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Neural networks have shown to be extremely effective tools for machine learning in broad contexts, including natural language processing, image processing, and adversarial game playing such as Chess and Go. Despite their success in a wide variety of contexts, the design of a neural network (which is inescapably tied to its performance) is often a matter of iterated re-engineering to find an architecture that performs the best on a small set of predetermined metrics. As such, this leaves the parsimony of such systems vague at best.

Over the past few years it has become apparent that the mathematics of topology can be used to understand some theoretical fundamentals of neural networks. Roughly speaking, topology is the field of math that studies spaces that are considered to be ``the same&#39;&#39; up to a continuous stretching (i.e., homeomorphism). For that reason it is known as ``rubber sheet geometry.&#39;&#39; The main reason that topology has provided tools to study neural networks is that a deep neural network can be thought of as an iterated sequence of continuous transformations between spaces.

In this work we develop an algorithm for automatically generating a trainable deep neural network with information obtained from the geometric and topological properties of training data. Our approach first finds a dense ellipsoidal covering of the training data set that is consistent with the classification information. We then find an (approximately) minimum sub-cover that models the classification information. A neural network is constructed that approximates the structure of the minimum sub-cover and which encodes logical statements representative of the data geometry. We show empirically that after training, the neural network retains the imprinted geometric information, making each module in the neural network geometrically interpretable. Theoretical and experimental results provide information on this approach across a variety of data sets. In addition to this we show how the proposed approach, when combined with methods from topological data analysis (specifically homology), can be used to quantify the likelihood that any neural network classifier will perform well on a given binary classifier data set before neural network engineering takes place. All results are illustrated using multiple data sets.

NAML 2021

Topological Data Analysis Methods for Data Set Characterization to Augment Machine Learning Methods

topological data analysis

neural network

Naval Information Warfare Center Pacific is partnering with AFCEA San Diego chapter to host the workshop.

The NAML workshop is an opportunity for researchers from Navy research and development centers and our partner organizations to exchange technical ideas and to come together as a team.

The goals of NAML are:

* To spread awareness of current machine learning research relevant to Naval applications

* To connect machine learning researchers with experts in military requirements

* To build and strengthen collaborations within the defense research community

**Watch this video to hear about the AFCEA purpose.**

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Neural networks have shown to be extremely effective tools for machine learning in broad contexts, including natural language processing, image processing, and adversarial game playing such as Chess and Go. Despite their success in a wide variety of contexts, the design of a neural network (which is inescapably tied to its performance) is often a matter of iterated re-engineering to find an architecture that performs the best on a small set of predetermined metrics. As such, this leaves the parsimony of such systems vague at best.

Over the past few years it has become apparent that the mathematics of topology can be used to understand some theoretical fundamentals of neural networks. Roughly speaking, topology is the field of math that studies spaces that are considered to be ``the same'' up to a continuous stretching (i.e., homeomorphism). For that reason it is known as ``rubber sheet geometry.'' The main reason that topology has provided tools to study neural networks is that a deep neural network can be thought of as an iterated sequence of continuous transformations between spaces.

In this work we develop an algorithm for automatically generating a trainable deep neural network with information obtained from the geometric and topological properties of training data. Our approach first finds a dense ellipsoidal covering of the training data set that is consistent with the classification information. We then find an (approximately) minimum sub-cover that models the classification information. A neural network is constructed that approximates the structure of the minimum sub-cover and which encodes logical statements representative of the data geometry. We show empirically that after training, the neural network retains the imprinted geometric information, making each module in the neural network geometrically interpretable. Theoretical and experimental results provide information on this approach across a variety of data sets. In addition to this we show how the proposed approach, when combined with methods from topological data analysis (specifically homology), can be used to quantify the likelihood that any neural network classifier will perform well on a given binary classifier data set before neural network engineering takes place. All results are illustrated using multiple data sets.

