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T. Nathan Mundhenk, Mikel Landajuela, Ruben Glatt, Claudio P. Santiago, Daniel M. Faissol, Brenden K. Petersen

Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem include neural-guided search (e.g. using reinforcement learning) and genetic programming. In this work, we introduce a hybrid neural-guided/genetic programming approach to symbolic regression and other combinatorial optimization problems. We propose a neural-guided component used to seed the starting population of a random restart genetic programming component, gradually learning better starting populations. On a number of common benchmark tasks to recover underlying expressions from a dataset, our method recovers 65% more expressions than a recently published top-performing model using the same experimental setup. We demonstrate that running many genetic programming generations without interdependence on the neural-guided component performs better for symbolic regression than alternative formulations where the two are more strongly coupled. Finally, we introduce a new set of 22 symbolic regression benchmark problems with increased difficulty over existing benchmarks. Source code is provided at www.github.com/brendenpetersen/deep-symbolic-optimization.

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We recently developed a deep learning method that can determine the critical peak stress of a material by looking at scanning electron microscope (SEM) images of the material's crystals. However, it has been somewhat unclear what kind of image features the network is keying off of when it makes its prediction. It is common in computer vision to employ an explainable AI saliency map to tell one what parts of an image are important to the network's decision. One can usually deduce the important features by looking at these salient locations. However, SEM images of crystals are more abstract to the human observer than natural image photographs. As a result, it is not easy to tell what features are important at the locations which are most salient. To solve this, we developed a method that helps us map features from important locations in SEM images to non-abstract textures that are easier to interpret.

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Mikel Landajuela Larma, Brenden K. Petersen, Soo K. Kim, Claudio P. Santiago, Ruben Glatt, T. Nathan Mundhenk, Jacob F. Pettit, Daniel M. Faissol

Many machine learning strategies designed to automate mathematical tasks leverage neural networks to search large combinatorial spaces of mathematical symbols. In contrast to traditional evolutionary approaches, using a neural network at the core of the search allows learning higher-level symbolic patterns, providing an informed direction to guide the search. When no labeled data is available, such networks can still be trained using reinforcement learning. However, we demonstrate that this approach can suffer from an early commitment phenomenon and from initialization bias, both of which limit exploration. We present two exploration methods to tackle these issues, building upon ideas of entropy regularization and distribution initialization. We show that these techniques can improve the performance, increase sample efficiency, and lower the complexity of solutions for the task of symbolic regression.

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We describe an explainable AI saliency map method for use with deep convolutional neural networks (CNN) that is much more efficient than popular gradient methods. It is also quantitatively similar and better in accuracy. Our technique works by measuring information at the end of each network scale which is then combined into a single saliency map. We describe how saliency measures can be made more efficient by exploiting Saliency Map Order Equivalence. Finally, we visualize individual scale/layer contributions by using a Layer Ordered Visualization of Information. This provides an interesting comparison of scale information contributions within the network not provided by other saliency map methods. Since our method only requires a single forward pass through a few of the layers in a network, it is at least 97x faster than Guided Backprop and much more accurate. Using our method instead of Guided Backprop, class activation methods such as Grad-CAM, Grad-CAM++ and Smooth Grad-CAM++ will run several orders of magnitude faster, have a significantly smaller memory footprint and be more accurate. This will make such methods feasible on resource limited platforms such as robots, cell phones and low cost industrial devices. This will also significantly help them work in extremely data intensive applications such as satellite image processing. All without sacrificing accuracy. Our method is generally straight forward and should be applicable to the most commonly used CNNs. We also show examples of our method used to enhance Grad-CAM++.

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We develop a set of methods to improve on the results of self-supervised learning using context. We start with a baseline of patch based arrangement context learning and go from there. Our methods address some overt problems such as chromatic aberration as well as other potential problems such as spatial skew and mid-level feature neglect. We prevent problems with testing generalization on common self-supervised benchmark tests by using different datasets during our development. The results of our methods combined yield top scores on all standard self-supervised benchmarks, including classification and detection on PASCAL VOC 2007, segmentation on PASCAL VOC 2012, and "linear tests" on the ImageNet and CSAIL Places datasets. We obtain an improvement over our baseline method of between 4.0 to 7.1 percentage points on transfer learning classification tests. We also show results on different standard network architectures to demonstrate generalization as well as portability. All data, models and programs are available at: https://gdo-datasci.llnl.gov/selfsupervised/.

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We have created a large diverse set of cars from overhead images, which are useful for training a deep learner to binary classify, detect and count them. The dataset and all related material will be made publically available. The set contains contextual matter to aid in identification of difficult targets. We demonstrate classification and detection on this dataset using a neural network we call ResCeption. This network combines residual learning with Inception-style layers and is used to count cars in one look. This is a new way to count objects rather than by localization or density estimation. It is fairly accurate, fast and easy to implement. Additionally, the counting method is not car or scene specific. It would be easy to train this method to count other kinds of objects and counting over new scenes requires no extra set up or assumptions about object locations.

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