Related papers: Shape Preserving Tree Transducers
Transformer networks are the de facto standard architecture in natural language processing. To date, there are no theoretical analyses of the Transformer's ability to capture tree structures. We focus on the ability of Transformer networks…
We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect…
In this paper, we give a deterministic pushdown transducer and a normal sequence of digits compressed by it. This solves positively a question left open in a previous paper by V. Becher, P. A. Heiber and the first author.
Given an $\mathbb{N}$-weighted tree automaton, we give a decision procedure for exponential vs polynomial growth (with respect to the input size) in quadratic time, and an algorithm that computes the exact polynomial degree of growth in…
Suppose a map $\phi$ on the set of positive definite matrices satisfies $\det(A+B)=\det(\phi(A)+\phi(B))$. Then we have $${\rm tr}(AB^{-1}) = {\rm tr}(\phi(A){\phi(B)}^{-1}).$$ Through this viewpoint, we show that $\phi$ is of the form…
Given a conserved and traceless energy-momentum tensor and a conformal Killing vector, one obtains a conserved current. We generalise this construction to superconformal theories in three, four, five and six dimensions with various amounts…
The study of topological superconductivity is largely based on the analysis of simple mean-field models that do not conserve particle number. A major open question in the field is whether the remarkable properties of these mean-field models…
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…
An ultrametric preserving function $f$ is said to be strongly ultrametric preserving if ultrametrics $d$ and $f \circ d$ define the same topology on $X$ for each ultrametric space $(X,d)$. The set of all strongly ultrametric preserving…
Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of…
A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or gets extinct. The outcome naturally depends on the…
Transformers can generate predictions in two approaches: 1. auto-regressively by conditioning each sequence element on the previous ones, or 2. directly produce an output sequences in parallel. While research has mostly explored upon this…
We address a long-standing problem in colloid and nanoparticle science: particle shape selection in solution synthesis. Our main finding is that a proper balance of two processes, preferential attachment of transported monomers at the…
Many countries are currently challenged with the extensive integration of renewable energy sources, which necessitates vast capacity expansion measures. These measures in turn require comprehensive power flow studies, which are often…
The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can…
Functional transductions realized by two-way transducers (or, equally, by streaming transducers or MSO transductions) are the natural and standard notion of "regular" mappings from words to words. It was shown in 2013 that it is decidable…
Transformer-based encoder-decoder models produce a fused token-wise representation after every encoder layer. We investigate the effects of allowing the encoder to preserve and explore alternative hypotheses, combined at the end of the…
Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class $\mathscr{C}$ can be $\mathsf{FO}$-transduced from a class of bounded-height…
Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the…
The significance of stripes in certain high-temperature superconductors has been hotly debated for decades. Now a consensus is emerging that there may, in fact, be two networks of different stripes in which shape resonances play a key role…