## Expedition at the GPU Technology Conference

/in Blog, Machine Learning, News /by Stephen JohnsonThis week the team at Expedition Technology had the opportunity to publicly discuss a couple of the compelling projects we are working here. At NVIDIA’s GPU Technology Conference in DC (GTC DC) we presented results on computer vision and on signal processing. The talks were:

- Object Detection and Tracking from Overhead Video with Deep Learning, by Ryan Crawford

- Machine Learning for Wireless Spectrum Awareness, by Enrico Mattei and Greg Harrison

Soon you will be able to watch the videos of these talks on NVIDIA’s site for the full experience and follow along with the slides above.

The projects outlined in these talks are great examples of the type of work we tackle here at EXP and are also representative of the state-of-the-art algorithms and results we are developing. If taking on these kinds of big ideas and building solutions to address them is the sort of thing you would love to be doing, drop us a line or check out our current job postings!

## Expedition Technology Ranks No. 489 on the 2018 Inc. 5000 With Three-Year Revenue Growth of 1,040 Percent

/in Awards, Blog, News /by Expedition Technology*Inc.*** Magazine Unveils Its 37th Annual List of ****America’s Fastest-Growing Private Companies—the Inc. 5000**

*Inc.*

**Expedition Technology ****Ranks No. 489 on the 2018 Inc. 5000**

**With Three-Year Revenue Growth of 1,040 ****Percent**

**NEW YORK, August 15, 2018** – *Inc.* magazine today revealed that Expedition Technology is No. 489 on its 37th annual Inc. 5000, the most prestigious ranking of the nation’s fastest-growing private companies. The list represents a unique look at the most successful companies within the American economy’s most dynamic segment—its independent small businesses. Microsoft, Dell, Domino’s Pizza, Pandora, Timberland, LinkedIn, Yelp, Zillow, and many other well-known names gained their first national exposure as honorees on the Inc. 5000.

“The more than tenfold increase in revenue growth over the last three years is the result of the dedicated drive of our employees and an array of incredibly supportive customers. We have worked hard to align our capabilities with some of the highest priority challenges facing our nation, and we anticipate this positioning will allow us to solve larger and more complex problems in the years to come,” says Marc Harlacher, President and CEO of Expedition Technology.

Not only have the companies on the 2018 Inc. 5000 (which are listed online at Inc.com, with the top 500 companies featured in the September issue of *Inc.*, available on newsstands August 15) been very competitive within their markets, but the list as a whole shows staggering growth compared with prior lists. The 2018 Inc. 5000 achieved an astounding three-year average growth of 538.2 percent, and a median rate of 171.8 percent. The Inc. 5000’s aggregate revenue was $206.1 billion in 2017, accounting for 664,095 jobs over the past three years.

Complete results of the Inc. 5000, including company profiles and an interactive database that can be sorted by industry, region, and other criteria, can be found at www.inc.com/inc5000.

“If your company is on the Inc. 5000, it’s unparalleled recognition of your years of hard work and sacrifice,” says Inc. editor in chief James Ledbetter. “The lines of business may come and go or come and stay. What doesn’t change is the way entrepreneurs create and accelerate the forces that shape our lives.”

The annual Inc. 5000 event honoring the companies on the list will be held October 17 to 19, 2018, at the JW Marriott San Antonio Hill Country Resort, in San Antonio, Texas. As always, speakers include some of the greatest innovators and business leaders of our generation.

Expedition Technology (EXP) offers expertise in algorithm and system development spanning application areas from radar, lidar, imaging and full motion video, to communications, navigation, signal intelligence, and data analytics. With backgrounds as active duty Naval Flight and Air Force officers, engineers, scientists, mission operators and executive managers, the EXP team understands the importance of evaluating challenges from the customer perspective. Our vision is to build EXP into a formidable provider of differentiated image and signal processing products for commercial, defense and intelligence customers.

