Related papers: Coinductive Streams in Monoidal Categories
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…
Two apparently unrelated fields -- normalizing flows and causality -- have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of…
Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature…
The analysis of games played on graph-like structures is of increasing importance due to the prevalence of social networks, both virtual and physical, in our daily life. As well as being relevant in computer science, mathematical analysis…
Path calculus, or graphical linear algebra, is a string diagram calculus for the category of matrices over a base ring. It is the usual string diagram calculus for a symmetric monoidal category, where the monoidal product is the direct sum…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
In this paper, we introduce a generalized topological quantum field theory based on the symmetric monoidal category which we call causal network condensation since it can be regarded as a generalization of spin network construction of Baez,…
We discuss string diagrams for timed process theories -- represented by duoidally-graded symmetric strict monoidal categories -- built upon the string diagrams of pinwheel double categories.
We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor…
Dataflow matrix machines are a powerful generalization of recurrent neural networks. They work with multiple types of arbitrary linear streams, multiple types of powerful neurons, and allow to incorporate higher-order constructions. We…
We present a neural network approach to compute stream functions, which are scalar functions with gradients orthogonal to a given vector field. As a result, isosurfaces of the stream function extract stream surfaces, which can be visualized…
DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal…
Machine learning from data streams is an active and growing research area. Research on learning from streaming data typically makes strict assumptions linked to computational resource constraints, including requirements for stream mining…
Graphs are ubiquitous and ever-present data structures that have a wide range of applications involving social networks, knowledge bases and biological interactions. The evolution of a graph in such scenarios can yield important insights…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
We universally characterize the produoidal category of monoidal lenses over a monoidal category. In the same way that each category induces a cofree promonoidal category of spliced arrows, each monoidal category induces a cofree produoidal…
Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To…
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,…