Related papers: On the implementation of construction functions fo…

Database analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural…

Starting with an algorithm to turn lists into full trees which uses non-obvious invariants and partial functions, we progressively encode the invariants in the types of the data, removing most of the burden of a correctness proof. The…

Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code…

Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…

With the goal of facilitating team collaboration, we propose a new approach to building vector representations of individual developers by capturing their individual contribution style, or coding style. Such representations can find use in…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

Model sets (also called cut and project sets) are generalizations of lattices, and multi-component model sets are generalizations of lattices with colourings. In this paper, we study self-similarities of multi-component model sets. The main…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class,…

We introduce Conflict-Aware Replicated Data Types (CARDs). CARDs are significantly more expressive than Conflict-free Replicated Data Types (CRDTs) as they support operations that can conflict with each other. Introducing conflicting…

State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the…

We propose a data-driven algorithm for numerical invariant synthesis and verification. The algorithm is based on the ICE-DT schema for learning decision trees from samples of positive and negative states and implications corresponding to…

In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our…

We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…

A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…

Constructor theory is a meta-theoretic approach that seeks to characterise concrete theories of physics in terms of the (im)possibility to implement certain abstract "tasks" by means of physical processes. Process theory, on the other hand,…

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…

A good feature representation is a determinant factor to achieve high performance for many machine learning algorithms in terms of classification. This is especially true for techniques that do not build complex internal representations of…