Image classification has been studied extensively but there has been limited work in the direction of using non-conventional, external guidance other than traditional image-label pairs to train such models. In this thesis we present a set of methods to leverage information about the semantic hierarchy induced by class labels. In the first part of the thesis, we inject label-hierarchy knowledge to an arbitrary classifier and empirically show that availability of such external semantic information in conjunction with the visual semantics from images boosts overall performance. Taking a step further in this direction, we model more explicitly the label-label and label-image interactions by using order-preserving embedding-based models, prevalent in natural language, and tailor them to the domain of computer vision to perform image classification. Although, contrasting in nature, both the CNN-classifiers injected with hierarchical information, and the embedding-based models outperform a hierarchy-agnostic model on the newly presented, real-world ETH Entomological Collection image dataset.

Chen, Boli, Huang, Xin, Xiao, Lin, Cai, Zixin, Jing, Liping

Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical relations. In fact, linguistic ontologies are intrinsic hierarchies. Besides the labels, the conceptual relations between words can also form hierarchical structures. Thus it can be a challenge to learn mappings from the word space to the label space, and vice versa. We propose to model the word and label hierarchies by embedding them jointly in the hyperbolic space. The main reason is that the tree-likeness of the hyperbolic space matches the complexity of symbolic data with hierarchical structures. A new hyperbolic interaction model (HyperIM) is designed to learn the label-aware document representations and make predictions for HMLC. Extensive experiments are conducted on three benchmark datasets. The results have demonstrated that the new model can realistically capture the complex data structures and further improve the performance for HMLC comparing with the state-of-the-art methods. To facilitate future research, our code is publicly available.

Nickel, Maximilian, Kiela, Douwe

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Nickel, Maximillian, Kiela, Douwe

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, state-of-the-art embedding methods typically do not account for latent hierarchical structures which are characteristic for many complex symbolic datasets. In this work, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We present an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings can outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Ganea, Octavian-Eugen, Bécigneul, Gary, Hofmann, Thomas

Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior work, we first advocate for using hyperbolic spaces which provably model tree-like structures better than Euclidean geometry. Second, we view hierarchical relations as partial orders defined using a family of nested geodesically convex cones. We prove that these entailment cones admit an optimal shape with a closed form expression both in the Euclidean and hyperbolic spaces. Moreover, they canonically define the embedding learning process. Experiments show significant improvements of our method over strong recent baselines both in terms of representational capacity and generalization.