technical paper

Many of the recent practical successes of artificial intelligence have been due to progress in machine learning, and in deep learning with neural networks in particular. However, such methods must be trained on large data sets, which may not be available for
all domains, and the resulting networks function as "black box" systems, without the capability to explain their conclusions. The lack of explainability impedes their safe application to some of the very domains that could most benefit from AI, including military,
intelligence, security, medical, and legal applications where decisions must be justified and the consequences of failure are too great. We are developing methods for combining deep learning's extremely powerful ability to find patterns in data with more traditional
AI techniques for representing and reasoning about knowledge to yield new techniques that combine the strengths of both. In particular, we believe that the knowledge-based machine learning approach case-based reasoning (CBR) is an ideal complementary partner
for deep learning. Case-based reasoning solves problems by retrieving and adapting cases encoding the solutions to prior similar problems. The CBR process leverages analogical reasoning with knowledge about similarity and about how to adapt solutions to new
circumstances, to enable reasoning from small data sets. CBR can exploit the intelligibility of cases to provide explanations in a form compelling to humans. We are investigating tight couplings of deep machine learning with case-based reasoning in order to
take advantage of the complementary strengths of these two approaches. Ongoing projects include hybrid approaches in which cases provide a human-intelligible vehicle for capturing and explaining decisions, while network learning methods support the CBR process
by generating similarity and case adaptation knowledge. This material is based upon work supported in part by the Department of the Navy, Office of Naval Research under award number N00014-19-1-2655.

Combining Deep Learning and Case-based Reasoning for Robust, Accurate, Explainable Systems


Adversarial attacks have demonstrated the ability to change image classification labels with minimal alterations to the input image across a wide variety of Deep Neural Network (DNN) algorithms. Specifically the Fast Gradient Attack (FGA) [2] method has been shown to change a model’s output classification label with minimal visual alterations. Goodfellow et. al. [1] conjectured that this may be due to the high dimensional nature of the input data, as well as the linearity of the Deep Learning (DL) algorithms. Our study investigates the efficacy of one mitigation strategy (attack defense), centered on a simple preprocessing method (median de-noising) on input images. The median filter is employed on images input into ResNet models of varying depth, which have been pre-trained on the CIFAR10 dataset. It is hypothesized that by employing this preprocessing mitigation technique to adversarial attacked images, the impact of the FGA method [1] can be reduced. This study is designed to test if de-noising an input image can mitigate adversarial attack effectiveness. Additionally, the median filter removes some information contained within the dataset. Therefore, we seek to characterize and quantify the robustness of the ResNet models with this transformation technique. This research provides insight into the nature of the FGA adversarial attack vector, a simple attack mitigation strategy, as well as the robustness of the Deep Learning models being studied.

[1] I. J. Goodfellow, J. Shlens and C. Szegedy, Explaining and Harnessing Adversarial Examples, arXiv e-prints, p. 1412.6572 December 2014
[2] Nicolae, Maria-Irina and Sinn, Mathieu and Tran, Minh Ngoc and Buesser, Beat and Rawat, Ambrish and Wistuba, Martin and Zantedeschi, Valentina and Baracaldo, Nathalie and Chen, Bryant and Ludwig, Heiko and Molloy, Ian and Edwards, Ben, Adversarial Robustness Toolbox v1.2.0 CoRR 1807.01069 https://arxiv.org/pdf/1807.01069 2018

Adversarial Attack Mitigation Techniques

Many real-world datasets are examples of a fortunate contradiction: they are at once high-dimensional, generated by intricate and complex physics, but at the same time low-dimensional, driven by only a small set of dominant phenomena. As an example, consider the flow of a fluid past a two-dimensional cylinder at low Reynolds number. This is a relatively simple flow that is used as a standard example in computational fluid dynamics, yet accurate simulations require millions of degrees of freedom. At the same time, it is well known that the resulting data can often be compressed into ten or fewer modal coefficients with less than 1% information loss. The sparse sensor placement optimization for classification (SSPOC) algorithm leverages this characteristic to distill high-dimensional datasets down to small feature sets that are especially relevant for answering specified classification questions. SSPOC works by first projecting a full dataset onto a truncated principal component analysis (PCA) subspace, then training a simple classification model using linear discriminant analysis (LDA), and then selecting features based on a sparsification of the LDA discriminant. The algorithm has proven effective in numerous fields, including image recognition, facial recognition, fluid flow classification, and cancer classification, among others.

Here we present a new extension of the SSPOC algorithm that is applicable to vector-valued data, enabling a number of new applications. First, we apply vector SSPOC to multi-channel data, demonstrating its benefits in situations where the cost deploying a sensor platform is much higher than the cost of placing sensors on that platform, as can be the case on ocean buoys. Next, we perform an image recognition task using image patches instead of individual pixels. Vector SSPOC is able to identify informative image regions with less noise and more confidence than standard/scalar SSPOC. Finally, we apply vector SSPOC to the simulated response of a vibrating plate, in order to distinguish between two possible forcing locations; this is a simple model for noise source localization on Navy vessels. Typically described as complex numbers, we encode the response data as a vector-valued signal using a real-composite representation. As a result, we are able to achieve high classification accuracy using only a handful of sensors.


