Learning Abstract Visual Reasoning via Task Decomposition: A Case Study in Raven Progressive Matrices

One of the challenges in learning to perform abstract reasoning is that problems are often posed as monolithic tasks, with no intermediate subgoals. In Raven Progressive Matrices (RPM), the task is to choose one of the available answers given a context, where both contexts and answers are composite images featuring multiple objects in various spatial arrangements. As this high-level goal is the only guidance available, learning is challenging and most contemporary solvers tend to be opaque. In this study, we propose a deep learning architecture based on the transformer blueprint which, rather than directly making the above choice, predicts the visual properties of individual objects and their arrangements. The multidimensional predictions obtained in this way are then directly juxtaposed to choose the answer. We consider a few ways in which the model parses the visual input into tokens and several regimes of masking parts of the input in self-supervised training. In experimental assessment, the models not only outperform state-of-the-art methods but also provide interesting insights and partial explanations about the inference. The design of the method also makes it immune to biases that are known to exist in some RPM benchmarks.

Ain't Nobody Got Time For Coding: Structure-Aware Program Synthesis From Natural Language

Program synthesis from natural language (NL) is practical for humans and, once technically feasible, would significantly facilitate software development and revolutionize end-user programming. We present SAPS, an end-to-end neural network capable of mapping relatively complex, multi-sentence NL specifications to snippets of executable code. The proposed architecture relies exclusively on neural components, and is built upon a tree2tree autoencoder trained on abstract syntax trees, combined with a pretrained word embedding and a bi-directional multi-layer LSTM for NL processing. The decoder features a doubly-recurrent LSTM with a novel signal propagation scheme and soft attention mechanism. When applied to a large dataset of problems proposed in a previous study, SAPS performs on par with or better than the method proposed there, producing correct programs in over 90% of cases. In contrast to other methods, it does not involve any non-neural components to post-process the resulting programs, and uses a fixed-dimensional latent representation as the only link between the NL analyzer and source code generator.

Learning to Play Othello with Deep Neural Networks

Achieving superhuman playing level by AlphaGo corroborated the capabilities of convolutional neural architectures (CNNs) for capturing complex spatial patterns. This result was to a great extent due to several analogies between Go board states and 2D images CNNs have been designed for, in particular translational invariance and a relatively large board. In this paper, we verify whether CNN-based move predictors prove effective for Othello, a game with significantly different characteristics, including a much smaller board size and complete lack of translational invariance. We compare several CNN architectures and board encodings, augment them with state-of-the-art extensions, train on an extensive database of experts' moves, and examine them with respect to move prediction accuracy and playing strength. The empirical evaluation confirms high capabilities of neural move predictors and suggests a strong correlation between prediction accuracy and playing strength. The best CNNs not only surpass all other 1-ply Othello players proposed to date but defeat (2-ply) Edax, the best open-source Othello player.

Distance Metric Ensemble Learning and the Andrews-Curtis Conjecture

Motivated by the search for a counterexample to the Poincar\'e conjecture in three and four dimensions, the Andrews-Curtis conjecture was proposed in 1965. It is now generally suspected that the Andrews-Curtis conjecture is false, but small potential counterexamples are not so numerous, and previous work has attempted to eliminate some via combinatorial search. Progress has however been limited, with the most successful approach (breadth-first-search using secondary storage) being neither scalable nor heuristically-informed. A previous empirical analysis of problem structure examined several heuristic measures of search progress and determined that none of them provided any useful guidance for search. In this article, we induce new quality measures directly from the problem structure and combine them to produce a more effective search driver via ensemble machine learning. By this means, we eliminate 19 potential counterexamples, the status of which had been unknown for some years.