Jane Street Tech Blog - L2 Regularization and Batch Norm This blog post is about an interesting detail about machine learning that I came across as a researcher at Jane Street - that of the interaction between L2 regularization, also known as weight decay, and batch normalization. In particular, when used together with batch normalization in a convolutional neural net with typical architectures, an L2 objective penalty no longer has its original regularizing effect. Instead it becomes essentially equivalent to an adaptive adjustment of the learning rate! This and similar interactions are already part of the awareness in the wider ML literature, for example in Laarhoven or Hoffer et al.. But from my experience at conferences and talking to other researchers, I’ve found it to be surprisingly easy to forget or overlook, particularly considering how commonly both batch norm and weight decay are used. For this blog post, we’ll assume that model fitting is done via stochastic gradient descent. L2 Regularization / Weight Decay Purpose/Intuition where:
La ponctuation - Bien écrire - ABC-Lettres par l'Obs 1. Autour de quels points de ponctuation met-on des espaces ? Le « truc » mnémotechnique ; les signes de ponctuation double sont précédés et suivis d’espaces… -Virgule : pas d’espace entre le mot et la virgule, un espace après la virgule. (sauf pour la virgule décimale comme dans 3,14116). 2. -N’abusez pas des points d’exclamation et d’interrogation, qui soulignent l’expression de vos sentiments, vos réactions. Retour au sommaire des guides de correspondance
How does Batch Normalization Help Optimization? – gradient science Supervised deep learning is, by now, relatively stable from an engineering point of view. Training an image classifier on any dataset can be done with ease, and requires little of the architecture, hyperparameter, and infrastructure tinkering that was needed just a few years ago. Nevertheless, getting a precise understanding of how different elements of the framework play their part in making deep learning stable remains a challenge. Today, we explore this challenge in the context of batch normalization (BatchNorm), one of the most widely used tools in modern deep learning. \begin{equation} BN(y_j)^{(b)} = \gamma \cdot \left(\frac{y_j^{(b)} - \mu(y_j)}{\sigma(y_j)}\right) + \beta, \end{equation} where denotes the value of the output on the -th input of a batch, is the batch size, and and are learned parameters controlling the mean and variance of the output. BatchNorm is also simple to implement, and can be used as a drop-in addition to a standard deep neural net architecture: Theorem 1.
FAQ - Batterie Lithium Dossiers > Accessoires EquipementsComment choisir sa batterie ? On choisi sa batterie en fonction de son usage , en premier lieu il faut que la capacité d’énergie soit suffisante pour les parcours envisagés, ensuite il faut s"'interroger sur sa durée de vie, l'investissement qu'on veut bien y mettre, sa capacité à alimenter son moteur (pour les kits 'haute puissance') , son temps de chargement, et aussi l'importance de son poids (suivant qu'on la porte dans son sac à dos ou sur le velo , qu'elle soit d'une grosse ou petite capacité , le poids n'a pas la même importance) Les unités de mesure - La capacité d'une batterie s'exprime en watts heure Wh , Puissance (nombre de watts) disponible pendant 1 heure, évidement si on utilise 2 fois moins de puissance , elle sera disponible 2 heures; 2 fois plus de puissance : 1/2heure , ... - La consommation s'exprime en Wh par km : Wh/km . Cette estimation est à pondérer par 2 facteurs : Les différentes technologies Photo batteries: Cellules LIPO
What is the difference between 'SAME' and 'VALID' padding in tf.nn.max_pool of tensorflow? Max Pooling is an operation to reduce the input dimensionality. The output is computed by taking maximum input values from intersecting input patches and a sliding filter window. At each step, the position of the filter window is updated according to the strides argument. When applying the filter to the border pixels some of the elements of the filter may not overlap the input elements. Therefore, in order to compute the values of those border regions input may be extended by padding with zero values. tf.nn.max_pool of tensorflow supports two types of padding, 'VALID' and 'SAME'. Formulas for computing output size and padding pixels for 'VALID' and SAME' options are given in tensorflow website. For 'SAME' option output dimensions and padding options are computed as: Padding is achieved by adding additional rows and columns at the top, bottom, left and right of input matrix depending on the above formulas.
