**tf.**

**GradientTape API**for automatic differentiation; that is, computing the gradient of a computation with respect to some inputs, usually tf. … TensorFlow then uses that tape to compute the gradients of a “recorded” computation using reverse mode differentiation.

Does TensorFlow use Eigen?

**eigen multidimensional matrix**.

### Contents

3 Answers. TF uses **automatic differentiation** and more specifically reverse-mode auto differentiation.

In tensorflow it seems that the entire backpropagation algorithm is performed by **a single running of an optimizer on a certain cost function**, which is the output of some MLP or a CNN. … A cost function can be defined for any model.

Forward mode automatic differentiation is accomplished by **augmenting the algebra of real numbers and obtaining a new arithmetic**. An additional component is added to every number to represent the derivative of a function at the number, and all arithmetic operators are extended for the augmented algebra.

A neural network starts with an initial set of weights and **calculates its first output as per the architecture of the network**. It then compares the output with the expected output present in the data and calculates the loss.

In TensorFlow, computation is described **using data flow graphs**. Each node of the graph represents an instance of a mathematical operation (like addition, division, or multiplication) and each edge is a multi-dimensional data set (tensor) on which the operations are performed.

- Include necessary modules and declaration of x and y variables through which we are going to define the gradient descent optimization. …
- Initialize the necessary variables and call the optimizers for defining and calling it with respective function.

Backpropagation (backward propagation) is an **important mathematical tool for improving the accuracy of predictions in data mining and machine learning**. Essentially, backpropagation is an algorithm used to calculate derivatives quickly.

You can use tf. function **to make graphs out of your programs**. It is a transformation tool that creates Python-independent dataflow graphs out of your Python code. This will help you create performant and portable models, and it is required to use SavedModel .

1 Answer. Keras does **backpropagation automatically**. There’s absolutely nothing you need to do for that except for training the model with one of the fit methods.

**Automatic Differentiation gives exact answers in constant time**. However, it does require introducing some unfamiliar math but it’s really simple after you skim it once.

Reverse mode automatic differentiation uses **an extension of the forward mode computational graph to enable the computation of a gradient by a reverse traversal of the graph**. As the software runs the code to compute the function and its derivative, it records operations in a data structure called a trace.

It is often said, that symbolic differentiation **operates on mathematical expressions and automatic differentiation on computer programs**. In the end, they are actually both represented as expression graphs. On the other hand, automatic differentiation also provides more modes.

Rounding is **a fundamentally nondifferentiable function**, so you’re out of luck there. … If you aren’t using the output for calculating your loss function though, you can go ahead and just apply it to the result and it doesn’t matter if it’s differentiable.

tf. gradients is only valid in a graph context. In particular, it is valid in the context of a tf. … gradients() adds ops to the **graph** to output the derivatives of ys with respect to xs . It returns a list of Tensor of length len(xs) where each tensor is the sum(dy/dx) for y in ys and for x in xs .

tf. stack **always adds a new dimension**, and always concatenates the given tensor along that new dimension. In your case, you have three tensors with shape [2] . … That is, each tensor would be a “row” of the final tensor.

Can TensorFlow replace NumPy? – Quora. Sure, **it could but it probably won’t**. Keep in mind that NumPy is the foundation for other libraries. Pandas data objects sit on top of NumPy arrays.

TensorFlow is based on **graph computation**; it allows the developer to visualize the construction of the neural network with Tensorboad. This tool is helpful to debug the program. Finally, Tensorflow is built to be deployed at scale. It runs on CPU and GPU.

Keras is a neural network library while TensorFlow is the open-source library for a number of various tasks in machine learning. TensorFlow **provides both high-level and low-level APIs** while Keras provides only high-level APIs. … Keras is built in Python which makes it way more user-friendly than TensorFlow.

- You can use ‘with’ statement to close a TensorFlow session automatically in your code. …
- If you run the above code, the TensorFlow session will automatically be closed after printing the output.
- You can watch this video on Tensorflow in 10 minutes to know tricks with TensorFlow:

- Choose an initial random value of w.
- Choose the number of maximum iterations T.
- Choose a value for the learning rate η∈[a,b]
- Repeat following two steps until f does not change or iterations exceed T. a.Compute: Δw=−η∇wf(w) b. update w as: w←w+Δw.