**CONTACT**:

Holly Palmer

571-429-6141

info@exptechinc.com

**More about Inc. and the Inc. 5000 ****Methodology**

The 2018 Inc. 5000 is ranked according to percentage revenue growth when comparing 2014 and 2017. To qualify, companies must have been founded and generating revenue by March 31, 2014. They had to be U.S.-based, privately held, for profit, and independent—not subsidiaries or divisions of other companies—as of December 31, 2017. (Since then, a number of companies on the list have gone public or been acquired.) The minimum revenue required for 2014 is $100,000; the minimum for 2017 is $2 million. As always, Inc. reserves the right to decline applicants for subjective reasons. Companies on the Inc. 500 are featured in *Inc.*’s September issue. They represent the top tier of the Inc. 5000, which can be found at http://www.inc.com/inc5000.

**About Inc. Media**

Founded in 1979 and acquired in 2005 by Mansueto Ventures, Inc. is the only major brand dedicated exclusively to owners and managers of growing private companies, with the aim to deliver real solutions for today’s innovative company builders. *Inc. *took home the National Magazine Award for General Excellence in both 2014 and 2012. The total monthly audience reach for the brand has been growing significantly, from 2,000,000 in 2010 to more than 18,000,000 today. For more information, visit www.inc.com.

The Inc. 5000 is a list of the fastest-growing private companies in the nation. Started in 1982, this prestigious list has become the hallmark of entrepreneurial success. The Inc. 5000 Conference & Awards Ceremony is an annual event that celebrates the remarkable achievements of these companies. The event also offers informative workshops, celebrated keynote speakers, and evening functions.

For more information on Inc. and the Inc. 5000 Conference, visit http://conference.inc.com/.

**For more information contact:**

Inc. Media

Drew Kerr

212-849-8250

dkerr@mansueto.com

## Fighting GAN Mode Collapse by Randomly Sampling the Latent Space

/0 Comments/in Blog, Machine Learning /by Andrew DraganovAt Expedition Technology (EXP) we develop a broad set of deep learning solutions for our customers. Each deep learning development cycle typically starts with

- Understanding the problem space
- Getting acquainted with the research landscape
- Tweaking an existing algorithm or developing entirely new architectures
- Training on an army of GPUs

This is the standard process, but with a constraint: it requires very large diverse data sets to get good results. As many of our customer’s problems grow more sophisticated, absence of that constraint is becoming an ever rarer occurence. In these cases where data is scarce, there is a necessary additional step – amplifying the data that you have.

For help with this, we have been turning to Generative Adversarial Networks (GANs). Despite their wide-ranging success, deep generative methods are hindered by well-known drawbacks such as unstable minima and mode collapse. We have recently made progress regarding the latter and would like to share our methods with the rest of the deep learning community. In this post we will introduce GANs, describe mode collapse, and then explain how we’ve attempted to mitigate this problem while adding justifications and results to support our claims.

**GANs**

Generative Adversarial Networks [1] (GANs) are an incredible technology. Although classification and segmentation are necessary problems, they don’t have the catchy, easy-to-appreciate results GANs do. After all, you can’t become a great artist just by learning to distinguish Van Gogh from Monet. You have to actually pick up a paintbrush and try your hand at it. Similarly, if we strive to make intelligent systems, they must be able to not only discriminate, but to generate believable outputs. That’s where we cross the border from a passive to an active agent.

GANs operate by combining two networks – one that creates output, and one that provides feedback. The ‘generator’, as it’s called, is provided a random input and tries to return a correspondingly random output. The ‘discriminator’ then compares this generated sample to real world ones and gives a zero to one score of how believable it is. It’s really just a competition: the generator is trying to fool an ever-improving discriminator. If you let them duke it out a few million times, you end up with a discriminator that learns the real world from the fake world, as well as a generator that does a pretty good job at making realistic looking samples.This is a powerful tool, as it theoretically allows for creating unlimited additional data. If the generated samples are within the set of all possible inputs, then we can turn 100 data points into 1000 by letting the generator hallucinate 900 new but plausible examples.

