Related papers: Global generation of the direct images of relative…
We give effective bounds on the generation of pushforwards of log-pluricanonical bundles twisted by ample line bundles. This gives a partial answer to a conjecture proposed by Popa and Schnell. We prove two types of statements: first, more…
We introduce a simple but effective unsupervised method for generating realistic and diverse images. We train a class-conditional GAN model without using manually annotated class labels. Instead, our model is conditional on labels…
We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.
Image generation from a single image using generative adversarial networks is quite interesting due to the realism of generated images. However, recent approaches need improvement for such realistic and diverse image generation, when the…
In this paper, we study pushforwards of log pluricanonical bundles on projective log canonical pairs $(Y,\Delta)$ over the complex numbers, partially answering a Fujita-type conjecture due to Popa and Schnell in the log canonical setting.…
Despite increasing progress in development of methods for generating visual counterfactual explanations, especially with the recent rise of Denoising Diffusion Probabilistic Models, previous works consider them as an entirely local…
Let $X$ be a smooth projective variety over an algebraically closed field $\mathbb{K}$ with arbitrary characteristic. Suppose $L$ is an ample and globally generated line bundle. By Castelnuovo--Mumford regularity, we show that $K_X \otimes…
Counterfactuals can explain classification decisions of neural networks in a human interpretable way. We propose a simple but effective method to generate such counterfactuals. More specifically, we perform a suitable diffeomorphic…
We prove the finiteness of relative log pluricanonical representations in the complex analytic setting. As an application, we discuss the abundance conjecture for semi-log canonical pairs within this framework. Furthermore, we establish the…
Current developments in computer vision and deep learning allow to automatically generate hyper-realistic images, hardly distinguishable from real ones. In particular, human face generation achieved a stunning level of realism, opening new…
In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which…
We give a characterizations of toposes which admit a generating family of objects which are internally cardinal finite (i.e. Kuratowski finite and decidable) in terms of "topological" conditions. The central result is that, constructively,…
We show that deep generative neural networks, based on global topology optimization networks (GLOnets), can be configured to perform the multi-objective and categorical global optimization of photonic devices. A residual network scheme…
Suppose that $X$ is an integral scheme (quasi-)projective over a complete local ring of mixed characteristic. Using ideas of Takamatsu-Yoshikawa and Bhatt-Ma-et. al, we define a notion of a $+$-test ideal on $X$, including for divisors and…
Text-to-image generative models have enabled high-resolution image synthesis across different domains, but require users to specify the content they wish to generate. In this paper, we consider the inverse problem -- given a collection of…
Despite their high accuracies, modern complex image classifiers cannot be trusted for sensitive tasks due to their unknown decision-making process and potential biases. Counterfactual explanations are very effective in providing…
Generative models have recently received renewed attention as a result of adversarial learning. Generative adversarial networks consist of samples generation model and a discrimination model able to distinguish between genuine and synthetic…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
We demonstrate that discriminative models inherently contain powerful generative capabilities, challenging the fundamental distinction between discriminative and generative architectures. Our method, Direct Ascent Synthesis (DAS), reveals…
It was shown that in a group of bijections of an infinite set some families of subsets, related to the cardinality of some eigenspaces, are generating. Besides, we derived a criterion for generating by sets of this kind.