Carl Allen

Alice Bizeul, Bernhard Schölkopf, Carl Allen

In self-supervised learning (SSL), representations are learned via an auxiliary task without annotated labels. A common task is to classify augmentations or different modalities of the data, which share semantic content (e.g. an object in an image) but differ in style (e.g. the object's location). Many approaches to self-supervised learning have been proposed, e.g. SimCLR, CLIP, and DINO, which have recently gained much attention for their representations achieving downstream performance comparable to supervised learning. However, a theoretical understanding of self-supervised methods eludes. Addressing this, we present a generative latent variable model for self-supervised learning and show that several families of discriminative SSL, including contrastive methods, induce a comparable distribution over representations, providing a unifying theoretical framework for these methods. The proposed model also justifies connections drawn to mutual information and the use of a ''projection head''. Learning representations by fitting the model generatively (termed SimVAE) improves performance over discriminative and other VAE-based methods on simple image benchmarks and significantly narrows the gap between generative and discriminative representation learning in more complex settings. Importantly, as our analysis predicts, SimVAE outperforms self-supervised learning where style information is required, taking an important step toward understanding self-supervised methods and achieving task-agnostic representations.

Ivana Balažević, Carl Allen, Timothy Hospedales

As data volumes continue to grow, the labelling process increasingly becomes a bottleneck, creating demand for methods that leverage information from unlabelled data. Impressive results have been achieved in semi-supervised learning (SSL) for image classification, nearing fully supervised performance, with only a fraction of the data labelled. In this work, we propose a probabilistically principled general approach to SSL that considers the distribution over label predictions, for labels of different complexity, from "one-hot" vectors to binary vectors and images. Our method regularises an underlying supervised model, using a normalising flow that learns the posterior distribution over predictions for labelled data, to serve as a prior over the predictions on unlabelled data. We demonstrate the general applicability of this approach on a range of computer vision tasks with varying output complexity: classification, attribute prediction and image-to-image translation.

David Chang, Ivana Balazevic, Carl Allen et al.

Much of biomedical and healthcare data is encoded in discrete, symbolic form such as text and medical codes. There is a wealth of expert-curated biomedical domain knowledge stored in knowledge bases and ontologies, but the lack of reliable methods for learning knowledge representation has limited their usefulness in machine learning applications. While text-based representation learning has significantly improved in recent years through advances in natural language processing, attempts to learn biomedical concept embeddings so far have been lacking. A recent family of models called knowledge graph embeddings have shown promising results on general domain knowledge graphs, and we explore their capabilities in the biomedical domain. We train several state-of-the-art knowledge graph embedding models on the SNOMED-CT knowledge graph, provide a benchmark with comparison to existing methods and in-depth discussion on best practices, and make a case for the importance of leveraging the multi-relational nature of knowledge graphs for learning biomedical knowledge representation. The embeddings, code, and materials will be made available to the communitY.

Carl Allen, Ivana Balažević, Timothy Hospedales

Much progress has been made in semi-supervised learning (SSL) by combining methods that exploit different aspects of the data distribution, e.g. consistency regularisation relies on properties of $p(x)$, whereas entropy minimisation pertains to the label distribution $p(y|x)$. Focusing on the latter, we present a probabilistic model for discriminative SSL, that mirrors its classical generative counterpart. Under the assumption $y|x$ is deterministic, the prior over latent variables becomes discrete. We show that several well-known SSL methods can be interpreted as approximating this prior, and can be improved upon. We extend the discriminative model to neuro-symbolic SSL, where label features satisfy logical rules, by showing such rules relate directly to the above prior, thus justifying a family of methods that link statistical learning and logical reasoning, and unifying them with regular SSL.

Benedek Rozemberczki, Carl Allen, Rik Sarkar

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

Carl Allen, Ivana Balažević, Timothy Hospedales

Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between entities, embeddings are typically compared in the latent space following a relation-specific mapping. Whilst their predictive performance has steadily improved, how such models capture the underlying latent structure of semantic information remains unexplained. Building on recent theoretical understanding of word embeddings, we categorise knowledge graph relations into three types and for each derive explicit requirements of their representations. We show that empirical properties of relation representations and the relative performance of leading knowledge graph representation methods are justified by our analysis.

Ivana Balažević, Carl Allen, Timothy Hospedales

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often exhibit multiple simultaneous hierarchies, which current hyperbolic models do not capture. To address this, we propose a model that embeds multi-relational graph data in the Poincaré ball model of hyperbolic space. Our Multi-Relational Poincaré model (MuRP) learns relation-specific parameters to transform entity embeddings by Möbius matrix-vector multiplication and Möbius addition. Experiments on the hierarchical WN18RR knowledge graph show that our Poincaré embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.

Carl Allen, Timothy Hospedales

Word embeddings generated by neural network methods such as word2vec (W2V) are well known to exhibit seemingly linear behaviour, e.g. the embeddings of analogy "woman is to queen as man is to king" approximately describe a parallelogram. This property is particularly intriguing since the embeddings are not trained to achieve it. Several explanations have been proposed, but each introduces assumptions that do not hold in practice. We derive a probabilistically grounded definition of paraphrasing that we re-interpret as word transformation, a mathematical description of "$w_x$ is to $w_y$". From these concepts we prove existence of linear relationships between W2V-type embeddings that underlie the analogical phenomenon, identifying explicit error terms.

Ivana Balažević, Carl Allen, Timothy M. Hospedales

Knowledge graphs are graphical representations of large databases of facts, which typically suffer from incompleteness. Inferring missing relations (links) between entities (nodes) is the task of link prediction. A recent state-of-the-art approach to link prediction, ConvE, implements a convolutional neural network to extract features from concatenated subject and relation vectors. Whilst results are impressive, the method is unintuitive and poorly understood. We propose a hypernetwork architecture that generates simplified relation-specific convolutional filters that (i) outperforms ConvE and all previous approaches across standard datasets; and (ii) can be framed as tensor factorization and thus set within a well established family of factorization models for link prediction. We thus demonstrate that convolution simply offers a convenient computational means of introducing sparsity and parameter tying to find an effective trade-off between non-linear expressiveness and the number of parameters to learn.

Carl Allen, Ivana Balažević, Timothy Hospedales

Word2Vec (W2V) and GloVe are popular, fast and efficient word embedding algorithms. Their embeddings are widely used and perform well on a variety of natural language processing tasks. Moreover, W2V has recently been adopted in the field of graph embedding, where it underpins several leading algorithms. However, despite their ubiquity and relatively simple model architecture, a theoretical understanding of what the embedding parameters of W2V and GloVe learn and why that is useful in downstream tasks has been lacking. We show that different interactions between PMI vectors reflect semantic word relationships, such as similarity and paraphrasing, that are encoded in low dimensional word embeddings under a suitable projection, theoretically explaining why embeddings of W2V and GloVe work. As a consequence, we also reveal an interesting mathematical interconnection between the considered semantic relationships themselves.