Extrapolatable Relational Reasoning With Comparators in Low-Dimensional Manifolds

While modern deep neural architectures generalise well when test data is sampled from the same distribution as training data, they fail badly for cases when the test data distribution differs from the training distribution even along a few dimensions. This lack of out-of-distribution generalisation is increasingly manifested when the tasks become more abstract and complex, such as in relational reasoning. In this paper we propose a neuroscience-inspired inductive-biased module that can be readily amalgamated with current neural network architectures to improve out-of-distribution (o.o.d) generalisation performance on relational reasoning tasks. This module learns to project high-dimensional object representations to low-dimensional manifolds for more efficient and generalisable relational comparisons. We show that neural nets with this inductive bias achieve considerably better o.o.d generalisation performance for a range of relational reasoning tasks. We finally analyse the proposed inductive bias module to understand the importance of lower dimension projection, and propose an augmentation to the algorithmic alignment theory to better measure algorithmic alignment with generalisation

Neural Diagrammatic Reasoning

Diagrams have been shown to be effective tools for humans to represent and reason about complex concepts. They have been widely used to represent concepts in science teaching, to communicate workflow in industries and to measure human fluid intelligence. Mechanised reasoning systems typically encode diagrams into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. This means the reasoning systems cannot be easily adapted to other diagrams without a new set of human-defined representation mapping and reasoning rules. Moreover such systems are not able to cope with diagram inputs as raw and possibly noisy images. The need for human input and the lack of robustness to noise significantly limit the applications of mechanised diagrammatic reasoning systems. A key research question then arises: can we develop human-like reasoning systems that learn to reason robustly without predefined reasoning rules? To answer this question, I propose Neural Diagrammatic Reasoning, a new family of diagrammatic reasoning systems which does not have the drawbacks of mechanised reasoning systems. The new systems are based on deep neural networks, a recently popular machine learning method that achieved human-level performance on a range of perception tasks such as object detection, speech recognition and natural language processing. The proposed systems are able to learn both diagram to symbol mapping and implicit reasoning rules only from data, with no prior human input about symbols and rules in the reasoning tasks. Specifically I developed EulerNet, a novel neural network model that solves Euler diagram syllogism tasks with 99.5% accuracy. Experiments show that EulerNet learns useful representations of the diagrams and tasks, and is robust to noise and deformation in the input data. I also developed MXGNet, a novel multiplex graph neural architecture that solves Raven Progressive Matrices (RPM) tasks. MXGNet achieves state-of-the-art accuracies on two popular RPM datasets. In addition, I developed Discrete-AIR, an unsupervised learning architecture that learns semi-symbolic representations of diagrams without any labels. Lastly I designed a novel inductive bias module that can be readily used in today’s deep neural networks to improve their generalisation capability on relational reasoning tasks.EPSRC Studentship and Cambridge Trust Scholarshi

Grounding semantic cognition using computational modelling and network analysis

The overarching objective of this thesis is to further the field of grounded semantics using a range of computational and empirical studies. Over the past thirty years, there have been many algorithmic advances in the modelling of semantic cognition. A commonality across these cognitive models is a reliance on hand-engineering “toy-models”. Despite incorporating newer techniques (e.g. Long short-term memory), the model inputs remain unchanged. We argue that the inputs to these traditional semantic models have little resemblance with real human experiences. In this dissertation, we ground our neural network models by training them with real-world visual scenes using naturalistic photographs. Our approach is an alternative to both hand-coded features and embodied raw sensorimotor signals. We conceptually replicate the mutually reinforcing nature of hybrid (feature-based and grounded) representations using silhouettes of concrete concepts as model inputs. We next gradually develop a novel grounded cognitive semantic representation which we call scene2vec, starting with object co-occurrences and then adding emotions and language-based tags. Limitations of our scene-based representation are identified for more abstract concepts (e.g. freedom). We further present a large-scale human semantics study, which reveals small-world semantic network topologies are context-dependent and that scenes are the most dominant cognitive dimension. This finding leads us to conclude that there is no meaning without context. Lastly, scene2vec shows promising human-like context-sensitive stereotypes (e.g. gender role bias), and we explore how such stereotypes are reduced by targeted debiasing. In conclusion, this thesis provides support for a novel computational viewpoint on investigating meaning - scene-based grounded semantics. Future research scaling scene-based semantic models to human-levels through virtual grounding has the potential to unearth new insights into the human mind and concurrently lead to advancements in artificial general intelligence by enabling robots, embodied or otherwise, to acquire and represent meaning directly from the environment