Keras Divide Two Tensors

We will train the architecture on the popular CIFAR-10 dataset which consists of 32x32 images belonging to 10 different classes. A tensor consists of a set of primitive(原始) values shaped into an array of any number of dimensions. saved_model import signature_constants from tensorflow. This direct relation together with the resolved hyperfine lines significantly simplified the simulation of single-crystal spectra in the three principal directions due to the reduction of free parameters and, thus, allowed us to define the magnetic g and A tensors of the molecule with a high degree of reliability. The requested operations are applied to each pair of elements independently. if I have tensors, v, w, I know how similar can two plaintext strings be and still generate the same hash?. In fact, all 2m+n tensor spaces of rank (m,n) with fixed m+ n are isomorphic. These tensors themselves generate a vector space by adding them together and multiplying them by scalars in the usual ways that we do for matrices and functions, and the collection of all such tensors so formed is the tensor product ⊗ of the two vector spaces themselves. Pytorch and why you might pick one library over the other. Flatten layer performs this task. This can also be achieved by adding the "conda-forge" channel in Anaconda Navigator and then searching for keras and tensorflow through the GUI to install them from there. is often called an. build_graph will be the tower function, so you need to follow some rules. tensordot (a, b, axes=2) [source] ¶ Compute tensor dot product along specified axes. One celebrated accom-plishment is the discovery of giant magnetoresistance in magnetic multilayer structures. Let's see how. What's New in TensorFlow 2. Deep Learning by Example on Biowulf Class #2: Analysis of sequence data using RNNs and 1D-CNNs Gennady Denisov, PhD. 2D and 2D. Since the input data for a deep learning model must be a single tensor (of shape e. Unit of dimensionality described within tensor is called rank. I have written a few simple keras layers. If you are the author of this layer, you can disable autocasting by passing autocast=False to the base Layer constructor. Like unnest, this function takes a single parameter and unrolls it into multiple rows, but unlike unnest we only need to use the function once, rather than once per column. Higher Gauge Theory, Division Algebras and Superstrings Classically, superstrings make sense when spacetime has dimension 3, 4, 6, or 10. An Introduction To Tensors for Students of Physics and Engineering Joseph C. rand method to generate a 3 by 2 random matrix using NumPy. Video captioning ( Seq2Seq in Keras ). I could get a few answers reading and searching for Tensors and NumPy arrays. As a compute graph, the above operation would appear as: Graphs can become much more complex. generalized for tensors of rank m and n. At its core, TensorFlow is a software package for the mathematical manipulation, storage, and transfer of tensors, a generalization of the concept of matrices. Printing a layer. 0 has fully embraced keras as the high-level Application Programming Interface (API). Guess what?. These tensors themselves generate a vector space by adding them together and multiplying them by scalars in the usual ways that we do for matrices and functions, and the collection of all such tensors so formed is the tensor product ⊗ of the two vector spaces themselves. The Keras deep learning network to which to add an ConvLSTM2D layer. The result of the multiplication depends on the sizes of the tensors. TensorFlow is a popular, open-source, machine learning software developed by Google's Brain Team. The Keras deep-learning library provides data scientists and developers working in R a state-of-the-art toolset for tackling deep-learning tasks. Video captioning ( Seq2Seq in Keras ). It takes a computational graph defined by users and automatically adds swap-in and swap-out nodes for transferring tensors from GPUs to the host and vice versa. Two community discovery algorithms, namely Fuzzy Walktrap and Fuzzy Newman-Girvan, based on different algorithm design principles are proposed and the performance of their Java implementation over Neo4j is experimentally assessed in terms of both total execution time and average graph cut cost on synthetic and real fuzzy graphs. Few fundamental conventions like Shared Tensors and operator signatures are different with MXNet. The main value add of Tensor Flow or any other similar framework (Keras, Pytorch etc. Building Deep Learning Applications with Keras 2. Convert tensors to numpy array and print. Like rank-2 tensors, rank-3. "Keras tutorial. This problem appeared as an assignment in the coursera course Convolution Networks which is a part of the Deep Learning Specialization (taught by Prof. The requested operations are applied to each pair of elements independently. Similarly a column/row matrix using a 1-D Tensor and so on. They are used in a lot of more advanced use of Keras but I couldn’t find a simple explanation of what they mean inside Keras. A TensorFlow Chatbot Two RNNs are trained jointly to maximize the conditional probability a list of tensors representing inputs to the encoder. fit in keras, takes a lot of code to accomplish in Pytorch. For higher-level dimensions, array. We will build a simple architecture with just one layer of inception module