GradientDescentOptimizer(0.01). minimize(error) where the training step is defined. It aims **to minimise the value of the error Variable**, which is defined earlier as the square of the differences (a common error function). The 0.01 is the step it takes to try learn a better value.

The backpropagation algorithm works by computing the gradient of the loss function with respect to each weight by the chain rule, computing the gradient one layer at a time, iterating backward from the last layer to avoid redundant calculations of intermediate terms in the chain rule; this is an example of **dynamic** …

Recurrent neural networks (RNN) are **the state of the art algorithm for sequential data** and are used by Apple’s Siri and and Google’s voice search. It is the first algorithm that remembers its input, due to an internal memory, which makes it perfectly suited for machine learning problems that involve sequential data.

Forward Propagation is the way to move from the Input layer (left) to the Output layer (right) in the neural network. The process of moving from the right to left i.e **backward** from the Output to the Input layer is called the Backward Propagation.

Input signatures The input signature **specifies the shape and type of each Tensor argument to the function using a tf**. TensorSpec object. More general shapes can be used. … It is an effective way to limit retracing when Tensors have dynamic shapes.

TensorFlow’s eager execution is **an imperative programming environment that evaluates operations immediately**, without building graphs: operations return concrete values instead of constructing a computational graph to run later.

- Choose the best model for the task. …
- Profile your model. …
- Profile and optimize operators in the graph. …
- Optimize your model. …
- Tweak the number of threads. …
- Eliminate redundant copies.

Popular Algorithms for Deep Learning with Keras **Convolution Neural Nets**. **Recurrent Neural Nets**. **Long Short Term Memory Nets**. **Deep Boltzmann Machine**(DBM)

The drawback with ReLU function is their fragility, that is, when a large gradient is made to flow through ReLU neuron, it **can render the neuron useless and make it unable to fire on** any other datapoint again for the rest of the process. In order to address this problem, leaky ReLU was introduced.

The rectified linear activation function or ReLU for short is a **piecewise linear function that will output the input directly if it is positive, otherwise, it will output zero**. … The rectified linear activation function overcomes the vanishing gradient problem, allowing models to learn faster and perform better.

**Robert Edwin Wengert**. A simple automatic derivative evaluation program. Communications of the ACM 7(8):463–4, Aug 1964.

Backpropagation is a special case of an extraordinarily powerful programming abstraction called **automatic differentiation** (AD). … For the kinds of problems we study in machine learning, reverse mode is almost always what we want, and backpropagation is a particular case of it applied to neural network architectures.

Thus, it is clear that **the numerical differentiation must be made as accurately as possible**. However, it is well known that the numerical differentiation is one of the most difficult numerical calculation methods to obtain reliable calculated values at all times.

The tape-based autograd in Pytorch simply refers to the uses of **reverse-mode automatic differentiation, source**. The reverse-mode auto diff is simply a technique used to compute gradients efficiently and it happens to be used by backpropagation, source.

- The Constant Rule: d/dx c = 0.
- The Symbol Rule: d/dx x = 1 , d/dx y = 0.
- The Sum Rule: d/dx (f + g) = (d/dx f) + (d/dx g)
- The Subtraction Rule: d/dx (f – g) = (d/dx f) – (d/dx g)
- The Product Rule: d/dx (f * g) = (d/dx f) * g + f * (d/dx g)

autograd is **PyTorch’s automatic differentiation engine that powers neural network training**. In this section, you will get a conceptual understanding of how autograd helps a neural network train.

**Df = diff( f , var )** differentiates f with respect to the differentiation parameter var . var can be a symbolic scalar variable, such as x , a symbolic function, such as f(x) , or a derivative function, such as diff(f(t),t) . Df = diff( f , var , n ) computes the n th derivative of f with respect to var .

Jacobian-vector products (JVPs) form **the backbone of many recent developments in Deep Networks** (DNs), with applications including faster constrained optimization, regularization with generalization guarantees, and adversarial example sensitivity assessments.

Differentiable programming is **a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation**. This allows for gradient based optimization of parameters in the program, often via gradient descent.

tf. **where will return the indices of condition that are True** , in the form of a 2-D tensor with shape (n, d). (Where n is the number of matching indices in condition , and d is the number of dimensions in condition ). Indices are output in row-major order.