The Convolution Exponential and Generalized Sylvester Flows

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood

MICK: A Meta-Learning Framework for Few-shot Relation Classification with Small Training Data

Few-shot relation classification seeks to classify incoming query instances after meeting only few support instances. This ability is gained by training with large amount of in-domain annotated data. In this paper, we tackle an even harder problem by further limiting the amount of data available at training time. We propose a few-shot learning framework for relation classification, which is particularly powerful when the training data is very small. In this framework, models not only strive to classify query instances, but also seek underlying knowledge about the support instances to obtain better instance representations. The framework also includes a method for aggregating cross-domain knowledge into models by open-source task enrichment. Additionally, we construct a brand new dataset: the TinyRel-CM dataset, a few-shot relation classification dataset in health domain with purposely small training data and challenging relation classes. Experimental results demonstrate that our framework brings performance gains for most underlying classification models, outperforms the state-of-the-art results given small training data, and achieves competitive results with sufficiently large training data

Equivariant Diffusion for Molecule Generation in 3D

This work introduces a diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Our E(3) Equivariant Diffusion Model (EDM) learns to denoise a diffusion process with an equivariant network that jointly operates on both continuous (atom coordinates) and categorical features (atom types). In addition, we provide a probabilistic analysis which admits likelihood computation of molecules using our model. Experimentally, the proposed method significantly outperforms previous 3D molecular generative methods regarding the quality of generated samples and efficiency at training time

Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics

Coarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several small- to medium-sized protein simulations, reproducing the CG equilibrium distribution, and preserving dynamics of all-atom simulations such as protein folding events

E(n) Equivariant Normalizing Flows

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D

Contribution of natural and economic capital to subjective well-being: Empirical evidence from a small-scale society in Kodagu (Karnataka), India

Subjective well-being is determined by several types of sources of satisfaction, defined as forms of capitals. Most of research has been focused on the links between economic capital and well-being, neglecting the contribution of other forms of capital as source of satisfaction. Here, we bring natural capital into the equation and explore the relations between economic and natural capital and subjective well-being. We approach well-being as a multidimensional concept and then focus on three of its dimensions: subsistence, security, and reproduction and care. Working with tribal communities from Kodagu (Karnataka, India), we found positive associations between economic and natural capital and subjective well-being. Nevertheless, the two types of capitals differed on their relative contribution to (a) overall subjective well-being and (b) the three selected dimensions. Natural capital can be more important than economic capital in fulfilling human well-being. Findings support ongoing calls for explicitly incorporating ecological assets and ecosystem services in the design of policies oriented to measure and improve well-being