using keras. This post will. 3 Decompositions. However, there are two cases in which you may need to care. Classifying movie reviews: a binary classification example Two-class classification, or binary classification, may be the most widely applied kind of machine-learning problem. Learning AI if You Suck at Math — Part 4 — Tensors Illustrated (with Cats!) — This one answers the ancient mystery: What the hell is a tensor? Learning AI if You Suck at Math — Part 5 — Deep Learning and Convolutional Neural Nets in Plain English — Here we create our first Python program and explore the inner workings of neural. Eigenvalues and Positive Definite Tensors. Finally, tensors can be formed by contraction from tensors of higher rank. I have written a few simple keras layers. The tolerance values are positive, typically very small numbers. layers import Input, Lambda from keras. This post will. In this article, object detection using the very powerful YOLO model will be described, particularly in the context of car detection for autonomous driving. (The code for reading and preparing data is in the module: data_utils_nn. Hadamard (entrywise) division then used to identify anomalies, to estimate missing values or to understand how the data was generated in the first place. Keras Backend. Keras layers and models are fully compatible with pure-TensorFlow tensors, and as a result, Keras makes a great model definition add-on for TensorFlow, and can even be used alongside other TensorFlow libraries. But in this scope a tensor is a generalization of vectors and matrices to potentially higher dimensions. Pytorch and why you might pick one library over the other. Writing Tile Code¶. Anyhow, we can observe tensors as n-dimensional arrays using which matrix operations are done easily and effectively. conda install -c conda-forge keras tensorflow or: pip install keras tensorflow I would recommend the first option. Keras offers out of the box image classification using MobileNet if the category you want to predict is available in the ImageNet categories. I have two tensors that must be multiply. 0’s documentation has not been fully updated), it is stated that: Output shape. Classifying movie reviews: a binary classification example Two-class classification, or binary classification, may be the most widely applied kind of machine-learning problem. Dimensions of Tensors in PyTorch. This is done as part of _add_inbound_node(). Thus, and are tensors of the type indicated by the suffixes. rand(10000, 10000). LoggingTensorHook (tensors = tensors_to_log, every_n_iter = 50) We store a dict of the tensors we want to log in tensors_to_log. TensorFlow is an open source deep learning library that is based on the concept of data flow graphs for building models. I have designed this TensorFlow tutorial for professionals and enthusiasts who are interested in applying Deep Learning Algorithm using TensorFlow to solve various problems. Faster division and modulo operation - the power of two The power of two - fast division and modulo operations There are some - admittedly rare - cases, when the division and modulo operations are responsible for a great percent of the total runtime. Softmax activation function in the last layer returns an array of 10 values which correspond to the probability scores that sum to 1. This tutorial helps NumPy or TensorFlow users to pick up PyTorch quickly. We'll cover later in. rand(10000, 10000). The following are code examples for showing how to use keras. output tensors of pow_op and useless_op) at the same time. moving_average_update Compute the moving average of a variable. Accordingly, we divide the material into three chapters. Tensors represent the connecting edges in any flow diagram called the Data Flow Graph. k_equal: Element-wise equality between two tensors. mean Mean of a tensor, alongside the specified axis. Keras provide y_true and y_false as input of loss function. Print() won't work because, well, I don't have tensors. One obvious way of representing tensors of rank two is by denoting them as matrices. This direct relation together with the resolved hyperfine lines significantly simplified the simulation of single-crystal spectra in the three principal directions due to the reduction of free parameters and, thus, allowed us to define the magnetic g and A tensors of the molecule with a high degree of reliability. (We can think of this as being the opposite of a Merge operation) I am given to understand that the only way to achieve this is currently using the Lambda layer since there is no "Split" functionality in Keras. If the category doesn’t exist in ImageNet categories, there is a method called fine-tuning that tunes MobileNet for your dataset and classes which. This similarity operation will be returned via the output of a secondary model - but more on how this is performed later. Higher Gauge Theory, Division Algebras and Superstrings Classically, superstrings make sense when spacetime has dimension 3, 4, 6, or 10. Working in a early stage startup gave me an opportunity to work on very diverse set of problems & applications ranging from deep learning (CNNs, GRUs, LSTMs) to web development (django, javascript, rest apis) under tight. We do it with the python slice operator. However there is another issue. As tensorflow is a low-level library when compared to Keras , many new functions can be implemented in a