ECE521 W17 Tutorial 1. Renjie Liao & Min Bai
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1 ECE521 W17 Tutorial 1 Renjie Liao & Min Bai
2 Schedule Linear Algebra Review Matrices, vectors Basic operations Introduction to TensorFlow NumPy Computational Graphs Basic Examples
3 Linear Algebra Review Vector: 1D array, row, column vectors Matrix: 2D array
4 Vector Addition, Scalar Multiplication
5 Vector Inner Product Properties: Conjugate Symmetry Linearity Positive-Definiteness
6 Vector Outer Product
7 Vector Norms Lp Norm: Example: For p = 1: Manhattan norm For p = 2: Euclidean norm
8 Geometric Interpretation
9 Matrix Addition, Scalar Multiplication
10 Broadcasting
11 Matrix Multiplication
12 Matrix Multiplication
13 Matrix Multiplication Properties: Not Commutative (In general) Distributive Transpose
14 Matrix Vector Multiplication Row/Column views
15 1D Convolution Discrete Definition: Continuous Definition
16 1D Visualization
17 2D Convolution
18 Convolution as Matrix Multiplication
19 Convolution as Matrix Multiplication
20 Convolution as Matrix Multiplication
21 Introduction to TensorFlow What is it? Open source library by Google for machine learning Supports CPU / GPU / mix / distributed computing Linux, Mac OS X, Windows versions How to get it?
22 NumPy Important python package, core component of TensorFlow Similar supports linear algebra and numerical operations similar to MATLAB Part of larger SciPy package which has even more numerical operations
23 NumPy and TensorFlow Comparisons Credit: Stanford CS224 Lecture Notes
24 TensorFlow Overview Unlike NumPy, TensorFlow does NOT perform operations immediately Need to explicitly run operation Represents data as multidimensional arrays, or tensors Basic procedure: Construct computational graph Create an operations session Initialize parameters of computational graph, if any (eg initial model weights) Feed data to graph (eg input image matrix) Execute computation operations which return data (eg output label for object in image)
25 TensorFlow - Basic Example 1 An example of the element-wise product of two vectors:
26 TensorFlow - Basic Example 1 Construct computational graph Note that c does NOT actually have a value The graph defines operational relationships between nodes Note that in this case, c has inferred the shape to be (4,) - but a node can have None as dimensions if unknown at construction time the resulting computation graph
27 TensorFlow - Basic Example 1 Create operations session: or Session defines an environment for the execution of operations The session keeps track of a set of actual values for variable nodes Can have multiple sessions to run copies of graphs in parallel tf.interactivesession() often used in ipython to set current session as default
28 TensorFlow - Basic Example 1 Initialize parameters in graph: Execute computation graph: Returns values for each node queried
29 TensorFlow - Basic Example 1
30 TensorFlow - Basic Example 2 Example 1 does not have a feeding mechanism Suppose we want to: All parameters in the graph were available in advance Define the graph Initialize nodes that correspond to model parameters - ONLY ONCE! Provide training data to some nodes and update model parameters via gradient descent We use the tf.placeholder() Arguments: data type (mandatory), shape (optional), name (optional) Specifying (the entirety or part of) shape restricts shapes of possible inputs to the node At run time, we feed using a feed_dict
31 TensorFlow - Basic Example 2
32 TensorFlow - Basic Example 3 The most important operation: optimization Define a loss function Select an optimizer Define optimization operation using selected optimizer sess.run(optimization operation) elementsquarederror = tf.square(y_predicted-y_target) meansquarederror = tf.reduce_mean(tf.reduce_sum(elementsquarederror, reduction_indices=1)) optimizer = tf.train.gradientdescentoptimizer(learning_rate=0.005) train = optimizer.minimize(loss=meansquarederror) sess.run(train)
33 TensorFlow - Basic Example 3 Example: is a 100 by 5 matrix (100 sets of 5-dimensional input data points) is a 1 by 100 target vector (100 target labels for each x) W is a 5 by 1 weights vector b is a scalar Model: Given X and Y, optimize for W and b under mean squared error over the 70 training examples: Example code at: Also download the two dataset files
34 TensorFlow - Basic Example 3 Automatic differentiation in TensorFlow can generate gradient of a computation graph with respect to the variables automatically.
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