Related papers: ViCAR: Visualizing Categories with Automated Rewri…
A new generalisation of the notion of space, called "vectoid", is suggested in this work. Basic definitions, examples and properties are presented, as well as a construction of direct product of vectoids. Proofs of more complicated…
Predicting program behavior and reasoning about code execution remain significant challenges in software engineering, particularly for large language models (LLMs) designed for code analysis. While these models excel at understanding static…
We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an…
We study monoidal profunctors as a tool to reason and structure pure functional programs both from a categorical perspective and as a Haskell implementation. From the categorical point of view we approach them as monoids in a certain…
Knowledge-based Visual Question Answering about Named Entities is a challenging task that requires retrieving information from a multimodal Knowledge Base. Named entities have diverse visual representations and are therefore difficult to…
In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to…
We study the monoidal structure of the standard strictification functor $\textrm{st}:\mathbf{Bicat} \rightarrow \mathbf{2Cat}$. In doing so, we construct monoidal structures on the 2-category whose objects are bicategories and on the…
Query Visualization (QV) is the problem of transforming a given query into a graphical representation that helps humans understand its meaning. This task is notably different from designing a Visual Query Language (VQL) that helps a user…
We construct a categorification of the braid groups associated with Coxeter groups inside the homotopy category of Soergel's bimodules. Classical actions of braid groups on triangulated categories should come from an action of this monoidal…
Deductive verification of concurrent programs under weak memory has thus far been limited to simple programs over a monolithic state space. For scalability, we also require modular techniques with verifiable library abstractions. This paper…
The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification…
Vector Quantization (VQ) techniques face significant challenges in codebook utilization, limiting reconstruction fidelity in image modeling. We introduce a Dual Codebook mechanism that effectively addresses this limitation by partitioning…
The basic method of rewriting for words in a free monoid given a monoid presentation is extended to rewriting for paths in a free category given a `Kan extension presentation'. This is related to work of Carmody-Walters on the Todd-Coxeter…
This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory -- categorifying the classical theory of categories enriched in a monoidal category -- up to a description of the free…
Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…
We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of…
Recently, we have developed an efficient generic partition refinement algorithm, which computes behavioural equivalence on a state-based system given as an encoded coalgebra, and implemented it in the tool CoPaR. Here we extend this to a…
We use a theory of colax Reedy diagrams to show that the category of Segal M-precategories with fixed set of objects has a model structure for a symmetric monoidal model category M = (M,\otimes,I). What is relevant here is when M is…
We give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated planar graphs. This presentation extends the Coxeter presentation. We deduce a simple criterion for a Coxeter group or braid group to act on a category.
Vision Transformers (ViTs) achieve strong performance in visual recognition, yet their decision-making remains difficult to interpret. We propose BiCAM, a bidirectional class activation mapping method that captures both supportive…