avatarKiran Yasmin

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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>

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How To Deal With Anxiety When Your Boyfriend Goes Out?

You may get upset; you may feel helpless, but there are so many things you can do. Let’s check out more…

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Relationships can be a pleasurable thing, but they can also be a breeding ground for restlessness and anxious feelings and thoughts. Relationship anxiety can arise at any stage of courtship. For a few people, even a single thought of losing someone can stir up stress. And for others, every stage of being in love can present endless worries.

Does he/she like me?

Is my beloved serious for me?

Will this work out?

How to take this relationship to the next level?

As a girl and boy get closer and things take a serious form, anxiety, and depression can get more intense.

Negative thoughts will keep flooding, especially in the minds of girls who love their boyfriends madly and want to get a marriage proposal as soon as possible.

Ways to Control Relationship Anxiety

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Here we’ve put together a list of some exciting and unique ideas of how to deal with anxiety when your boyfriend or husband goes out.

1. Communicate With Your Beloved

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Falling in love is easy, but the fear of losing someone is more common in females or girls than in males or boys.

As you get into a relationship, the things will not always remain the same between both of you. Sometimes, it will bring you lots of happiness, and sometimes you’ll feel depressed and hopeless.

The best and most important way to deal with relationship anxiety is calling your boyfriend or husband once a while. If they’re out for some time, you should keep calling them every hour to remind them how much you love them.

There’s no need to get stressed if your boyfriend or husband remains out for several hours. Maybe, they’ve some urgent works to do. You just have to be polite and speak nicely, make them realize that you care for them and want them to come back as soon as possible.

2. Exercise Or Brisk Walk

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This is not a joke; anxiety is a serious mental condition and that means you’ll have to manage it in any way. Exercise is indeed a good way to control the way you feel.

It has now been proved that brisk walk or exercise is a powerful and comprehensive way to control anxiety symptoms.

3. Start Over

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If the trust has gone, you should talk to your partner instantly and start over. Trust and respect are the foundations of a relationship, and if things aren’t going as planned, you’ll have to redo everything needed to strengthen this relationship.

It’ll take you weeks or even months to get back to a normal life. At the same time, you should not fall back into old habits.

4. Stay Mentally Busy

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Being busy will be difficult if your partner is out for many hours. However, you need to do so in order to improve your mood. You can begin reading a book, watch television or cook some food for your beloved.

You should do all the things that can keep your mind off your partner for some time. Gardening is also a good idea, or else, you can play some video games.

In the end, we’d like to say that you should give them some freedom. Maybe, your partner wants to focus on his career or some other things, so you need to understand their feelings and happily allow them to stay away from you for as much time as they want.

What do you do when your boyfriend or husband doesn’t respond to your calls?

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