We thank the reviewers for their valuable feedback. The way DEQ "ignores" depth and solves for the equilibrium suggests a different view of output modeling and further We also agree with the reviewers that the runtime discussion should be moved into the main text. We thank reviewer #1 for the valuable feedback. DEQ approach is very different from techniques like gradient checkpointing (GC). It is an implementation-based methodology that is practical on almost any layer-based network. Quantitatively, we have followed the reviewer's suggestion and compared GC and DEQ using a 70-layer TrellisNet (w/ We find that GC works best when we checkpoint after every 9 layers, and record a 5.2GB The training speed of GC is approximately 1.6 We thank reviewer #3 for the comments, and for taking the time to check our proof and read our code.

Let's turn our brain structures into code. The invention of deep learning by Geoffrey Hinton in 2006 [1] opened various research possibilities. He is also inventor of the backpropagation. The deep layered structure resembles the cortex zones of the human brain. But the more layers in the neural network are presented, the more complex it is to train.

Let's start with a brief summary of the main ideas discussed in Part I. Industrial applications of anomaly detection are too many to list: fraud detection in banking, preventive maintenance in heavy industries, threat detection in cybersecurity, etc. In all these problems, defining outliers explicitly can be very challenging. Variational autoencoders (VAEs) automatically learn the general structure of the training data to isolate only its discriminative features, which are summarised in a compact latent vector. The latent vector constitutes an information bottleneck that forces the model to be very selective about what to encode. We train an encoder to produce the latent vector and a decoder to reconstruct the original data from the latent vector as faithfully as possible.

Sebastian Flennerhag, Yannick Schroecker, Tom Zahavy, Hado van Hasselt, David Silver, and Satinder Singh won an ICLR 2022 outstanding paper award for their work Bootstrapped meta-learning. We spoke to Sebastian about how the team approached the problem of meta-learning, how their algorithm performs, and plans for future work. Meta-learning, generally, is the problem of learning to learn. So what is meant by that is that when you specify a machine learning problem, you need some algorithm that does that learning. However, it's not clear which algorithm is actually the most efficient one for the specific problem that you have in mind.

Neural networks are designed to mimic the behavior of human brains, to understand various relationships in the data. These networks have the power to understand complex non-linear relationships and can help us to make more intelligent decisions. Neural networks are used in fields like image processing, natural language processing, etc., and can outperform the traditional machine learning algorithms. But one basic drawback with the traditional neural network is that it cannot memorize things. Let's say, we are playing a game and we need a model to predict the next move of a player. This depends a lot on the previous moves and traditional neural networks will not perform well here.

They consist of a probabilistic decoder and a probabilistic encoder. Probabilistic encoder encodes the input data into a Gaussian multivariate distribution, such that it produces a mean vector and a diagonal covariance matrix. The dimension of this distribution is determined by how many nodes you have in the latent layer. Then, probabilistic decoder samples the encoded distribution and creates the reconstructed data after forward propagating the sample. The loss function (to be minimized) consists of two parts: negative reconstruction likelihood ensuring that it will be likely to produce data similar to those in training dataset, and KL divergence from a prior Gaussian (usually N(0,I)) which acts as a regularizer.

GAN has a very simple task to do, that is, to generate data from the scratch, data of a quality that can fool even humans. Invented by Ian Goodfellow and colleagues in 2014, this model consists of two Neural -- Networks(Generator and Discriminator) competing with one another resulting in the generation of some authentic content. The purpose of two Networks may be summarised as to learn the underlying structure of the input database as much as possible and using that knowledge to create similar content which fits all the parameters to fit in the same category. As shown above, the input was that of human faces, where it learned exactly what it is that makes a human face, well, human. Using that understanding it generated random human faces which otherwise might have been real as well.

Humans do not reboot their understanding of language each time we hear a sentence. Given an article, we grasp the context based on our previous understanding of those words. One of the defining characteristics we possess is our memory (or retention power). Can an algorithm replicate this? The first technique that comes to mind is a neural network (NN).

Before we start, here's the code: I worked on this project with Minh Le. You've probably heard this phrase "Don't roll your own ___" thousands of times if you're a CS major. It can be filled with crypto, standard library, parser, etc. I think nowadays, it should also contain ML library. Regardless of this fact, it's still an amazing lesson to learn from. People take tensorflow and similar libraries for granted nowadays; they treat it like a black box and let it run.

At this time, I knew nothing about backpropagation, and was completely ignorant about the differences between a Feedforward, Con-volutional and a Recurrent Neural Network. As I navigated through the humongous amount of data available on deep learning online, I found myself quite frustrated when it came to really understand what deep learning is, and not just applying it with some available library . In particular, the backpropagation update rules are seldom derived, and never in index form. Unfortunately for me, I have an "index" mind: seeing a 4 Dimensional convolution formula in matrix form does not do it for me. Since I am also stupid enough to like recoding the wheel in low level programming languages, the matrix form cannot be directly converted into working code either. I therefore started some notes for my personal use, where I tried to rederive everything from scratch in index form. I did so for the vanilla Feedforward network, then learned about L1 and L2 regularization, dropout[1], batch normalization[2], several gradient descent optimization techniques... Then turned to convolutional networks, from conventional single digit number of layer conv-pool architectures[3] to recent VGG[4] ResNet[5] ones, from local contrast normalization and rectification to bacthnorm... And finally I studied Recurrent Neural Network structures[6], from the standard formulation to the most recent LSTM one[7]. As my work progressed, my notes got bigger and bigger, until a point when I realized I might have enough material to help others starting their own deep learning journey .