Mix serves as a data augmentation strategy by gray-scale image morphological mixup, which regularizes various solution methods and overco…
Psychologists recognize Raven's Progressive Matrices as a very effective test of general human intelligence. While many computational models have been developed by the AI community to investigate different forms of top-down, deliberative reasoning on the test, there has been less research on bottom-up perceptual processes, like Gestalt image completion, that are also critical in human test performance. In this work, we investigate how Gestalt visual reasoning on the Raven's test can be modeled using generative image inpainting techniques from computer vision. We demonstrate that a self-supervi…
IBM Research – Zurich（IBM苏黎世研究院）；ETH Zürich（苏黎世联邦理工学院）
Neither deep neural networks nor symbolic AI alone has approached the kind of intelligence expressed in humans. This is mainly because neural networks are not able to decompose joint representations to obtain distinct objects (the so-called binding problem), while symbolic AI suffers from exhaustive rule searches, among other problems. These two problems are still pronounced in neuro-symbolic AI which aims to combine the best of the two paradigms. Here, we show that the two problems can be addressed with our proposed neuro-vector-symbolic architecture (NVSA) by exploiting its powerful operator…
Singapore University of Technology and Design（新加坡科技设计大学）；Nanyang Technological University（南洋理工大学）；Singapore Polytechnic（新加坡理工学院）
We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic computation. The fundamental algebraic objects of interest are the ideals of some suitably initialized polynomial ring. We shall explain how solving Raven's Progressive Matrices (RPMs) can be realized as computational problems in algebra, which combine various well-known algebraic subroutines that include: Computing the Gröbner basis of an ideal, checking for ideal con…
Raven's Progressive Matrices (RPM) is highly correlated with human intelligence, and it has been widely used to measure the abstract reasoning ability of humans. In this paper, to study the abstract reasoning capability of deep neural networks, we propose the first unsupervised learning method for solving RPM problems. Since the ground truth labels are not allowed, we design a pseudo target based on the prior constraints of the RPM formulation to approximate the ground truth label, which effectively converts the unsupervised learning strategy into a supervised one. However, the correct answer …
We present a novel computational model, "SAViR-T", for the family of visual reasoning problems embodied in the Raven's Progressive Matrices (RPM). Our model considers explicit spatial semantics of visual elements within each image in the puzzle, encoded as spatio-visual tokens, and learns the intra-image as well as the inter-image token dependencies, highly relevant for the visual reasoning task. Token-wise relationship, modeled through a transformer-based SAViR-T architecture, extract group (row or column) driven representations by leveraging the group-rule coherence and use this as the induc…
While achieving unmatched performance on many well-defined tasks, deep learning models have also been used to solve visual abstract reasoning tasks, which are relatively less well-defined, and have been widely used to measure human intelligence. However, current deep models struggle to match human abilities to solve such tasks with minimum data but maximum generalization. One limitation is that current deep learning models work in a monotonic way, i.e., treating different parts of the input in essentially fixed orderings, whereas people repeatedly observe and reason about the different parts o…
Abstract reasoning refers to the ability to analyze information, discover rules at an intangible level, and solve problems in innovative ways. Raven's Progressive Matrices (RPM) test is typically used to examine the capability of abstract reasoning. The subject is asked to identify the correct choice from the answer set to fill the missing panel at the bottom right of RPM (e.g., a 3$\times$3 matrix), following the underlying rules inside the matrix. Recent studies, taking advantage of Convolutional Neural Networks (CNNs), have achieved encouraging progress to accomplish the RPM test. However, …
Tel Aviv University（特拉维夫大学）；Facebook AI Research（Facebook人工智能研究院）；and Tel Aviv University（特拉维夫大学（重复部分不重复提取））
Raven's Progressive Matrices are multiple-choice intelligence tests, where one tries to complete the missing location in a $3\times 3$ grid of abstract images. Previous attempts to address this test have focused solely on selecting the right answer out of the multiple choices. In this work, we focus, instead, on generating a correct answer given the grid, without seeing the choices, which is a harder task, by definition. The proposed neural model combines multiple advances in generative models, including employing multiple pathways through the same network, using the reparameterization trick a…
