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Learning Representations of Entities and Relations

arXiv.org Artificial Intelligence

Encoding facts as representations of entities and binary relationships between them, as learned by knowledge graph representation models, is useful for various tasks, including predicting new facts, question answering, fact checking and information retrieval. The focus of this thesis is on (i) improving knowledge graph representation with the aim of tackling the link prediction task; and (ii) devising a theory on how semantics can be captured in the geometry of relation representations. Most knowledge graphs are very incomplete and manually adding new information is costly, which drives the development of methods which can automatically infer missing facts. The first contribution of this thesis is HypER, a convolutional model which simplifies and improves upon the link prediction performance of the existing convolutional state-of-the-art model ConvE and can be mathematically explained in terms of constrained tensor factorisation. The second contribution is TuckER, a relatively straightforward linear model, which, at the time of its introduction, obtained state-of-the-art link prediction performance across standard datasets. The third contribution is MuRP, first multi-relational graph representation model embedded in hyperbolic space. MuRP outperforms all existing models and its Euclidean counterpart MuRE in link prediction on hierarchical knowledge graph relations whilst requiring far fewer dimensions. Despite the development of a large number of knowledge graph representation models with gradually increasing predictive performance, relatively little is known of the latent structure they learn. We generalise recent theoretical understanding of how semantic relations of similarity, paraphrase and analogy are encoded in the geometric interactions of word embeddings to how more general relations, as found in knowledge graphs, can be encoded in their representations.


Generalized Shape Metrics on Neural Representations

arXiv.org Machine Learning

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are trained on, or biologically adapted to, similar tasks. A standardized set of analysis tools is now needed to identify how network-level covariates -- such as architecture, anatomical brain region, and model organism -- impact neural representations (hidden layer activations). Here, we provide a rigorous foundation for these analyses by defining a broad family of metric spaces that quantify representational dissimilarity. Using this framework we modify existing representational similarity measures based on canonical correlation analysis to satisfy the triangle inequality, formulate a novel metric that respects the inductive biases in convolutional layers, and identify approximate Euclidean embeddings that enable network representations to be incorporated into essentially any off-the-shelf machine learning method. We demonstrate these methods on large-scale datasets from biology (Allen Institute Brain Observatory) and deep learning (NAS-Bench-101). In doing so, we identify relationships between neural representations that are interpretable in terms of anatomical features and model performance.


Learning Operators with Coupled Attention

arXiv.org Artificial Intelligence

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function in the training set measurements is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.


Conical Classification For Computationally Efficient One-Class Topic Determination

arXiv.org Artificial Intelligence

As the Internet grows in size, so does the amount of text based information that exists. For many application spaces it is paramount to isolate and identify texts that relate to a particular topic. While one-class classification would be ideal for such analysis, there is a relative lack of research regarding efficient approaches with high predictive power. By noting that the range of documents we wish to identify can be represented as positive linear combinations of the Vector Space Model representing our text, we propose Conical classification, an approach that allows us to identify if a document is of a particular topic in a computationally efficient manner. We also propose Normal Exclusion, a modified version of Bi-Normal Separation that makes it more suitable within the one-class classification context. We show in our analysis that our approach not only has higher predictive power on our datasets, but is also faster to compute.


Turing approximations, toric isometric embeddings & manifold convolutions

arXiv.org Artificial Intelligence

Convolutions are fundamental elements in deep learning architectures. Here, we present a theoretical framework for combining extrinsic and intrinsic approaches to manifold convolution through isometric embeddings into tori. In this way, we define a convolution operator for a manifold of arbitrary topology and dimension. We also explain geometric and topological conditions that make some local definitions of convolutions which rely on translating filters along geodesic paths on a manifold, computationally intractable. A result of Alan Turing from 1938 underscores the need for such a toric isometric embedding approach to achieve a global definition of convolution on computable, finite metric space approximations to a smooth manifold.


A Survey of Knowledge Enhanced Pre-trained Models

arXiv.org Artificial Intelligence

Pre-trained models learn contextualized word representations on large-scale text corpus through a self-supervised learning method, which has achieved promising performance after fine-tuning. These models, however, suffer from poor robustness and lack of interpretability. Pre-trained models with knowledge injection, which we call knowledge enhanced pre-trained models (KEPTMs), possess deep understanding and logical reasoning and introduce interpretability to some extent. In this survey, we provide a comprehensive overview of KEPTMs for natural language processing. We first introduce the progress of pre-trained models and knowledge representation learning. Then we systematically categorize existing KEPTMs from three different perspectives. Finally, we outline some potential directions of KEPTMs for future research.


