avatarEllie Salvaje

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Abstract

/a> as the most robust model (<a href="https://arxiv.org/abs/1706.06083">Madry et al.</a>). This fact highlights just how far away we are from robust recognition models – even for simple handwritten digits.</p><p id="c3ca">In our <a href="https://arxiv.org/abs/1805.09190">recent paper</a>, we introduce a new concept to classify images robustly. The idea is very simple: if an image is classified as a seven, than it should contain roughly two lines – one shorter, one longer – that touch each other at one end. That’s a generative way to think about digits, which is pretty natural for humans and which allows us to easily spot the signal (the lines) even amidst large amounts of noise and perturbations. Having such a model should make it easy to classify the adversarial examples featured above into the correct class. Learning a generative model of digits (say zeros) is pretty straightforward (using a <a href="https://arxiv.org/abs/1606.05908">Variational Autoencoder</a>) and, in a nutshell, works as follows: we start from a latent space of nuisance variables (which might capture things like thickness or tilt of the digit and are learnt from the data) and generate an image using a neural network. We then show examples of handwritten zeros and train the network to produce similar ones. At the end of training, the network has learnt about the natural variations of handwritten zeros:</p><figure id="9127"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*Y6O2le5_-9PLg_n4iWN_6w.png"><figcaption>A generative model of zeros learns the typical variations of handwritten digits (right side).</figcaption></figure><p id="3e0c">We learn such a generative model for each digit. Then, when a new input comes along, we check which digit model can best approximate the new input. This procedure is typically called <i>analysis-by-synthesis</i>, because we <i>analyse</i> the content of the image according to the model that can best <i>synthesise</i> it. Standard feedforward networks, on the other hand, have no feedback mechanisms to check whether the input image really resembles the inferred class:</p><figure id="e38b"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*qfe00YnTC58Up5hOmVuC8g.png"><figcaption>Feedforward networks directly go from image to class and have no way to check that the classification makes sense. Our analysis-by-synthesis model checks what image features are present and classifies according to which class makes most sense.</figcaption></figure><p id="f1e5">That’s really the key difference: feedforward networks have no way to check their predictions, you have to trust them. Our analysis-by-synthesis model, on the other hand, looks whether certain image features are really present in the input before jumping to a conclusion.</p><p id="031b">We do not need a pe

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rfect generative model for this procedure to work. Our model of handwritten digits is certainly not perfect: look at the blurry edges. Nonetheless, our model can classify hand-written digits with high accuracy (99,0%) and its decisions make a lot of sense to humans. For example, the model will always signal low confidence on noise images, because they don’t look like any of the digits it has seen before. The images closest to noise that the analysis-by-synthesis model still classifies as digits with high confidence make a lot of sense to humans:</p><figure id="5507"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*fjhRFQkEFDMWuwwFv2tEaQ.png"><figcaption>We tried to synthesise unrecognisable images that are still classified as zeros with high confidence by our analysis-by-synthesis model. This is the best we got.</figcaption></figure><p id="b7c5">In the current state-of-the-art model by Madry et al. we found that minimal perturbations of clean digits are often sufficient to derail the classification of the model. Doing the same for our analysis-by-synthesis model yields strikingly different results:</p><figure id="f6b0"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*aedBhqczyEb_pd4y9ubzEg.png"><figcaption>Adversarial examples for the analysis-by-synthesis model. Can you guess what the original number was?</figcaption></figure><p id="7e30">Note that the perturbations make a lot of sense to humans and it is sometimes difficult to decide into which class the image should be classified. That’s exactly what we expect to happen for a robust classification model.</p><p id="5452">Our model has several other notable features. For example, the decisions of the analysis-by-synthesis model are much easier to interpret as one can directly see which features sway the model towards a particular decision. In addition, we can even derive some lower bounds of its robustness.</p><p id="7ce5">The analysis-by-synthesis model does not quite match human perception yet and there is still a long way to go (see the full analysis in our <a href="https://arxiv.org/abs/1805.09190">manuscript</a>). Nonetheless, we believe these results are extremely encouraging and we hope that our work will pave the way towards a new class of classification models that are accurate, robust and interpretable. We still have to learn a lot about these new models, least of all how to make inference more efficient and how to scale them to more complex data sets (like CIFAR or ImageNet). We are working hard to answer these questions and are looking forward to sharing more results with you in the future.</p><h2 id="7aaa">Towards the first adversarially robust neural network model on MNIST</h2><p id="284d">Lukas Schott, Jonas Rauber, Matthias Bethge, Wieland Brendel arXiv:1805.09190</p></article></body>

POLITICS

Donald Trump Blasts Jeffrey Epstein for Dumping Him in Favor of Stephen Hawking

Mean Girls 2: Electric Boogaloo

“Slanted Steven is a SAD SIGHT of stupid!” Trump screams. Picture from ITV.

