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We present a semantic parser for Abstract Meaning Representations which learns to parse strings into tree representations of the compositional structure of an AMR graph. This allows us to use standard neural techniques for supertagging and…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
Automatic sample identification (ASID), the detection and identification of portions of audio recordings that have been reused in new musical works, is an essential but challenging task in the field of audio query-based retrieval. While a…
We characterize regular string transductions as programs in a linear $\lambda$-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions,…
A large class of non-smooth practical optimization problems can be written as minimization of a sum of smooth and partly smooth functions. We examine such structured problems which also depend on a parameter vector and study the problem of…
Hierarchical structures exist in both linguistics and Natural Language Processing (NLP) tasks. How to design RNNs to learn hierarchical representations of natural languages remains a long-standing challenge. In this paper, we define two…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
We define a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type $F_4$. In this way, we obtain a set of…
For classification tasks, dictionary learning based methods have attracted lots of attention in recent years. One popular way to achieve this purpose is to introduce label information to generate a discriminative dictionary to represent…
Music structure analysis (MSA) methods traditionally search for musically meaningful patterns in audio: homogeneity, repetition, novelty, and segment-length regularity. Hand-crafted audio features such as MFCCs or chromagrams are often used…
Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is…
Remote sensing image segmentation faces persistent challenges in distinguishing morphologically similar categories and adapting to diverse scene variations. While existing methods rely on implicit representation learning paradigms, they…
We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) to total functional programming languages with expressive type systems featuring the combination of - tuple types; - sum types; -…
Topologists are sometimes interested in space-valued diagrams over a given index category, but it is tricky to say what such a diagram even is if we look for a notion that is stable under equivalence. The same happens in (homotopy) type…
Form understanding depends on both textual contents and organizational structure. Although modern OCR performs well, it is still challenging to realize general form understanding because forms are commonly used and of various formats. The…