Sparse sensor placement optimization for classification (SSPOC) for vector-valued data

Dictionary learning is a prototypical machine learning problem with broad applications throughout computer vision and signal processing. Given a set of training data, the goal is to learn a dictionary of prototype patterns that provide a sparse (parsimonious) representation of the data. Such a dictionary then enables a variety of problems to be solved by exploiting sparse structure; example problems include noise removal, super-resolution, deblurring, imputing missing data, and classification. Like many problems in machine learning, dictionary learning can be formulated as an optimization problem. Unfortunately, this optimization problem is non-convex, making it potentially difficult to solve to global optimality. Additional questions arise in how to deal with multi-modal data and distributed data, such as might be collected by multiple satellites, UAVs, etc. This presentation will summarize our team’s research on theory and algorithms for solving non-convex matrix-valued optimization problems such as dictionary learning, particularly in multi-modal, distributed, and streaming contexts. We welcome the opportunity to discuss further transitioning this technology for Naval applications.

Fast Communication-efficient Algorithms for Distributed and Multi-modal Dictionary Learning

The arithmetic logic units in neuromorphic accelerators for the edge are moving from 32-bit precision to ultra-low (<8bits) to leverage resource and energy efficiency. Conventional data formats, like fixed-point representation and the floating pointdata format deteriorates the performance of deep neural networks(DNN) at low-precision. One solution to mitigate the accuracyreduction is to fit the distribution of the representable numbers to the distribution of the DNN parameters. Recent findings showthat general posit has similar distribution and dynamic range as the weight and activation values across the deep neural networklayers. In this study, we design an ASIC softcore for the general posit MAC operations and, analyze the energy dissipation andmemory utilization of DNNs incorporating posits on accelerators for different benchmarks. We demonstrate the advantage ofthe proposed numerical format by comparing it to the existing fixed-point and floating point formats. The general posit offerssignificant improvement in accuracy over fixed-point and floating-point formats with minimal energy dissipation.

Neuromorphic Accelerators with Low-PrecisionGeneral Posit for the Edge

Pursuit-evasion games have been studied for decades under perfect information and analytically-derived policies for static environments. Here, we incorporate uncertainty in a target’s position via simulated measurements and propose a continuous deep reinforcement learning (RL) approach to support pursuit of a speed-advantaged target. An OpenAI gym environment was created for simulating pursuit game play. A Kalman filter was implemented for simulating data fusion of uncertainties associated with imperfect range and bearing measurements from the pursuer to the target. An actor-critic based, model-free, deep discrete policy gradient (DDPG) method was implemented for incrementally training an agent to compete at a speed-overmatched pursuit game. The resulting RL policy was tested under many scenarios and performance exceeded that of a baseline course-aligned strategy. Emerging reinforcement learning success strategies were analyzed and manually abstracted into grouped behaviors. An online decision-making framework is discussed for leveraging conditional past performance to predict future performance.

Reinforcement Learning Approach to Speed-Overmatched Maritime Targets with Uncertain Information

The Emulation Ground Vehicle (EGV) is a robotic wheeled vehicle designed and manufactured in-house at NAWCAD Lakehurst to be used as an aircraft-representative interface for testing deck handling control systems at Lakehurst’s Advanced Deck Handling Technology Evaluation Center (ADHaTEC). The EGV utilizes dynamic models of existing aircraft along with Model Reference Adaptive Control (MRAC), an adaptive machine learning strategy, to closely emulate the taxiing dynamics of those aircraft. Its size is comparable to that of shipboard aircraft, and it is equipped with functions possessed by those craft on the flight deck, such as wing folding, launch bar actuation, and tail hook actuation. Integration with the Robot Operating System (ROS) streamlines the capability of the EGV to function as a testbed for any kind of taxiing control method for both teleoperation and autonomous navigation, including methods based on machine learning strategies. Successful full scale tests of the vehicle have been performed, clearing a path for future work utilizing the platform. Plans include implementing a Fuzzy Adaptive Resonance Theory (FuzzyART) neural network-based gesture recognition control system that has already been tested on smaller robotic vehicles. Going forward, the EGV could be used to evaluate various machine learning-based control methods for aircraft operating in the shipboard environment before those methods transition to fleet use.