Normal people would do everything in their power to not be associated with Jeffrey Epstein. Which is proof that narcissists are not normal people.

Donald Trump’s euphoria after winning the Iowa Caucus was short lived. He remembered that his name was revealed on Jeffrey Epstein’s list, and took to Truth Social to type as fast as his tiny thumbs can jump on the keypad.

“Look, I might have hung out with Jeff in the 90s. He was a dear friend of mine, and loves beautiful girls as much as I do. But I didn’t sexually assault any girls on that island. How could I when I have a micropenis? Those girls couldn’t feel anything through penetration! Is that even rape at that point?

“What I did to those girls isn’t THAT bad. I just fondled a bit with their pert nipples. I can’t help it that those young girls had attractive boobies.

“I’m not Bill Clinton. Dude will do anything to get blow jobs. I will do anything to provide no jobs.

“That’s one of the reasons why I stopped hanging out with Epstein. Dude was a shady businessman. He let Democrats get away with anything, while forcing Republicans like me to follow the rules. But it’s all good. I’m not a fan of hanging out with perverts who can abuse little girls on private islands and jets. I’m only a fan of doing so during Miss Teen America pageants.”

Trump’s explanation of distancing himself from Epstein was labeled as misinformation by Twitter’s fact checking bot. The bot pulled up a testimony from Jeffrey Epstein’s brother Mark on how the friendship between the two spiraled down.

“I’ve also heard Jeffrey say that he stopped hanging out with Donald Trump when he realized Trump was a crook. Epstein would rather hang out with people he admired, like physicist Stephen Hawking.”

We were amused that Epstein dumped Trump instead of the other way around. We reached out to Trump on behaving like a jilted ex. In a fit of rage, Trump slammed Epstein’s choice in a shouting match against the clouds.

“Every time I speak of losers and haters, I do so with great love and affection. They cannot help the fact that they were all born fucked up.

“I mean, seriously. These lightweights claim that a man who can’t speak is smarter than me. Sorry losers and haters, but my I.Q. is one of the highest — and you all know it! Please don’t feel so stupid or insecure, it’s not your fault.

“Like, I was the President of the United States on my first try. I think that would qualify as not smart, but genius. And a very stable genius at that!

“Even Stephen Hawking wishes he was as smart as me. But look at the poor guy. You ought to see the guy. Dude looks like a hot dog. Him standing up is like my stand up.

“Slanted Stephen is a retarded loser who is very unattractive both inside and out. You can see his nipples sagging as low as his balls in his suit. Very, very disrespectful. Stephen’s balls hang so low that his girls can lick them while standing up.

“How does insecure Jeffrey Epstein choose him over me as his best pal? Epstein doesn’t know me, but Slanted Stephen would definitely NOT beat me in a fight. He would go down fast and hard, crying all the way.”

Donald Trump paused to gasp for breath.

“But Jeffrey was always dumb. He even admired Bill Clinton. Why would you hang out with a guy with one impeachment when I have TWO impeachments? Two is better than one! It’s simple math, dumb dumbs.

“I mean, I can’t believe I was ever trying to be Jeff’s best friend. He should be GRATEFUL that I would allow him in my presence. I don’t care for what he did to little girls. I never let him around Ivanka. No one can bang her but me.

“Sorry Lousy Jeff. You think you dumped me? That’s what you told yourself to sleep better in jail. You just can’t handle the fact that I discarded you. It’s awfully pathetic. SAD.”

Trump’s rant drew so much praise. Especially from athlete Aaron Rodgers. Rodgers empathized with Trump’s butthurt of being blacklisted from Epstein so much that the former NFL quarterback retired from the league in protest.

Disclaimer: All characters and events in this article, even those based on real people and events, are entirely fictional. It is written to poke fun at the subjects mentioned. It is satire. For now.

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