Volume 32 Number 1
Exploring the Microsoft CNTK Machine Learning Tool
The Microsoft Computational Network Toolkit (CNTK) is a very powerful command-line system that can create neural network prediction systems. Because CNTK was originally developed for internal use at Microsoft, the documentation is a bit intimidating. In this article I walk you through the process of installing CNTK, setting up a demo prediction problem, creating a neural network model, making a prediction,and interpreting the results.
Figure 1 gives you an idea of what the CNTK is and a preview of where this article is headed. Although it’s not visible in the image, I ran the CNTK tool by entering the command:
> cntk.exe configFile=MakeModel.cntk makeMode=false
Figure 1 CNTK in Action
The image shows only the last part of the output messages. The configuration file with a .cntk extension contains information about input files and about the design of a neural network to use. A prediction model was created and saved to disk.
After creating the prediction model, I used it to make a prediction. The input values are in file NewData.txt and are (4.0, 7.0). The CNTK tool was used with a second configuration file named MakePrediction.cntk to compute a prediction. The prediction results were saved to file Prediction_txt.pn and are (0.271139, 0.728821, 0.000040), which means that the predicted outcome is the second of three possible output values.
This article assumes you have familiarity working with command-line programs and a rough idea of what neural networks are, but doesn’t assume you’re a machine learning (ML) expert or know anything about CNTK. You can also get the code and data from the accompanying download.
Setting up the Problem
Imagine a scenario where you want to predict a person’s political leaning (conservative, moderate, liberal) from their age and annual income. This is called a classification problem. The idea is to take some data with known values and create a prediction model. Here, you can think of the model as a kind of complex math function that accepts two numeric input values and then emits a value indicating one of three classes.
Now take a look at the graph in Figure 2. There are 24 data points. The two input variables, called features in ML terminology, are x0 and x1. The three colors indicate three different classes, sometimes called labels in ML terminology. Although a human being can quickly see a pattern, trying to create a prediction model for even this simple data set is very challenging for a computer system.
Figure 2 Training Data
After CNTK uses the data shown in Figure 2 to create a neural network prediction model, the model will be applied to the nine test data points shown in Figure 3. As you’ll see, CNTK correctly predicts eight out of the nine test cases. The test item at (8.0, 8.0), which is actually class “red,” will be incorrectly predicted to be class “blue.”
Figure 3 Test Data (Open Circles)
Installing CNTK is just a matter of downloading a .zip folder from GitHub and extracting the files. The main CNTK portal site is located at github.com/Microsoft/CNTK. On that page you’ll find a link to the current releases (github.com/Microsoft/CNTK/releases). One of the keys to the power of CNTK is that it can optionally use a GPU instead of your machine’s CPU. The releases page gives you the choice to download binaries for a CPU-only version or a GPU+CPU version.
For demonstration purposes, I recommend you select the CPU-only version, even though you can direct the GPU+CPU version to use only the CPU. Clicking on the associated link on the releases page brings you to a page where you’ll need to accept some licensing terms, and after you click the Accept button, you’ll get a dialog where you can save a file with a name something like CNTK-1-6-Windows-64bit-CPU-Only.zip (the version number could be different, of course) to your machine.
Download the .zip file to your desktop or any convenient directory. Then extract all files directly to the C: drive (most common) or to the C:\Program Files directory.
The extracted download will have a single root directory named cntk. That root directory will contain several directories, including another directory also named cntk that contains all the binaries, including the key cntk.exe file. To finish the installation process, add the path to the cntk.exe file to your system PATH environment variable (typically C:\cntk\cntk).
Creating the Data Files
To create and run a CNTK project, you need a configuration file with a .cntk extension, and at least one file that contains training data. Most CNTK projects will have a file of test data, too. Additionally, the CNTK tool will create several output files when a project is run.
There are many ways to organize the files used with a CNTK project. I recommend you create a project root directory that holds your data files and the .cntk configuration file, and run CNTK from that directory.
I had an existing C:\Data directory on my machine. For the demo, I created a new subdirectory in that directory named CNTK_Projects. And inside that directory I created a subdirectory named SimpleNeuralNet to act as the demo project root directory to hold my .cntk file and a training data file and a test data file.
The CNTK system can work with several different types of data files. The demo uses simple text files. Open an instance of Notepad and use the 24 data items from Figure 4, or manually create the data using the information in Figure 2, then save the file as TrainData.txt in the SimpleNeuralNet directory.