Excess Capacity and Backdoor Poisoning

arXiv.org Machine Learning

A backdoor data poisoning attack is an adversarial attack wherein the attacker injects several watermarked, mislabeled training examples into a training set. The watermark does not impact the test-time performance of the model on typical data; however, the model reliably errs on watermarked examples. To gain a better foundational understanding of backdoor data poisoning attacks, we present a formal theoretical framework within which one can discuss backdoor data poisoning attacks for classification problems. We then use this to analyze important statistical and computational issues surrounding these attacks. On the statistical front, we identify a parameter we call the memorization capacity that captures the intrinsic vulnerability of a learning problem to a backdoor attack. This allows us to argue about the robustness of several natural learning problems to backdoor attacks. Our results favoring the attacker involve presenting explicit constructions of backdoor attacks, and our robustness results show that some natural problem settings cannot yield successful backdoor attacks. From a computational standpoint, we show that under certain assumptions, adversarial training can detect the presence of backdoors in a training set. We then show that under similar assumptions, two closely related problems we call backdoor filtering and robust generalization are nearly equivalent. This implies that it is both asymptotically necessary and sufficient to design algorithms that can identify watermarked examples in the training set in order to obtain a learning algorithm that both generalizes well to unseen data and is robust to backdoors.


Structured Prediction in NLP -- A survey

arXiv.org Artificial Intelligence

Over the last several years, the field of Structured prediction in NLP has had seen huge advancements with sophisticated probabilistic graphical models, energy-based networks, and its combination with deep learning-based approaches. This survey provides a brief of major techniques in structured prediction and its applications in the NLP domains like parsing, sequence labeling, text generation, and sequence to sequence tasks. We also deep-dived into energy-based and attention-based techniques in structured prediction, identified some relevant open issues and gaps in the current state-of-the-art research, and have come up with some detailed ideas for future research in these fields.


MatSat: a matrix-based differentiable SAT solver

arXiv.org Artificial Intelligence

We propose a new approach to SAT solving which solves SAT problems in vector spaces as a cost minimization problem of a non-negative differentiable cost function J^sat. In our approach, a solution, i.e., satisfying assignment, for a SAT problem in n variables is represented by a binary vector u in {0,1}^n that makes J^sat(u) zero. We search for such u in a vector space R^n by cost minimization, i.e., starting from an initial u_0 and minimizing J to zero while iteratively updating u by Newton's method. We implemented our approach as a matrix-based differential SAT solver MatSat. Although existing main-stream SAT solvers decide each bit of a solution assignment one by one, be they of conflict driven clause learning (CDCL) type or of stochastic local search (SLS) type, MatSat fundamentally differs from them in that it continuously approach a solution in a vector space. We conducted an experiment to measure the scalability of MatSat with random 3-SAT problems in which MatSat could find a solution up to n=10^5 variables. We also compared MatSat with four state-of-the-art SAT solvers including winners of SAT competition 2018 and SAT Race 2019 in terms of time for finding a solution, using a random benchmark set from SAT 2018 competition and an artificial random 3-SAT instance set. The result shows that MatSat comes in second in both test sets and outperforms all the CDCL type solvers.


Classifying Textual Data with Pre-trained Vision Models through Transfer Learning and Data Transformations

arXiv.org Artificial Intelligence

Knowledge is acquired by humans through experience, and no boundary is set between the kinds of knowledge or skill levels we can achieve on different tasks at the same time. When it comes to Neural Networks, that is not the case, the major breakthroughs in the field are extremely task and domain specific. Vision and language are dealt with in separate manners, using separate methods and different datasets. In this work, we propose to use knowledge acquired by benchmark Vision Models which are trained on ImageNet to help a much smaller architecture learn to classify text. After transforming the textual data contained in the IMDB dataset to gray scale images. An analysis of different domains and the Transfer Learning method is carried out. Despite the challenge posed by the very different datasets, promising results are achieved. The main contribution of this work is a novel approach which links large pretrained models on both language and vision to achieve state-of-the-art results in different sub-fields from the original task. Without needing high compute capacity resources. Specifically, Sentiment Analysis is achieved after transferring knowledge between vision and language models. BERT embeddings are transformed into grayscale images, these images are then used as training examples for pre-trained vision models such as VGG16 and ResNet Index Terms: BERT, Convolutional Neural Networks, Domain Adaptation, image classification, Natural Language Processing, t-SNE, text classification, Transfer Learning