Emulation Ground Vehicle (EGV)

SeeByte US has been supporting the MK 18 program, integrating the commercial collaborative autonomy. SeeByte US has also been partnering with small businesses as an SBIR subcontractor, mainly to increase the level of autonomy of the Original Equipment Manufacturers (OEMS). This talk will give an overview of the levels of autonomy and how advanced sensor processing is applied to increase the capability of Unmanned Underwater Vehicles (UUVs) and Remote Operated Vehicles (ROVs). There are three Naval application examples that will be discussed. The first will be a real-world demonstration using MK 18 Mod2 UUVs for Mine Counter Measure (MCM). The second is a simulation of feature-based navigation and the third is a discussion on using small class ROVs for Explosive Ordinance Disposal (EOD) intervention tasks. The talk concludes on what is needed to help advanced sensor processing algorithms using Machine Learning, Artificial Intelligence and Computer Vision to increase levels of autonomy.

Increasing Levels of Autonomy Through Advanced Sensor Processing

The Marine Corps Tactical Systems Support Activity (MCTSSA) Advanced Concepts Cell (AC2) collaborated with Booz Allen to deliver one of the first successful artificial intelligence (AI) projects developed by the command. The project, Digital Fortress, employs computer vision (CV) at the edge to enhance force protection efforts at the MCTSSA compound. Live full-motion video feeds from cameras placed at the entry control point of the front gate fed computer vision algorithms that not only detected vehicles and pedestrians, but further classified vehicle type, color, and captured license plate information for purposes of identifying vehicles of interest. Results from the algorithms were stored in a data log of incoming and outgoing traffic that could be queried directly by the end user and/or used for real-time alerts in emergency situations. The data was displayed in a dashboard for easy and accessible interaction by the end user. 

During the development of Digital Fortress, data scientists on the project explored both custom and opensource off-the-shelf solutions. In this presentation, the team will discuss the software and network architectures of Digital Fortress, as well as the data science pipeline developed to perform inference at the edge.

Digital Fortress: Enhanced Force Protection through Computer Vision at the Edge

State of the art techniques for learning predictive models from naturally occurring data are plagued by the fundamental problem of shortcut learning – often thought of as overfitting in classical machine learning settings. One of these ways is the now infamous adversarial example to a deep image classifier – an imperceptible perturbation (highly correlated with an incorrect label) of the input that drastically reduces the model’s accuracy (Szegedy et al., 2013). A plethora of mitigation strategies have been proposed, the most effective of which rely on adversarial training: teaching the model to be invariant to these kinds of spurious signals by exposing it to adversarial examples themselves during training (Madry et al., 2017).In this talk, we demonstrate that although state-of-the-art adversarial training techniques mitigate spurious correlations that are based on noise, adversarial training does not mitigate more semantically meaningful shortcuts. For example, we show that a model defended with adversarial training will associate the “balance beam” label with the presence of a gymnast in the ImageNet dataset, even though a human would not make that same association to assist in classifying an image as a balance beam. We show the presence of this spurious correlation in the trained model by constructing a series of adversarial examples which are both recognizable to a human, in that adversarial example targeting the stingray class resemble images of stingrays also containing a recognizable snorkeler, demonstrating a semantically incorrect association between the class and the learned features. Using examples like these, we then argue that adversarial training does not solve the core shortcut learning problem -- rather the problem persists at a higher semantic level. 

This finding is important to the Navy: if adversarial training causes models to infer semantically meaningful spurious correlations, and these correlations reveal critical information about the method by which the data was collected, then adversarial training will violate policies related to data security. To this end, we provide proof of concept tools for examining the shortcuts taken by models defended with adversarial training. 

References:
Szegedy, C., Zaremba, W., Sutskever, I., Bruna, J., Erhan, D., Goodfellow, I., & Fergus, R. (2013). Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199.

Madry, A., Makelov, A., Schmidt, L., Tsipras, D., & Vladu, A. (2017). Towards deep learning models resistant to adversarial attacks. arXiv preprint arXiv:1706.06083.

Deng, J., Dong, W., Socher, R., Li, L. J., Li, K., & Fei-Fei, L. (2009, June). Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition (pp. 248-255). Ieee.

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Topological Data Analysis Methods for Data Set Characterization to Augment Machine Learning Methods

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