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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.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:<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>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 analysis-by-synthesis, because we analyse the content of the image according to the model that can best synthesise it. Standard feedforward networks, on the other hand, have no feedback mechanisms to check whether the input image really resembles the inferred class:<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>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.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:<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>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:<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>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.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.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.<h2 id="7aaa">Towards the first adversarially robust neural network model on MNIST</h2>Lukas Schott, Jonas Rauber, Matthias Bethge, Wieland Brendel arXiv:1805.09190</article></body>

Do You Live Life as a ‘NCIC’? (1)

A NCIC is no longer just human, but a new species: a ‘GodMan,’ This is Living Life Powerfully as ‘A New Creation In Christ’

Spiritually we are all a ‘NCIC’ (a New Creation In Christ), IF we’re in the family of Jesus (II Cor 5:17). This is experienced more if we understand and live his gospel, like these episodes will show.

We’ve been made new in Jesus. We’re no longer only human, but we’re a mixture of God and man: a ‘GodMan’ (both male and female). Said another way, it’s like we are a new SPECIES.

God takes up residence in us. In the Old Testament God VISITED humans. In the New, he INHABITS us if we’re born again. More than once, the gospel calls us ‘God’s house,’ and even ‘God’s temple.’

Religion Paints a Very Different Picture of Us

The problem is if we don’t know the gospel, religion paints a very different picture of us.

And it’s NOT one of being a NCIC!

This is why Jesus says to repent of all other beliefs and only believe his gospel! The devil uses religion, and even non-gospel preachers, and he does all he can do to blind us from living in the light of gospel truth (II Cor 4:3–4). He used to use snakes but I guess they became outdated.

RELIGION blinds us to God’s reality. THE GOSPEL establishes us so we live in the power of God. These are in total conflict. Thus Paul says anything that is not the gospel should be cursed (Gal 1:8–9).

BIOS: Biological Life Compared to ZOE: God’s Life

Until we’re part of God’s family, we live a BIOS, or biological life only. In Jesus, we live in God’s own, personal ZOE life. The gospel paints a picture of us living life as a NCIC, and not just being part of what might be called religious mainstream ‘CHURCHIANITY.’

(I wrote and perform a humorous song: Churchianity Talkin’ Blues. To listen to it: http://www.gospelpowerofgod.com/churchianity . It’s about a guy who ‘talks the talk,’ but doesn’t ‘walk the walk.’)

God doesn’t require much out of us but we must be open to his gospel, and living in the blessings it gives us, so we get on the right track. Then God takes over and his gospel answers most of our questions.

Bing inages free to use and share: **https://tinyurl.com/yxbacksv**

In the Old Testament, God required two things from the Jews: (1) Forsake all religions and gods, (2) Only believe and live his law.

In the New Testament, God requires two things from Christians: (1) Forsake and repent of all other beliefs, (2) Only believe and live his gospel.

The Jews failed! Studies show the church isn’t doing any better!

A NCIC is Our New Identity in Jesus

A NCIC is who we are in Jesus. It’s called our ‘IDENTITY’. Religion doesn’t deal with identity, but with what to DO, and DON’T do: “DO read your Bible, pray, attend church, and do these other things…” DON’T lie, cuss, cheat, steal, or be a brat.”

NCICs look like everyone else on the outside but inside they are very different. Their hearts are open to God. They know God looks at their hearts and motives more than anything else (I Sam 16:7).

Religious Folks Live in Law, NCICs Live in Love

Religion is often called living by standards, rules, principles and precepts. It’s living by external guides that are supposed to make us better inside. It’s out-side-in living. NCICs live in love. Jesus says to love others, and the GOSPEL empowers us to love others better. Love never initiates in us, but always in God. We respond to God: sharing his love with others.

We saw this: NCICs live the ZOE life of God, not just BIOS, human life.

**Images of Bing free to use and share: https://tinyurl.com/y69hx925**

Now we live in God’s love first (his AGAPE love, not our human love), and then we give his love to others. Paul says we first of all INCREASE in God’s love, like a balloon so full we’re ready to pop, then we ABOUND, or spill over onto other people (I Thes 3:12).

Human love is nice, it just can’t begin to compare with God’s love.

I call it ‘used love’ — we use it, then share it. The more we ‘hang out’ with God, the more we know his love for us. The more we are saturated in his love, the more we know we have of it to give away to others. Jesus says, “Love others AS I have loved you…” “You have freely received, so freely give.”

NCICs know God loves us like crazy, and they know he’s not angry with us because of our trust in Jesus. Jesus took our sin and gave us his righteousness (II Cor 5:21). He says not to even think we will be accused of anything in heaven because he took our judgment (John 5:45).