We model the electron density in the topside of the ionosphere with an improved machine learning (ML) model and compare it to existing empirical models, specifically the International Reference Ionosphere (IRI) and the Empirical‐Canadian High Arctic Ionospheric Model (E‐CHAIM). In prior work, an artificial neural network (NN) was developed and trained on two solar cycles worth of Defense Meteorological Satellite Program data (113 satellite‐years), along with global drivers and indices to predict topside electron density. In this paper, we highlight improvements made to this NN, and present a detailed comparison of the new model to E‐CHAIM and IRI as a function of location, geomagnetic condition, time of year, and solar local time. We discuss precision and accuracy metrics to better understand model strengths and weaknesses. The updated neural network shows improved mid‐latitude performance with absolute errors lower than the IRI by 2.5 × 109to 2.5 × 1010e−/m3, modestly improved performance in disturbed geomagnetic conditions with absolute errors reduced by about 2.5 × 109 e−/m3at high Kp compared to the IRI, and high Kp percentage errors reduced by >50% when compared to E‐CHAIM.
Taxonomizing local versus global structure in neural network loss landscapes
Viewing neural network models in terms of their loss landscapes has a long history in the statistical mechanics approach to learning, and in recent years it has received attention within machine learning proper. Among other things, local metrics (such as the smoothness of the loss landscape) have been shown to correlate with global properties of the model (such as good generalization performance). Here, we perform a detailed empirical analysis of the loss landscape structure of thousands of neural network models, systematically varying learning tasks, model architectures, and/or quantity/quality of data. By considering a range of metrics that attempt to capture different aspects of the loss landscape, we demonstrate that the best test accuracy is obtained when: the loss landscape is globally well-connected; ensembles of trained models are more similar to each other; and models converge to locally smooth regions. We also show that globally poorly-connected landscapes can arise when models are small or when they are trained to lower quality data; and that, if the loss landscape is globally poorly-connected, then training to zero loss can actually lead to worse test accuracy. Our detailed empirical results shed light on phases of learning (and consequent double descent behavior), fundamental versus incidental determinants of good generalization, the role of load-like and temperature-like parameters in the learning process, different influences on the loss landscape from model and data, and the relationships between local and global metrics, all topics of recent interest.
more »
« less
- Award ID(s):
- 1703678
- NSF-PAR ID:
- 10327339
- Date Published:
- Journal Name:
- Advances in Neural Information Processing Systems 34 (NeurIPS 2021)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract -
Learning to optimize (L2O) has gained increasing popularity, which automates the design of optimizers by data-driven approaches. However, current L2O methods often suffer from poor generalization performance in at least two folds: (i) applying the L2O-learned optimizer to unseen optimizees, in terms of lowering their loss function values (optimizer generalization, or “generalizable learning of optimizers”); and (ii) the test performance of an optimizee (itself as a machine learning model), trained by the optimizer, in terms of the accuracy over unseen data (optimizee generalization, or “learning to generalize”). While the optimizer generalization has been recently studied, the optimizee generalization (or learning to generalize) has not been rigorously studied in the L2O context, which is the aim of this paper. We first theoretically establish an implicit connection between the local entropy and the Hessian, and hence unify their roles in the handcrafted design of generalizable optimizers as equivalent metrics of the landscape flatness of loss functions. We then propose to incorporate these two metrics as flatness-aware regularizers into the L2O framework in order to meta-train optimizers to learn to generalize, and theoretically show that such generalization ability can be learned during the L2O meta-training process and then transformed to the optimizee loss function. Extensive experiments consistently validate the effectiveness of our proposals with substantially improved generalization on multiple sophisticated L2O models and diverse optimizees.more » « less
-