Australian Institute for Machine Learning（澳大利亚机器学习研究所）；The University of Adelaide（阿德莱德大学）
One of the primary challenges faced by deep learning is the degree to which current methods exploit superficial statistics and dataset bias, rather than learning to generalise over the specific representations they have experienced. This is a critical concern because generalisation enables robust reasoning over unseen data, whereas leveraging superficial statistics is fragile to even small changes in data distribution. To illuminate the issue and drive progress towards a solution, we propose a test that explicitly evaluates abstract reasoning over visual data. We introduce a large-scale benchm…
As a step towards improving the abstract reasoning capability of machines, we aim to solve Raven's Progressive Matrices (RPM) with neural networks, since solving RPM puzzles is highly correlated with human intelligence. Unlike previous methods that use auxiliary annotations or assume hidden rules to produce appropriate feature representation, we only use the ground truth answer of each question for model learning, aiming for an intelligent agent to have a strong learning capability with a small amount of supervision. Based on the RPM problem formulation, the correct answer filled into the miss…
University of Nottingham Ningbo China（宁波诺丁汉大学）；Nanyang Technological University（南洋理工大学）
Raven's Progressive Matrices (RPMs) are frequently used in evaluating human's visual reasoning ability. Researchers have made considerable efforts in developing systems to automatically solve the RPM problem, often through a black-box end-to-end convolutional neural network for both visual recognition and logical reasoning tasks. Based on the two intrinsic natures of RPM problem, visual recognition and logical reasoning, we propose a Two-stage Rule-Induction Visual Reasoner (TRIVR), which consists of a perception module and a reasoning module, to tackle the challenges of real-world visual reco…
Max-Planck-Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Mila（米拉研究所）；Amazon Web Services（亚马逊云科技）
Modern neural network architectures can leverage large amounts of data to generalize well within the training distribution. However, they are less capable of systematic generalization to data drawn from unseen but related distributions, a feat that is hypothesized to require compositional reasoning and reuse of knowledge. In this work, we present Neural Interpreters, an architecture that factorizes inference in a self-attention network as a system of modules, which we call \emph{functions}. Inputs to the model are routed through a sequence of functions in a way that is end-to-end learned. The …
KTH Royal Institute of Technology（瑞典皇家理工学院）；Sharif University of Technology（谢里夫理工大学）；Cold Spring Harbor Laboratory（冷泉港实验室）
We develop an algorithm for systematic design of a large artificial neural network using a progression property. We find that some non-linear functions, such as the rectifier linear unit and its derivatives, hold the property. The systematic design addresses the choice of network size and regularization of parameters. The number of nodes and layers in network increases in progression with the objective of consistently reducing an appropriate cost. Each layer is optimized at a time, where appropriate parameters are learned using convex optimization. Regularization parameters for convex optimiza…
Tsinghua University（清华大学）；Bar Ilan University（巴伊兰大学）；Huawei Technologies（华为技术有限公司）
Graph Neural Networks (GNNs) with attention have been successfully applied for learning visual feature matching. However, current methods learn with complete graphs, resulting in a quadratic complexity in the number of features. Motivated by a prior observation that self- and cross- attention matrices converge to a sparse representation, we propose ClusterGNN, an attentional GNN architecture which operates on clusters for learning the feature matching task. Using a progressive clustering module we adaptively divide keypoints into different subgraphs to reduce redundant connectivity, and employ…
Unrolling Graph-based Douglas-Rachford Algorithm for Image Interpolation with Informed Initialization
Shandong Provincial Key Laboratory of Smart Mine Information Technology, China（山东省智慧矿山信息技术重点实验室）；Qingdao Key Laboratory of Intelligent Sensing and Virtual Emergency Simulation, China（青岛市智能感知与虚拟应急仿真重点实验室）；College of Computer Science and Engineering, Shandong University of Science and Technology, China（山东科技大学计算机科学与工程学院）；Dept of EECS, York University, Canada（约克大学电气工程与计算机科学系）