better way in tensorflow than in Keras for example , any activation fucntion etc… And also the fine-tuning and tweaking of the model is very flexible in tensorflow than in Keras due to much more parameters being available. This TensorRT 6. It was born from lack of existing function to add attention inside keras. In this post we learned how to deal with data for deep learning models. print(random_tensor_two_ex) We see again that we have a PyTorch IntTensor of size 2x3x4, and it's a random tensor that has numbers between 0 and 10. Deep Learning with Python introduces the field of deep learning using the Python language and the powerful Keras library. - If necessary, we build the layer to match the shape of the input(s). What you'll learn. Element-wise inequality between two tensors. k_equal: Element-wise equality between two tensors. If all outputs in the model are named, you can also pass a list mapping output names to data. One can not obtain a tensor or “derive any physical meaning” on dividing a vector with another vector. When the component tensors. This article is a brief introduction to TensorFlow library using Python programming language. Dot(axes, normalize=False) Layer that computes a dot product between samples in two tensors. We might say that road for 2. By selecting different configuration options, the tool in the PyTorch site shows you the required and the latest wheel for your host platform. If you are the author of this layer, you can disable autocasting by passing autocast=False to the base Layer constructor. Building Deep Learning Applications with Keras 2. **kwargs: Standard layer keyword arguments. Make sure you have already installed keras beforehand. This tutorial helps NumPy or TensorFlow users to pick up PyTorch quickly. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way. Learn how to use Tensors, build a Linear Regression model and a simple. Let's see how. **kwargs: Standard layer keyword arguments. 2) supports Tensors. Other Challenges. Fast algorithms for structured matrices and tensors are of particular importance in data analysis, and signal and image processing. separate stacking model. They are extracted from open source Python projects. I could get a few answers reading and searching for Tensors and NumPy arrays. over different tensor element types (e. As might be suspected, tensors can be defined to all orders. About Keras in R. TensorFlow data tensors). In Minkowski space and under Poincaré transformations, tensors are "Lorentz tensors", or, "4­tensors". generalized for tensors of rank m and n. That is possible since the constructs are defined definitely as arrays/matrices. Keras-MXNet is upto 3X faster than Keras-TF on multi-GPU training. In this tutorial, we create a multi-label text classification model for predicts a probability of each type of toxicity for each comment. 1D and 1D Returns the dot product between the two tensors (scalar). For beginners; Writing a custom Keras layer. The tolerance values are positive, typically very small numbers. Please note that the TensorFlow Java API is an experimental API and hence not covered under any stability guarantee. Tensors represent the connecting edges in any flow diagram called the Data Flow Graph. Fast algorithms for structured matrices and tensors are of particular importance in data analysis, and signal and image processing. The PARAFAC [4] (also called CP) decomposition is one of the most popular among the many tensor factorizations flavors [5], as it factorizes a tensor into a sum of rank-1 tensors. concatenate, essentially) to perform some different operations on the two parts, before c. - If necessary, we build the layer to match the shape of the input(s). The data is a 2D list where individual samples have length 6, 5, and 3 respectively. Being able to go from idea to result with the least possible delay is key to doing good research. Tensors in 4 Dimensions Let us now consider the specific nature of tensors on four-dimensional space-time. images = images / 255. [Keras] Returning the hidden state in keras RNNs with return_state There is a lot of confusion about return_state in Keras. A is second order tensor and B is fourth order tensor. This problem appeared as an assignment in the coursera course Convolution Networks which is a part of the Deep Learning Specialization (taught by Prof. If set to True, then the output of the dot product is the cosine proximity between the two samples. Experiments 5. A merging 'mode' must be specified, check below for the different options. Rank-2 tensors may be called dyads although this, in common use, may be restricted to the outer product of two vectors and hence is a special case of rank-2 tensors assuming it meets the requirements of a tensor and hence transforms as a tensor. The tensor that we’ve discussed, namely the Maxwell stress tensor, is an example of a \rank-2 tensor". Printing a layer. Keras and PyTorch differ in terms of the level of abstraction they operate on. This conference has two major objectives. functional module. What mathematical tool would one use to describe the ow of a tensor? I ask this question not to make your brain hurt, but to open your mind to more and richer possibilities. One obvious way of representing tensors of rank two is by denoting them as matrices. Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices. I'm not qualified to say whether or not this is the correct way, but the following code will calculate (r1 - r2)**2 as you request. Scaling Keras Model Training to Multiple GPUs. • Two main tools – PARAFAC – Tucker • Both find row-, column-, tube-groups – but in PARAFAC the three groups are identical • ( To solve: Alternating Least Squares ). In CNTK, the same operations will produce an array of dimensions (9, 8, 7, 4, 9, 8, 7, 5) which might not be desired. However there is another issue. Closed (None, 15, 200), how can i compute this in Keras? It is a basic operation in Keras , sorry about not knowing. For most deep learning networks that you build, the Sequential model is likely what you will use. Wallace 1985; Jost & Herrmann 1989) often ‘decompose’ moment tensors, that is, they write them as sums of other moment tensors. Tensors are identified by the following three parameters − Rank. batch_size. Integer or list of integers, axis or axes along which to take the dot product. This model capable of detecting different types of toxicity like threats, obscenity, insults, and identity-based hate. In this article, we will learn about basic arithmetic operators supported by the Tensorflow. A scalar value is represented by a 0-dimensional Tensor. For example, taking the sum of two network nodes creates a new network node that represents the summation operation which takes the two nodes as inputs. Input and feature_column at the same time? Or is there an alternative than tf. The tensor that we’ve discussed, namely the Maxwell stress tensor, is an example of a \rank-2 tensor". 0 has fully embraced keras as the high-level Application Programming Interface (API). This function is part of a set of Keras backend functions that enable lower level access to the core operations of the backend tensor engine (e. Keras Backend. Tensors are created and manipulated similarly to numpy matrices: >>> a = np. in keras: R Interface to 'Keras' rdrr. In section3, we construct holographic states and codes by building networks of perfect tensors. For example, if you want to build a custom layer that computes the element-wise euclidean distance between two input tensors, you would define the function to compute the value itself, as well as one that returns the output shape from this function, like so:. Printing a layer. They are extracted from open source Python projects. Recently, he was busy building the Apache MXNet backend for Keras, and he is also an active contributor and committer for Apache MXNet, one of the most popular, scalable and easy to use deep learning frameworks. This similarity operation will be returned via the output of a secondary model - but more on how this is performed later. GEOMETRIC AND KINEMATIC RELATIONS Consider a simply-connected body of elastic-plastic material, prior to. Keras generate a derivative of the computation you make in the loss function and doesn’t use it anymore after that, so python print won’t work within it. We need to split data to implement the loss function. It does not handle low-level operations such as tensor products, convolutions and so on itself. Pre-trained models and datasets built by Google and the community. switch(condition, then_expression, else_expression) Switches between two operations depending on a scalar value. In this tutorial, we'll cover the theory behind text generation using a Recurrent Neural Networks. l2_normalize(fc2, …. They also generally assume open boundary conditions, such that the end MPS tensors have only one link and one site index. In the example below, we define two order-1 tensors (vectors) with and calculate the tensor product. For higher-level dimensions, array. Coding Inception Module using Keras. Execute the allreduce operation on the fusion buffer. Keras-MXNet is upto 3X faster than Keras-TF on multi-GPU training. The concept of multi-GPU model on Keras divide the input's model and the model into each GPU then use the CPU to combine the result from each GPU into one model. When the component tensors. two of the eigenvalues are equal, one of the eigenvectors will be unique but the other two directions will be arbitrary – one can choose any two principal directions in the plane perpendicular to the uniquely determined direction, in order to form an orthonormal set. It shows how you can take an existing model built with a deep learning framework and use that to build a TensorRT engine using the provided parsers. build_graph() takes inputs tensors that matches what you’ve defined in inputs(). Declaring the input shape is only required of the first layer – Keras is good enough to work out the size of the tensors flowing through the model from there. Regards, Ian. Tensors and TensorFlow A tensor is a vector or matrix of n-dimensions that represents all types of data. Rather than picking one single tensor library and making the implementation of Keras tied to that library, Keras handles the problem in a modular way, and several different backend engines can be plugged seamlessly into Keras. But a tensor could be obtained by operating two vectors through a DYADIC PRODUCT. Let's see how. If set to TRUE, then the output of the dot product is the cosine proximity between the two samples. Structured Matrices and Tensors: Analysis, Algorithms and Applications. k_equal: Element-wise equality between two tensors. It does not handle low-level operations such as tensor products, convolutions and so on