Related papers: Mathematical Interpretation between Genotype and P…
A genetic algorithm is suitable for exploring large search spaces as it finds an approximate solution. Because of this advantage, genetic algorithm is effective in exploring vast and unknown space such as molecular search space. Though the…
For theoretical analyses there are two specifics distinguishing GP from many other areas of evolutionary computation. First, the variable size representations, in particular yielding a possible bloat (i.e. the growth of individuals with…
This paper explores the genotype-phenotype relationship. It outlines conditions under which the dependence of a quantitative trait on the genome might be predictable, based on measurement of a limited subset of genotypes. It uses the theory…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…
In this paper we suggest that, under suitable conditions, supervised learning can provide the basis to formulate at the microscopic level quantitative questions on the phenotype structure of multicellular organisms. The problem of…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
In the field of evolutionary robotics, choosing the correct encoding is very complicated, especially when robots evolve both behaviours and morphologies at the same time. With the objective of improving our understanding of the mapping…
Generative adversarial networks (GANs) learn a latent space whose samples can be mapped to real-world images. Such latent spaces are difficult to interpret. Some earlier supervised methods aim to create an interpretable latent space or…
We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…
The grand challenges in biology today are being shaped by powerful high-throughput technologies that have revealed the genomes of many organisms, global expression patterns of genes and detailed information about variation within…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…
Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. More precisely, is it possible to capture certain quantum idiosyncrasies within the symplectic…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…
In the present paper, we define the concept of a \( q \)-cosymplectic manifold, on which we study the Hamiltonian, gradient, local gradient, and \( q \)-evolution vector fields. Several Liouville--Arnold-type theorems and a \( q…