Related papers: Localisable Monads
In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…
Multi-label image classification, which can be categorized into label-dependency and region-based methods, is a challenging problem due to the complex underlying object layouts. Although region-based methods are less likely to encounter…
Characterizing graph properties is fundamental to the analysis and to our understanding of real-world networked systems. The local clustering coefficient, and the more recently introduced, local closure coefficient, capture powerful…
We establish how a two-dimensional local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
In the context of MDPs with high-dimensional states, downstream tasks are predominantly applied on a compressed, low-dimensional representation of the original input space. A variety of learning objectives have therefore been used to attain…
Distributed word embeddings have shown superior performances in numerous Natural Language Processing (NLP) tasks. However, their performances vary significantly across different tasks, implying that the word embeddings learnt by those…
The majority of computer vision algorithms fail to find higher-order (abstract) patterns in an image so are not robust against adversarial attacks, unlike human lateralized vision. Deep learning considers each input pixel in a homogeneous…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
Pebble games are a powerful tool in the study of finite model theory, constraint satisfaction and database theory. Monads and comonads are basic notions of category theory which are widely used in semantics of computation and in modern…
Symbol grounding (Harnad, 1990) describes how symbols such as words acquire their meanings by connecting to real-world sensorimotor experiences. Recent work has shown preliminary evidence that grounding may emerge in (vision-)language…
We study a composition operation on monads, equivalently presented as large equational theories. Specifically, we discuss the existence of tensors, which are combinations of theories that impose mutual commutation of the operations from the…
Until quite recently, the backbone of nearly every state-of-the-art computer vision model has been the 2D convolution. At its core, a 2D convolution simultaneously mixes information across both the spatial and channel dimensions of a…
Several relational program logics have been introduced for integrating reasoning about relational properties of programs and measurement of quantitative difference between computational effects. Towards a general framework for such logics,…
Positional encodings enable Transformers to incorporate sequential information, yet their theoretical understanding remains limited to two properties: distance attenuation and translation invariance. Because natural language lacks purely…
Cognitive maps are a proposed concept on how the brain efficiently organizes memories and retrieves context out of them. The entorhinal-hippocampal complex is heavily involved in episodic and relational memory processing, as well as spatial…
Effects of feedbacks on self-organization phenomena in networks of diffusively coupled bistable elements are investigated. For regular trees, an approximate analytical theory for localized stationary patterns under application of global…
The success of style-based generators largely benefits from style modulation, which helps take care of the cross-instance variation within data. However, the instance-wise stochasticity is typically introduced via regular convolution, where…