itself. Welcome everyone to an updated deep learning with Python and Tensorflow tutorial mini-series. While tensors are defined independent of any basis, the literature on physics often refers to them by their components in a basis related to a particular coordinate system. It allows you to easily stack sequential layers (and even recurrent layers) of the network in order from input to output. ) l A A A =. Hint: If you want to see a list of allocated tensors when OOM happens, add report_tensor_allocations_upon_oom to RunOptions for current allocation info. With python, the data scientists need not spend all the day debugging. from keras import backend as K. Written by Keras creator and Google AI researcher François Chollet, this book builds your understanding through intuitive explanations and practical examples. Highlights Dislocation networks are automatically identified in atomistic simulations. These are some examples. There are various reasons for its popularity and one of them is that python has a large collection of libraries. layers is a flattened list of the layers comprising the model. The result is a tensor of the same dimensions as the tensors to which they are applied, and unless otherwise specified it is also of the same type. If the category doesn't exist in ImageNet categories, there is a method called fine-tuning that tunes MobileNet for your dataset and classes which. Consumers. The last two entries in the array (extracted here as w and h) specify the width and height of the box. And this just for additions! If we add more operations, or mix them, the network needs to grog even more rules like this. dependent on the other two. When used to express machine learning operations, the Tile language is reasonably close to mathematical notation, while also being amenable to conversion into optimized GPU kernels. Let's see how. Note that if. For that purpose, I will use Keras. A zero-dimensional tensor is called a scalar, a one-dimensional tensor is called a vector, and a two-dimensional tensor is called a matrix. Being able to go from idea to result with the least possible delay is key to doing good research. In particular, you'll probably find yourself working with the keras layers API. For example, in the code below, we defined two constant tensors and add one value to another:. Pytorch and why you might pick one library over the other. They are used in a lot of more advanced use of Keras but I couldn’t find a simple explanation of what they mean inside Keras. My dataset is the INRIA Holidays Dataset , a set of 1491 photos from 500 different vacations. So, here the multiplication has been performed considering (9,8,7) as the batch size or equivalent. Results are comparable to experiments on a larger length scale. RNN layers). Keras Backend. In this example, you'll learn to classify movie reviews as positive or negative, based on the text content of the reviews. If the category doesn’t exist in ImageNet categories, there is a method called fine-tuning that tunes MobileNet for your dataset and classes which. You can also decide to experiment with a technique called parameter tuning. 3 Decompositions. At the same time, it lets you work directly with tensors and perform advanced customization of neural network architecture and hyperparameters. This will run the whole graph to get the required output tensors. ; predictions (tf. This problem appeared as an assignment in the coursera course Convolution Networks which is a part of the Deep Learning Specialization (taught by Prof. generalized for tensors of rank m and n. Tensors of order three have an array of 27 components and tensors of order four have 81 components and so on. In this article, we list down 10 comparisons between these two deep learning frameworks. When used to express machine learning operations, the Tile language is reasonably close to mathematical notation, while also being amenable to conversion into optimized GPU kernels. They accomplished this by reducing redundancy, full keras integration, and a major shift away from static graphs to eager execution. Chollet describes the mathematical building blocks of neural networks, starting off with the various types of tensors, including scalars, vectors, and multi-dimensional matrices. As can be observed, Keras supplies a merge operation with a mode argument which we can set to ‘cos’ – this is the cosine similarity between the two word vectors, target, and context. First, I will train a convolutional neural network from scratch and measure its performance. conda install -c conda-forge keras tensorflow or: pip install keras tensorflow I would recommend the first option. The module itself is pure Python with no dependencies on modules or packages outside the standard Python distribution and keras. fit_generator() in Python are two seperate deep learning libraries which can be used to train our machine learning and deep learning models. import numpy as np from keras. Print inject a print command inside the graph of the derivative to eval print the content of tensor while training the network (I suppose it works like that ). PlaidML uses a language called Tile to construct GPU kernels. switch(condition, then_expression, else_expression) Switches between two operations depending on a scalar value. TensorFlow, CNTK, Theano, etc. Tensors and transformations are inseparable. saved_model import signature_constants from tensorflow. 