Music Theory for Musicians and Normal People by Toby W. Rush This page includes links to each of the individual Music Theory pages I've created in PDF form. This is a work in progress; I am writing new ones regularly and fixing errors and omissions on existing ones as I find them. If you find them useful for your theory studies, you are welcome to use them, and if you find errors or have suggestions, I invite you to contact me. Click the thumbnails to view or download each page as a PDF for free! These pages are available for free under a Creative Commons BY-NC-ND license. This collection is a work in progress, but if you would prefer, you can download all the current pages as a single PDF. Music Theory for Musicians and Normal People is proud to be the official music theory guide for Ready Set Gig! Each and every one of these pages is available is an 18" x 24" poster. These pages are available in multiple translations and localizations! Interested in helping translate these pages to your own language? What is Music Theory? Beaming
Understanding Convolutions In a previous post, we built up an understanding of convolutional neural networks, without referring to any significant mathematics. To go further, however, we need to understand convolutions. If we just wanted to understand convolutional neural networks, it might suffice to roughly understand convolutions. But the aim of this series is to bring us to the frontier of convolutional neural networks and explore new options. To do that, we’re going to need to understand convolutions very deeply. Thankfully, with a few examples, convolution becomes quite a straightforward idea. Lessons from a Dropped Ball Imagine we drop a ball from some height onto the ground, where it only has one dimension of motion. Let’s break this down. Now after this first drop, we pick the ball up and drop it from another height above the point where it first landed. Let’s think about this with a specific discrete example. However, this isn’t the only way we could get to a total distance of 3. \[...~~ f(0)\! Conclusion
What is a photon? Introduction Popular science writing about quantum mechanics leaves many people full of questions about the status of photons. I want to answer some of these without using any tricky mathematics. One of the challenges is that photons are very different to ordinary everyday objects like billiard balls. One of my goals is to avoid saying anything original. The simple harmonic oscillator Here's a mass hanging on a spring: Suppose it's initially sitting in equilibrium so that the net force acting on it is zero. It's actually a sine wave but that detail doesn't matter for us right now. An oscillator where the restoring force is proportional to the displacement from the equilibrium point is called a simple harmonic oscillator and its oscillation is always described by a sine wave. Note that I'm ignoring friction here. Masses on springs aren't all that important in themselves. If you have one of these systems, then in principle you can set it in motion with as little energy as you like. Caveat
Machine Learning for Beginners: An Introduction to Neural Networks - victorzhou.com Here’s something that might surprise you: neural networks aren’t that complicated! The term “neural network” gets used as a buzzword a lot, but in reality they’re often much simpler than people imagine. This post is intended for complete beginners and assumes ZERO prior knowledge of machine learning. Let’s get started! 1. First, we have to talk about neurons, the basic unit of a neural network. 3 things are happening here. x1→x1∗w1x2→x2∗w2 Next, all the weighted inputs are added together with a bias b: (x1∗w1)+(x2∗w2)+b Finally, the sum is passed through an activation function: y=f(x1∗w1+x2∗w2+b) The activation function is used to turn an unbounded input into an output that has a nice, predictable form. The sigmoid function only outputs numbers in the range (0,1). A Simple Example Assume we have a 2-input neuron that uses the sigmoid activation function and has the following parameters: w=[0,1]b=4 w=[0,1] is just a way of writing w1=0,w2=1 in vector form. Coding a Neuron 2. 3. 4.
Les dernières lettres de Marie Jelen Dernière modification de cette page : 01/23/2012 20:21:23 Les dernières lettres de la petite Marie Jelen, 10 ans, permettent de suivre son itinéraire. Marie a été arrêtée à Paris, le 16 juillet 1942, lors de la rafle du Vél'd'hiv, avec sa mère. L'arrestation : la rafle du Vél' d'Hiv', juillet 1942 Cliquez sur les lettres pour les agrandir Transportée à Pithiviers Marie et sa mère Estéra sont tranférées, avec des dizaines d'autres enfants, au camp de Pithiviers, dans le Loiret. Le camp de Pithiviers, gardé par un gendarme français Là, les conditions de vie sont difficiles pour les enfants, souvent séparés de leurs parents. Cliquez sur les lettres pour les agrandir L'infirmerie de Pithiviers Cliquez sur les lettres pour les agrandir Cliquez sur les lettres pour les agrandir Cliquez sur les lettres pour les agrandir La dernière lettre
How to build your own Neural Network from scratch in Python Motivation: As part of my personal journey to gain a better understanding of Deep Learning, I’ve decided to build a Neural Network from scratch without a deep learning library like TensorFlow. I believe that understanding the inner workings of a Neural Network is important to any aspiring Data Scientist. This article contains what I’ve learned, and hopefully it’ll be useful for you as well! Most introductory texts to Neural Networks brings up brain analogies when describing them. Neural Networks consist of the following components An input layer, xAn arbitrary amount of hidden layersAn output layer, ŷA set of weights and biases between each layer, W and bA choice of activation function for each hidden layer, σ. The diagram below shows the architecture of a 2-layer Neural Network (note that the input layer is typically excluded when counting the number of layers in a Neural Network) Creating a Neural Network class in Python is easy. Training the Neural Network Feedforward Loss Function Phew!
Calvin & Hobbes Search Engine - by Bing I have always been a big fan of Calvin & Hobbes comics, and their author, Bill Watterson. Since discovering the complete script online, as well as a collection of every daily strip on another website, I knew I could make the two reference each other and therefore create a "Calvin & Hobbes Search Engine" for lack of a better name. So I set out to do it. Currently the search only looks for EXACT phrases (not case sensitive), so if you're looking for a comic with the words "balloon" and "airplane" you cannot enter them both, or it will search for "balloon airplane" together. Perhaps in the future I will fix this, but it's actually a lot more difficult than leaving it as-is. There is one exception though! Please find the credits for everything found on this page below. - Michael "Bing" Yingling Calvin & Hobbes : Copyright & All Rights Reserved by Bill Watterson and Andrews McMeel Universal Calvin & Hobbes Search Engine by Michael "Bing" Yingling Script from Scribd, likely from S.
A Recipe for Training Neural Networks Some few weeks ago I posted a tweet on “the most common neural net mistakes”, listing a few common gotchas related to training neural nets. The tweet got quite a bit more engagement than I anticipated (including a webinar :)). Clearly, a lot of people have personally encountered the large gap between “here is how a convolutional layer works” and “our convnet achieves state of the art results”. So I thought it could be fun to brush off my dusty blog to expand my tweet to the long form that this topic deserves. 1) Neural net training is a leaky abstraction It is allegedly easy to get started with training neural nets. >>> your_data = # plug your awesome dataset here>>> model = SuperCrossValidator(SuperDuper.fit, your_data, ResNet50, SGDOptimizer)# conquer world here These libraries and examples activate the part of our brain that is familiar with standard software - a place where clean APIs and abstractions are often attainable. That’s cool! 2) Neural net training fails silently 1. 2. 3. 4.