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Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
With multiple outcomes in empirical research, a common strategy is to define a composite outcome as a weighted average of the original outcomes. However, the choices of weights are often subjective and can be controversial. We propose an…
A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just…
In reversible computations one is interested in the development of mechanisms allowing to undo the effects of executed actions. The past research has been concerned mainly with reversing single actions. In this paper, we consider the…
<Q>_e is the effective list of all finite predicate logic programs. <T_e> is the list of recursive trees. We modify constructions of Marek, Nerode, and Remmel [25] to construct recursive functions f and g such that for all indices e, (i)…
Reversible computing is a new paradigm that has emerged recently and extends the traditional forwards-only computing mode with the ability to execute in backwards, so that computation can run in reverse as easily as in forward. Two…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
Petri nets are a mathematical language for modeling and reasoning about distributed systems. In this paper we propose an approach to Petri nets for embedding reversibility, i.e., the ability of reversing an executed sequence of operations…
Reversing a (forward) computation history means undoing the history. In concurrent systems, undoing the history is not performed in a deterministic way but in a causally consistent fashion, where states that are reached during a backward…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking…
We study the logical content of several maximality principles related to the finite intersection principle ($F\IP$) in set theory. Classically, these are all equivalent to the axiom of choice, but in the context of reverse mathematics their…
Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
Retrosynthesis is the task of planning a series of chemical reactions to create a desired molecule from simpler, buyable molecules. While previous works have proposed algorithms to find optimal solutions for a range of metrics (e.g.…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade's theorem is determined. The results are illustrated by an…
Reversible CCS (RCCS) is a well-established, formal model for reversible communicating systems, which has been built on top of the classical Calculus of Communicating Systems (CCS). In its original formulation, each CCS process is equipped…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…