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Register a new userFast Neural Models for Symbolic Regression at Scale
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Added by
Rumen Dangovski
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Deep learning owes much of its success to the astonishing expressiveness of neural networks. However, this comes at the cost of complex, black-boxed models that extrapolate poorly beyond the domain of the training dataset, conflicting with goals of finding analytic expressions to describe science, engineering and real world data. Under the hypothesis that the hierarchical modularity of such laws can be captured by training a neural network, we introduce OccamNet, a neural network model that finds interpretable, compact, and sparse solutions for fitting data, `{a} la Occams razor. Our model defines a probability distribution over a non-differentiable function space. We introduce a two-step optimization method that samples functions and updates the weights with backpropagation based on cross-entropy matching in an evolutionary strategy: we train by biasing the probability mass toward better fitting solutions. OccamNet is able to fit a variety of symbolic laws including simple analytic functions, recursive programs, implicit functions, simple image classification, and can outperform noticeably state-of-the-art symbolic regression methods on real world regression datasets. Our method requires minimal memory footprint, does not require AI accelerators for efficient training, fits complicated functions in minutes of training on a single CPU, and demonstrates significant performance gains when scaled on a GPU. Our implementation, demonstrations and instructions for reproducing the experiments are available at https://github.com/druidowm/OccamNet_Public.
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Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved amazing levels of accuracy on image recognition and natural language processing tasks, but are often seen as black-box models that are difficult to interpret and typically extrapolate poorly. Here we use a neural network-based architecture for symbolic regression called the Equation Learner (EQL) network and integrate it with other deep learning architectures such that the whole system can be trained end-to-end through backpropagation. To demonstrate the power of such systems, we study their performance on several substantially different tasks. First, we show that the neural network can perform symbolic regression and learn the form of several functions. Next, we present an MNIST arithmetic task where a separate part of the neural network extracts the digits. Finally, we demonstrate prediction of dynamical systems where an unknown parameter is extracted through an encoder. We find that the EQL-based architecture can extrapolate quite well outside of the training data set compared to a standard neural network-based architecture, paving the way for deep learning to be applied in scientific exploration and discovery.
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute.
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