Related papers: Custom Representations of Inductive Families
We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…
In this thesis, we try to build a connection between the two schools by introducing syntactic inductive biases for deep learning models. We propose two families of inductive biases, one for constituency structure and another one for…
A well-known problem in the theory of dependent types is how to handle so-called nested data types. These data types are difficult to program and to reason about in total dependently typed languages such as Agda and Coq. In particular, it…
We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic…
Fonts are ubiquitous across documents and come in a variety of styles. They are either represented in a native vector format or rasterized to produce fixed resolution images. In the first case, the non-standard representation prevents…
We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…
Recent works show that discourse analysis benefits from modeling intra- and inter-sentential levels separately, where proper representations for text units of different granularities are desired to capture both the meaning of text units and…
Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
This paper studies emulation of induction by coinduction in a call-by-name language with control operators. Since it is known that call-by-name programming languages with control operators cannot have general initial algebras, interaction…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
Vector-based word representations help countless Natural Language Processing (NLP) tasks capture the language's semantic and syntactic regularities. In this paper, we present the characteristics of existing word embedding approaches and…
First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…
We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappingsfrom finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described…
Syntactic structures used to play a vital role in natural language processing (NLP), but since the deep learning revolution, NLP has been gradually dominated by neural models that do not consider syntactic structures in their design. One…
Most spoken language understanding systems use a pipeline approach composed of an automatic speech recognition interface and a natural language understanding module. This approach forces hard decisions when converting continuous inputs into…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…
Inductive reasoning is a core component of human intelligence. In the past research of inductive reasoning within computer science, formal language is used as representations of knowledge (facts and rules, more specifically). However,…
Despite the extensive success of pretrained language models as encoders for building NLP systems, they haven't seen prominence as decoders for sequence generation tasks. We explore the question of whether these models can be adapted to be…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…