Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.
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Weak supervision searches have in principle the advantages of both being able to train on experimental data and being able to learn distinctive signal properties. However, the practical applicability of such searches is limited by the fact that successfully training a neural network via weak supervision can require a large amount of signal. In this work, we seek to create neural networks that can learn from less experimental signal by using transfer and meta-learning. The general idea is to first train a neural network on simulations, thereby learning concepts that can be reused or becoming a more efficient learner. The neural network would then be trained on experimental data and should require less signal because of its previous training. We find that transfer and meta-learning can substantially improve the performance of weak supervision searches.
Selecting an evaluation metric is fundamental to model development, but uncertainty remains about when certain metrics are preferable and why. This paper introduces the concept of resolving power to describe the ability of an evaluation metric to distinguish between binary classifiers of similar quality. This ability depends on two attributes: 1. The metric's response to improvements in classifier quality (its signal), and 2. The metric's sampling variability (its noise). The paper defines resolving power generically as a metric's sampling uncertainty scaled by its signal. The primary application of resolving power is to assess threshold-free evaluation metrics, such as the area under the receiver operating characteristic curve (AUROC) and the area under the precision-recall curve (AUPRC). A simulation study compares the AUROC and the AUPRC in a variety of contexts. It finds that the AUROC generally has greater resolving power, but that the AUPRC is better when searching among high-quality classifiers applied to low prevalence outcomes. The paper concludes by proposing an empirical method to estimate resolving power that can be applied to any dataset and any initial classification model.
Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this contribution, we provide a rigorous justification of these approaches for a two-layers neural network model called the committee machine. We also introduce a version of the approximate message passing (AMP) algorithm for the committee machine that allows to perform optimal learning in polynomial time for a large set of parameters. We find that there are regimes in which a low generalization error is information-theoretically achievable while the AMP algorithm fails to deliver it, strongly suggesting that no efficient algorithm exists for those cases, and unveiling a large computational gap.
Although metaheuristics have been widely recognized as efficient techniques to solve real-world optimization problems, implementing them from scratch remains difficult for domain-specific experts without programming skills. In this scenario, metaheuristic optimization frameworks are a practical alternative as they provide a variety of algorithms composed of customized elements, as well as experimental support. Recently, many engineering problems require to optimize multiple or even many objectives, increasing the interest in appropriate metaheuristic algorithms and frameworks that might integrate new specific requirements while maintaining the generality and reusability principles they were conceived for. Based on this idea, this paper introduces JCLEC-MO, a Java framework for both multi- and many-objective optimization that enables engineers to apply, or adapt, a great number of multi-objective algorithms with little coding effort. A case study is developed and explained to show how JCLEC-MO can be used to address many-objective engineering problems, often requiring the inclusion of domain-specific elements, and to analyze experimental outcomes by means of conveniently connected R utilities.
The approach to analysing compositional data has been dominated by the use of logratio transformations, to ensure exact subcompositional coherence and, in some situations, exact isometry as well. A problem with this approach is that data zeros, found in most applications, have to be replaced to allow the logarithmic transformation. An alternative new approach, called the `chiPower' transformation, which allows data zeros, is to combine the standardization inherent in the chi-square distance in correspondence analysis, with the essential elements of the Box-Cox power transformation. The chiPower transformation is justified because it} defines between-sample distances that tend to logratio distances for strictly positive data as the power parameter tends to zero, and are then equivalent to transforming to logratios. For data with zeros, a value of the power can be identified that brings the chiPower transformation as close as possible to a logratio transformation, without having to substitute the zeros. Especially in the area of high-dimensional data, this alternative approach can present such a high level of coherence and isometry as to be a valid approach to the analysis of compositional data. Furthermore, in a supervised learning context, if the compositional variables serve as predictors of a response in a modelling framework, for example generalized linear models, then the power can be used as a tuning parameter in optimizing the accuracy of prediction through cross-validation. The chiPower-transformed variables have a straightforward interpretation, since they are each identified with single compositional parts, not ratios.
Fully decentralized learning is gaining momentum for training AI models at the Internet's edge, addressing infrastructure challenges and privacy concerns. In a decentralized machine learning system, data is distributed across multiple nodes, with each node training a local model based on its respective dataset. The local models are then shared and combined to form a global model capable of making accurate predictions on new data. Our exploration focuses on how different types of network structures influence the spreading of knowledge - the process by which nodes incorporate insights gained from learning patterns in data available on other nodes across the network. Specifically, this study investigates the intricate interplay between network structure and learning performance using three network topologies and six data distribution methods. These methods consider different vertex properties, including degree centrality, betweenness centrality, and clustering coefficient, along with whether nodes exhibit high or low values of these metrics. Our findings underscore the significance of global centrality metrics (degree, betweenness) in correlating with learning performance, while local clustering proves less predictive. We highlight the challenges in transferring knowledge from peripheral to central nodes, attributed to a dilution effect during model aggregation. Additionally, we observe that central nodes exert a pull effect, facilitating the spread of knowledge. In examining degree distribution, hubs in Barabasi-Albert networks positively impact learning for central nodes but exacerbate dilution when knowledge originates from peripheral nodes. Finally, we demonstrate the formidable challenge of knowledge circulation outside of segregated communities.
A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method to model weak discontinuities using nonconforming finite-element meshes. The essence of LET is in treating the elements that are cut by an interface as simple laminates of the two phases, and this idea is here extended to propagating interfaces so that the volume fraction of the phases and the lamination orientation vary accordingly. In the proposed LET-PF approach, the phase-field variable (order parameter), which is governed by an evolution equation of the Ginzburg-Landau type, plays the role of a level-set function that implicitly defines the position of the (sharp) interface. The mechanical equilibrium subproblem is then solved using the semisharp LET technique. Performance of LET-PF is illustrated by numerical examples. In particular, it is shown that, for the problems studied, LET-PF exhibits higher accuracy than the conventional phase-field method so that, for instance, qualitatively correct results can be obtained using a significantly coarser mesh, and thus at a lower computational cost.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.
Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.
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