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Deep learning methods have revolutionized speech recognition, image recognition, and natural language processing since 2010. Each of these tasks involves a single modality in their input signals. However, many applications in the artificial…

The objective of knowledge graph embedding is to encode both entities and relations of knowledge graphs into continuous low-dimensional vector spaces. Previously, most works focused on symbolic representation of knowledge graph with…

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…

Bidirectional models are considered essential for strong text embeddings. Recent approaches to adapt autoregressive language models (LMs) into strong text embedding models have largely had the requirement to modify the LM architecture to be…

Sentence embeddings are central to modern NLP and AI systems, yet little is known about their internal structure. While we can compare these embeddings using measures such as cosine similarity, the contributing features are not…

In essence, embedding algorithms work by optimizing the distance between a word and its usual context in order to generate an embedding space that encodes the distributional representation of words. In addition to single words or word…

Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…

Bilingual word embeddings have been widely used to capture the similarity of lexical semantics in different human languages. However, many applications, such as cross-lingual semantic search and question answering, can be largely benefited…

Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph…

In recent years, there has been a resurgence in methods that use distributed (neural) representations to represent and reason about semantic knowledge for robotics applications. However, while robots often observe previously unknown…

In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…

Ribbon graphs embedded on a Riemann surface provide a useful way to describe the double line Feynman diagrams of large N computations and a variety of other QFT correlator and scattering amplitude calculations, e.g in MHV rules for…

We introduce a modified homology and cohomology theory for involutory biquandles (also known as \textit{bikei}). We use bikei 2-cocycles to enhance the bikei counting invariant for unoriented knots and links as well as unoriented and…

Word embeddings are a key component of high-performing natural language processing (NLP) systems, but it remains a challenge to learn good representations for novel words on the fly, i.e., for words that did not occur in the training data.…

Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…

We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinatorial encoding of a Bernoulli process with continuous state…

There has been a steadily growing interest in development of novel methods to learn a representation of a given input data and subsequently using them for several downstream tasks. The field of natural language processing has seen a…

Chain-of-thought (CoT) reasoning has enabled transformer-based language models to excel at complex mathematics and multi-step planning. However, in standard decoder-only architectures, these reasoning steps are externalized in natural…

Recent advances in cross-lingual word embeddings have primarily relied on mapping-based methods, which project pretrained word embeddings from different languages into a shared space through a linear transformation. However, these…