1D and 1D Returns the dot product between the two tensors (scalar). Arguments: inputs: Can be a tensor or list/tuple of tensors. Note that this tutorial assumes that you have configured Keras to use the TensorFlow backend (instead of Theano). Just as most programs start by declaring variables, most TensorFlow applications start by creating tensors. Why is it so much better for you, the developer? One high-level API for building models (that you know and love) - Keras. So working at this level is harder than working in the rest of Keras. keras backends what is a "backend"? keras is a model-level library, providing high-level building blocks for developing deep learning models. GEOMETRIC AND KINEMATIC RELATIONS Consider a simply-connected body of elastic-plastic material, prior to. In this paper, we propose two novel algorithms called Support Tensor Machines (STM) and TensorLeastSquare(TLS). It takes a computational graph defined by users and automatically adds swap-in and swap-out nodes for transferring tensors from GPUs to the host and vice versa. Keras provides an example of a Siamese network as part of the distribution. In this post we describe our attempt to re-implement a neural architecture for automated question answering called R-NET, which is developed by the Natural Language Computing Group of Microsoft Research Asia. Unit of dimensionality described within tensor is called rank. If the category doesn't exist in ImageNet categories, there is a method called fine-tuning that tunes MobileNet for your dataset and classes which. to_categorical function to convert our numerical labels stored in y to a binary form (e. 1 Developer Guide demonstrates how to use the C++ and Python APIs for implementing the most common deep learning layers. **kwargs: Standard layer keyword arguments. maximum Element-wise maximum of two tensors. Also, please note that we used Keras' keras. Because this interface is specialized for single-cost training. RNN layers). In addition, you can also create custom models that define their own forward-pass logic. Keras is designed around TF and Theano conventions and operators. Re Keras, I'm sure I've heard the name before, and just checked it out. Keras is an API for building neural networks written in Python capable of running on top of Tensorflow, CNTK, or Theano. Poised to be a lifestyle destination for Singaporeans, ActiveSG will offer individuals, families and communities ample opportunities to experience a diverse and exciting line-up of sporting activities suited for all. Copy data from the fusion buffer into the output tensors. As you will recall, working with tensors is a two step process. By simple data preparation, we can convert this data into tensors, as numpy arrays, for our Keras neural network model to process. Training small models is easy, and we mostly do this at first, but as soon as we get to the rest of the pipeline, complexity rapidly mounts. In this post, we show how to implement a custom loss function for multitask learning in Keras and perform a couple of simple experiments with itself. Lastly, the Predict signature allows for a dynamic number of input and output tensors. [Keras] Returning the hidden state in keras RNNs with return_state There is a lot of confusion about return_state in Keras. Note that both then_expression and else_expression should be symbolic tensors of the same shape. Scalars vs. Working with Classes and Tensors. PyTorch has been developed by Facebook which is based on Torch while TensorFlow, an open sourced machine learning library, developed by Google Brain is based on the idea of data flow graphs for building models. The first two entries in the array (extracted in the above code as x and y) specify the horizontal and vertical positions of the top left corner of the bounding box. In this line we again nest two operations in one — first the subtraction is done and then the division. batch_size. In this post, we show how to implement a custom loss function for multitask learning in Keras and perform a couple of simple experiments with itself. This function is part of a set of Keras backend functions that enable lower level access to the core operations of the backend tensor engine (e. Keras is without a doubt the easier option if you want a plug & play framework: to quickly build, train, and evaluate a model, without spending much time on mathematical implementation details. > Hint: If you want to see a list of allocated tensors when OOM happens, add report_tensor_allocations_upon_oom to RunOptions for current allocation info. The input and output of the function are mostly input and output tensors. The main value add of Tensor Flow or any other similar framework (Keras, Pytorch etc. Zero tensor 0 has all its components zero in all coord systems. Tensors is a generalization of scalars, vectors, matrices, and so on. Tensors, defined mathematically, are simply arrays of numbers, or functions, that transform according to certain rules under a change of coordinates. The PARAFAC [4] (also called CP) decomposition is one of the most popular among the many tensor factorizations flavors [5], as it factorizes a tensor into a sum of rank-1 tensors. Sequential # is a Module which contains other Modules, and applies them in sequence to # produce its output. Regards, Ian. name_scope Returns a context manager for use when defining a Python op.