Related papers: Poincar\'e Embeddings for Learning Hierarchical Re…

This paper presents primarily two Euclidean embeddings of the quotient space generated by matrices that are identified modulo arbitrary row permutations. The original application is in deep learning on graphs where the learning task is…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Obtaining continuous representations of structural data such as directed acyclic graphs (DAGs) has gained attention in machine learning and artificial intelligence. However, embedding complex DAGs in which both ancestors and descendants of…

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…

Hierarchical data arise in countless domains, from biological taxonomies and organizational charts to legal codes and knowledge graphs. Residual Quantization (RQ) is widely used to generate discrete, multitoken representations for such data…

Dimensionality reduction (DR) offers a useful representation of complex high-dimensional data. Recent DR methods focus on hyperbolic geometry to derive a faithful low-dimensional representation of hierarchical data. However, existing…

By representing words with probability densities rather than point vectors, probabilistic word embeddings can capture rich and interpretable semantic information and uncertainty. The uncertainty information can be particularly meaningful in…

Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…

Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad…

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…

Models for image representation learning are typically designed for either recognition or generation. Various forms of contrastive learning help models learn to convert images to embeddings that are useful for classification, detection, and…

The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end…

We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

Visual recognition tasks are often limited to dealing with a small subset of classes simply because the labels for the remaining classes are unavailable. We are interested in identifying novel concepts in a dataset through representation…

Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…

In semi-supervised learning, methods that rely on confidence learning to generate pseudo-labels have been widely proposed. However, increasing research finds that when faced with noisy and biased data, the model's representation network is…

Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…