While cross entropy (CE) is the most commonly used loss function to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empirical performance. Among them, which one is the best to use is still a mystery, because there seem to be multiple factors affecting the answer, such as properties of the dataset, the choice of network architecture, and so on. This paper studies the choice of loss function by examining the last-layer features of deep networks, drawing inspiration from a recent line work showing that the global optimal solution of CE and mean-square-error (MSE) losses exhibits a Neural Collapse phenomenon. That is, for sufficiently large networks trained until convergence, (i) all features of the same class collapse to the corresponding class mean and (ii) the means associated with different classes are in a configuration where their pairwise distances are all equal and maximized. We extend such results and show through global solution and landscape analyses that a broad family of loss functions including commonly used label smoothing (LS) and focal loss (FL) exhibits Neural Collapse. Hence, all relevant losses (i.e., CE, LS, FL, MSE) produce equivalent features on training data. In particular, based on the unconstrained feature model assumption, we provide either the global landscape analysis for LS loss or the local landscape analysis for FL loss and show that the (only!) global minimizers are neural collapse solutions, while all other critical points are strict saddles whose Hessian exhibit negative curvature directions either in the global scope for LS loss or in the local scope for FL loss near the optimal solution. The experiments further show that Neural Collapse features obtained from all relevant losses (i.e., CE, LS, FL, MSE) lead to largely identical performance on test data as well, provided that the network is sufficiently large and trained until convergence.more » « less
-
null (Ed.)Abstract As an important class of spiking neural networks (SNNs), recurrent spiking neural networks (RSNNs) possess great computational power and have been widely used for processing sequential data like audio and text. However, most RSNNs suffer from two problems. First, due to the lack of architectural guidance, random recurrent connectivity is often adopted, which does not guarantee good performance. Second, training of RSNNs is in general challenging, bottlenecking achievable model accuracy. To address these problems, we propose a new type of RSNN, skip-connected self-recurrent SNNs (ScSr-SNNs). Recurrence in ScSr-SNNs is introduced by adding self-recurrent connections to spiking neurons. The SNNs with self-recurrent connections can realize recurrent behaviors similar to those of more complex RSNNs, while the error gradients can be more straightforwardly calculated due to the mostly feedforward nature of the network. The network dynamics is enriched by skip connections between nonadjacent layers. Moreover, we propose a new backpropagation (BP) method, backpropagated intrinsic plasticity (BIP), to boost the performance of ScSr-SNNs further by training intrinsic model parameters. Unlike standard intrinsic plasticity rules that adjust the neuron's intrinsic parameters according to neuronal activity, the proposed BIP method optimizes intrinsic parameters based on the backpropagated error gradient of a well-defined global loss function in addition to synaptic weight training. Based on challenging speech, neuromorphic speech, and neuromorphic image data sets, the proposed ScSr-SNNs can boost performance by up to 2.85% compared with other types of RSNNs trained by state-of-the-art BP methods.more » « less
-
In the present paper, we introduce a new neural network-based tool for the prediction of formation energies of atomic structures based on elemental and structural features of Voronoi-tessellated materials. We provide a concise overview of the connection between the machine learning and the true material–property relationship, how to improve the generalization accuracy by reducing overfitting, how new data can be incorporated into the model to tune it to a specific material system, and preliminary results on using models to preform local structure relaxations. The present work resulted in three final models optimized for (1) highest test accuracy on the Open Quantum Materials Database (OQMD), (2) performance in the discovery of new materials, and (3) performance at a low computational cost. On a test set of 21,800 compounds randomly selected from OQMD, they achieve a mean absolute error (MAE) of 28, 40, and 42 meV/atom, respectively. The second model provides better predictions in a test case of interest not present in the OQMD, while the third reduces the computational cost by a factor of 8. We collect our results in a new open-source tool called SIPFENN (Structure-Informed Prediction of Formation Energy using Neural Networks). SIPFENN not only improves the accuracy beyond existing models but also ships in a ready-to-use form with pre-trained neural networks and a GUI interface. By virtue of this, it can be included in DFT calculations routines at nearly no cost.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