**Mode collapse**

There’s a problem, though. Let’s look at the following situation [2] as a GAN tries to make pictures of cars:

- After bumbling around for a bit, the generator learns to draw convincing Honda Civics
- The discriminator picks up on this and starts labeling most Honda Civics as generated
- In response to this, the generator tweaks its algorithm a bit and begins making a similar but separate class – Honda Accords
- Now the discriminator has to adjust, so it starts calling Honda Accords fake
- While the discriminator is distracted by Accords, the opportunity presents itself to start making convincing Civics again, which the generator happily reverts to
- Repeat steps 2-5

This infinite loop of similar outputs is termed *mode collapse*, and it is one of the things restricting GANs from being widely used as a data amplification tool. The consequence of mode collapse is that we cannot create an unlimited supply of unique samples, since our generator only flicks back and forth between a couple very similar outputs. This minimally satisfies the job of fooling the discriminator but is ultimately unhelpful if we are trying to stretch the effectiveness of our currently available data.

**How to avoid mode collapse**

To reconcile this, we decided to add a constraint: the generator outputs must be random, but in such a way that any such random output is believable. An intuitive way to enforce this is to find some compressed space *Χ* that is densely packed with examples, such that any point within that space corresponds to a true data sample. If we can also find a bijection *f: Χ→Y* from *X*, our densely packed space, to *Y*, our space of real examples, then we can randomly sample *Χ*, and convert those points to plausible outputs.

Luckily for us, autoencoders are great at finding exactly such a space and such a function. The basic idea is that an autoencoder takes input, processes it to a lower dimensionality vector, then reconstructs the input from that vector. The bottleneck in the middle, then, contains the relevant information about the input with fewer variables, providing us a compressed space, referred to as the *latent space*. The decoder, given a point in that space, recreates the input that was encoded, which provides us with our bijection *f*. This relies on two assumptions that we will provide evidence for in the next section.

To employ this effectively, we make a small GAN that finds a sub-basis of this latent space, and then take random samples from this sub-basis. In practice, this means that we train a GAN to generate a batch of vectors, enforce that they are orthogonal using their dot product, and then take random linear combinations of these vectors. The discriminator then decides whether these linear combinations are convincing latent space encodings. Those that fool the discriminator get decoded into realistic samples. Due to the sampling being random and the decoder being a bijection, our results are *random* elements that are indiscernible from the true data. See the figure below for some examples of non-cherrypicked eights generated by the network.

The reason for having the GAN find a sub-basis is that it is difficult to find a perfect dimensionality of the latent space. This means that not every one of the axes is guaranteed to be utilized evenly. Therefore, it is more sensible to choose a dimensionality that allows the autoencoder some leniency, and to then let the generator learn the necessary basis of ‘highest plausibility’.

This approach is reminiscent of variational autoencoders (VAEs) [4], which also encode the data samples for the purposes of generation. VAEs, however, sample the latent space differently, electing instead to add random std. normal vectors to the encodings. In a VAE, the normal vectors are based on a mean and standard deviation that are also created by the encoder. In our approach, the encoder simply defines the latent space, which is then sampled by a wholly separate GAN.

**Reasoning for why this works**

There are two critical assumptions that substantiate our approach:

- The latent space is densely packed
- The decoder approaches a bijection

We provide two points of evidence to show that the latent space is densely packed. The first is a thought experiment. Given inputs that have 10 independent variables, and an encoded vector of length 5, we should expect that an autoencoder learns to utilize every degree of freedom to its fullest extent. If, instead, it only uses three axes of the five provided to it, the autoencoder will be further from representing the ten independent variables of the input space, implying that an easy lower minimum is available on the error landscape. This presents the caveat that our encodings need to be smaller in dimensionality than the number of independent variables in the input space. Such a requirement ensures that the optimal encoder takes advantage of every axis provided to it. Simply said, if you don’t give the encoder adequate dimensionality to represent the information, it must learn to take advantage of everything it has.

