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Register a new userNeural Coarse-Graining: Extracting slowly-varying latent degrees of freedom with neural networks
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Martin Biehl
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to choose sub-sets of a problem which are most amenable to its abilities to focus on solving, while discarding distracting elements that interfere with its learning. To do this, the network first transforms the raw data into a higher-level categorical representation, and then trains a predictor from that new time series to its future. To prevent a trivial solution of mapping the signal to zero, we introduce a measure of non-triviality via a contrast between the prediction error of the learned model with a naive model of the overall signal statistics. The transform can learn to discard uninformative and unpredictable components of the signal in favor of the features which are both highly predictive and highly predictable. This creates a coarse-grained model of the time-series dynamics, focusing on predicting the slowly varying latent parameters which control the statistics of the time-series, rather than predicting the fast details directly. The result is a semi-supervised algorithm which is capable of extracting latent parameters, segmenting sections of time-series with differing statistics, and building a higher-level representation of the underlying dynamics from unlabeled data.
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Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proven that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features upon which to machine learn the force field. In the present contribution, we build upon the advance of Wang et al.and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learns their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems.
Unrolled neural networks emerged recently as an effective model for learning inverse maps appearing in image restoration tasks. However, their generalization risk (i.e., test mean-squared-error) and its link to network design and train sample size remains mysterious. Leveraging the Steins Unbiased Risk Estimator (SURE), this paper analyzes the generalization risk with its bias and variance components for recurrent unrolled networks. We particularly investigate the degrees-of-freedom (DOF) component of SURE, trace of the end-to-end network Jacobian, to quantify the prediction variance. We prove that DOF is well-approximated by the weighted textit{path sparsity} of the network under incoherence conditions on the trained weights. Empirically, we examine the SURE components as a function of train sample size for both recurrent and non-recurrent (with many more parameters) unrolled networks. Our key observations indicate that: 1) DOF increases with train sample size and converges to the generalization risk for both recurrent and non-recurrent schemes; 2) recurrent network converges significantly faster (with less train samples) compared with non-recurrent scheme, hence recurrence serves as a regularization for low sample size regimes.
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Planning for Autonomous Unmanned Ground Vehicles (AUGV) is still a challenge, especially in difficult, off-road, critical situations. Automatic planning can be used to reach mission objectives, to perform navigation or maneuvers. Most of the time, the problem consists in finding a path from a source to a destination, while satisfying some operational constraints. In a graph without negative cycles, the computation of the single-pair shortest path from a start node to an end node is solved in polynomial time. Additional constraints on the solution path can however make the problem harder to solve. This becomes the case when we need the path to pass through a few mandatory nodes without requiring a specific order of visit. The complexity grows exponentially with the number of mandatory nodes to visit. In this paper, we focus on shortest path search with mandatory nodes on a given connected graph. We propose a hybrid model that combines a constraint-based solver and a graph convolutional neural network to improve search performance. Promising results are obtained on realistic scenarios.
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