Related papers: Flattening subtyping by eta expansion
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following…
We study the notion of subtyping for session types in a logical setting, where session types are propositions of multiplicative/additive linear logic extended with least and greatest fixed points. The resulting subtyping relation admits a…
Internet-scale distributed systems often replicate data at multiple geographic locations to provide low latency and high availability. The Conflict-free Replicated Data Type (CRDT) is a framework that provides a principled approach to…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
The ability to identify interesting and repetitive substructures is an essential component to discovering knowledge in structural data. We describe a new version of our SUBDUE substructure discovery system based on the minimum description…
Understanding the decisions made by deep neural networks is essential in high-stakes domains such as medical imaging and autonomous driving. Yet, these models often lack transparency, particularly in computer vision.…
We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
As fine-tuning becomes impractical at scale, probing is emerging as the preferred evaluation protocol. However, standard linear probing can understate the capability of models whose pre-training optimizes local representations rather than…
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…
This paper presents an approach to Prolog-style term encoding of typed feature structures. The type feature structures to be encoded are constrained by appropriateness conditions as in Carpenter's ALE system. But unlike ALE, we impose a…
We present a novel deep neural network architecture for unsupervised subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel…
We show that it is possible to change from a {\it subnatural} electromagnetically induced transparency (EIT) feature to a {\it subnatural} electromagnetically induced absorption (EIA) feature in a (degenerate) three-level $\Lambda$ system.…
Tensor shape mismatch is a common source of bugs in deep learning programs. We propose a new type-based approach to detect tensor shape mismatches. One of the main features of our approach is the best-effort shape inference. As the tensor…
To offer accurate and diverse recommendation services, recent methods use auxiliary information to foster the learning process of user and item representations. Many SOTA methods fuse different sources of information (user, item, knowledge…
We present a new way to control the unfolding of definitions in dependent type theory. Traditionally, proof assistants require users to fix whether each definition will or will not be unfolded in the remainder of a development; unfolding…
Downsampling images and labels, often necessitated by limited resources or to expedite network training, leads to the loss of small objects and thin boundaries. This undermines the segmentation network's capacity to interpret images…
Automated deduction lies at the core of Artificial Intelligence (AI), underpinning theorem proving, formal verification, and logical reasoning. Despite decades of progress, reconciling deductive completeness with computational efficiency…
In the realm of natural language processing, the understanding of tabular data has perpetually stood as a focal point of scholarly inquiry. The emergence of expansive language models, exemplified by the likes of ChatGPT, has ushered in a…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…