Some of the most successful knowledge graph embedding (KGE) models for link prediction - CP, RESCAL, TUCKER, COMPLEX - can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits - constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design.

Although very successfully used in conventional machine learning, convolution based neural network architectures - believed to be inconsistent in function space - have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a computer. We prove a universality theorem to show that CNOs can approximate operators arising in PDEs to desired accuracy. CNOs are tested on a novel suite of benchmarks, encompassing a diverse set of PDEs with possibly multi-scale solutions and are observed to significantly outperform baselines, paving the way for an alternative framework for robust and accurate operator learning.

Robust inference for non-linear regression models from the tsallis score:812 Application to coronavirus disease 2019 contagion in italy.

Preparing training data for deep vision models is a labor-intensive task. To address this, generative models have emerged as an effective solution for generating synthetic data. While current generative models produce image-level category labels, we propose a novel method for generating pixel-level semantic segmentation labels using the text-to-image generative model Stable Diffusion (SD). By utilizing the text prompts, cross-attention, and self-attention of SD, we introduce three new techniques: class-prompt appending, class-prompt cross-attention, and self-attention exponentiation. These techniques enable us to generate segmentation maps corresponding to synthetic images. These maps serve as pseudo-labels for training semantic segmenters, eliminating the need for labor-intensive pixel-wise annotation. To account for the imperfections in our pseudo-labels, we incorporate uncertainty regions into the segmentation, allowing us to disregard loss from those regions. We conduct evaluations on two datasets, PASCALVOC and MSCOCO, and our approach significantly outperforms concurrent work.