The second point is empirical, as seen by traveling through a latent space. It turns out, if we encode two handwritten MNIST digits to a latent space, the points between their encodings also represent plausible outputs, as seen in the figure [3] below. This implies that, given two known points in latent space, any point randomly between them is likely to also represent believable outputs. Our approach treats the latent representations differently by making a unique space for each digit, rather than a single latent space for all of them. In either case, the result should still hold.

Towards the second assumption, it is not true that the decoder is a true bijection, in part due to the discrete nature of the dataset. However, we can make a case that the decoder of a functional autoencoder will approach a bijection, as long as the encodings map to a densely packed space. We do this by showing that the encoder approaches a bijection from true inputs to a unique point in the latent space. The decoder then, as the inverse of the encoder, must learn the inverse bijection.Before explaining the reasoning for the decoder being a bijection, we want to touch on why this is necessary. A bijection is a function *f*: *X *→*Y* that is both ‘onto’ and ‘one-to-one’. This means that any possible value *O** *∈ {Outputs} has exactly one corresponding input *I* for which f(I) = *O*. If both the encoder and the decoder are bijections, then any point randomly sampled in the latent space *must* have a unique, correspondingly random point in the true data space.

We can claim that the encoder is ‘onto’ as a consequence of our reasoning for the latent space being densely filled. In order to fill that dimensionality, the encoder must attempt to map the inputs into different locations within the latent space. As such, if the whole constrained-dimensionality latent space is filled, then the encoder is onto. We can also show that a working autoencoder’s encoder is ‘one-to-one’ by contradiction. If it were not one-to-one, then two different inputs could map to the same latent representation. Due to the assumption that the autoencoder is functional, this point in the latent space would be decoded back out to the two different inputs. This is not possible by the definition of a function. As such, an optimal encoder approaches a bijection, therefore the decoder must also do the same.

These assumptions come together for the logic of our generative approach. Autoencoders can find a latent space in which every point maps to plausible outputs, and simultaneously approximate the bijection between this latent space and the output space. Therefore, randomly sampling the dense latent space corresponds to randomly sampling the set of realistic data samples. The quality of decoded samples is then a direct result of how ‘bijective’ the encoding and decoding operations are.

**Results**

The ultimate goal is to amplify our existing data by generating new samples that are indiscernible from the original set. To this end, we set up an experiment where we trained a basic MNIST classifier on the full train set, on a tenth of the train set, and on a tenth of the train set along with generated samples. The GAN in this case was also trained on the same tenth.

We trained the GAN on each digit independently and created 5000 new samples for each. Upon training the classifier with GAN input, we split each batch as either 25, 50 or 75 percent composed of generated digits. The rest of each batch was taken from the tenth of the train set.

We found that the network trained on a tenth of the dataset plus generated samples is more accurate on the test set than the network trained without generated samples. Specifically, we see a decrease in the error rate of up to 17% after training on our amplified dataset.

Train set | All train data | Tenth of train data | Tenth of train data and generated 75/25 | Tenth of train data and generated 50/50 | Tenth of train data and generated 25/75 |

Test set accuracy | 96.85% | 94% | 94.3% | 95% | 92.6% |

References:

- Goodfellow, Ian, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. “Generative adversarial nets.” In Advances in neural information processing systems, pp. 2672-2680. 2014
- Nibali, http://aiden.nibali.org/blog/2017-01-18-mode-collapse-gans/
- Despois, https://medium.com/@juliendespois/latent-space-visualization-deep-learning-bits-2-bd09a46920df
- Kingma, Welling. “Auto-Encoding Variational Bayes.” https://arxiv.org/pdf/1312.6114.pdf
- Chollet,
*“*Building Autoencoders in Keras”, https://blog.keras.io/building-autoencoders-in-keras.html, 2016 - Chablani, “GAN – Introduction and Implementation”, https://towardsdatascience.com/gan-introduction-and-implementation-part1-implement-a-simple-gan-in-tf-for-mnist-handwritten-de00a759ae5c, 2017