Related papers: Categorical Comprehensions and Recursion
Guarded recursion is a framework allowing for a formalisation of streams in classical programming languages. The latter take their semantics in cartesian closed categories. However, some programming paradigms do not take their semantics in…
Conformal predictions make it possible to define reliable and robust learning algorithms. But they are essentially a method for evaluating whether an algorithm is good enough to be used in practice. To define a reliable learning framework…
A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$. It does this by taking examples $(a,f(a)) \in A\times B$, and…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
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…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in…
We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Classification is a well-studied machine learning task which concerns the assignment of instances to a set of outcomes. Classification models support the optimization of managerial decision-making across a variety of operational business…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…
A circular program contains a data structure whose definition is self-referential or recursive. The use of such a definition allows efficient functional programs to be written and can avoid repeated evaluations and the creation of…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context -- and for each type a set of terms of said type. This is the case for…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…