Figure 4 The Training Data
|features 1.0 5.0 |labels 1 0 0 |features 1.0 2.0 |labels 1 0 0 |features 3.0 8.0 |labels 1 0 0 |features 4.0 1.0 |labels 1 0 0 |features 5.0 8.0 |labels 1 0 0 |features 6.0 3.0 |labels 1 0 0 |features 7.0 5.0 |labels 1 0 0 |features 7.0 6.0 |labels 1 0 0 |features 1.0 4.0 |labels 1 0 0 |features 2.0 7.0 |labels 1 0 0 |features 2.0 1.0 |labels 1 0 0 |features 3.0 1.0 |labels 1 0 0 |features 5.0 2.0 |labels 1 0 0 |features 6.0 7.0 |labels 1 0 0 |features 7.0 4.0 |labels 1 0 0 |features 3.0 5.0 |labels 0 1 0 |features 4.0 4.0 |labels 0 1 0 |features 5.0 5.0 |labels 0 1 0 |features 4.0 6.0 |labels 0 1 0 |features 4.0 5.0 |labels 0 1 0 |features 6.0 1.0 |labels 0 0 1 |features 7.0 1.0 |labels 0 0 1 |features 8.0 2.0 |labels 0 0 1 |features 7.0 2.0 |labels 0 0 1 The training data looks like: |features 1.0 5.0 |labels 1 0 0 |features 1.0 2.0 |labels 1 0 0 . . . |features 7.0 2.0 |labels 0 0 1
The “|features” tag indicates input values and the “|labels” tag indicates output values. Neither “features” nor “labels” are reserved words, so you could use something like “|predictors” and “|predicteds” if you prefer. Values can be delimited using a blank space or the tab character (the demo data uses blank spaces). Neural networks only understand numeric values so class labels like “red” and “blue” must be encoded as numbers. Neural network classifier models use what’s called 1-of-N encoding. For three possible class labels, you’d use 1 0 0 for the first class (“red” in the demo), 0 1 0 for the second class (“blue”) and 0 0 1 for the third class (“green”). It’s up to you to keep track of how each label value is encoded.
In a non-demo scenario, you might have to worry about input data normalization. In situations where the input values differ greatly in magnitude, you get better results if you scale data so that all magnitudes are roughly the same. For example, suppose the input data is a person’s age (like 32.0) and annual income (like $48,500.00). You could preprocess the data by dividing all age values by 10 and all income values by 10,000, giving normalized input values like (3.20, 4.85). The three most common forms of input data normalization are called z-score normalization, min-max normalization and order of magnitude normalization.
After you’ve created and saved the TrainData.txt file, create and save the following nine items of test data as TestData.txt file in the SimpleNeuralNet directory:
|features 1.0 1.0 |labels 1 0 0 |features 3.0 9.0 |labels 1 0 0 |features 8.0 8.0 |labels 1 0 0 |features 3.0 4.0 |labels 0 1 0 |features 5.0 6.0 |labels 0 1 0 |features 3.0 6.0 |labels 0 1 0 |features 8.0 3.0 |labels 0 0 1 |features 8.0 1.0 |labels 0 0 1 |features 9.0 2.0 |labels 0 0 1
Understanding Neural Network Input and Output
To understand how to use CNTK you need a basic understanding of what a neural network is, how it computes output values and how to interpret those output values. Take a look at Figure 5. The diagram shows the neural network that corresponds to the demo problem.
Figure 5 Neural Network Input and Output
There are two input nodes that hold values (8.0, 3.0), and three output nodes with values (0.3090, 0.0055, 0.6854). The network also has five hidden processing nodes.
Each input node has lines connecting it to all hidden nodes. And each hidden node has lines connecting it to all output nodes. These lines represent numeric constants called weights. Nodes are identified using 0-based indexing, so the top-most nodes are . So, the weight from input to hidden is 2.41 and the weight from hidden to output is -0.85.
Each hidden node and each output node have an additional arrow. These are called the bias values. The bias for hidden is -1.42 and the bias for output is -1.03.
The input-output calculations are best explained with an example. First, hidden node values are computed. The middle hidden node, hidden has value 0.1054 and is calculated by summing the products of all connected inputs and their associated weights plus the bias value, and then taking the hyperbolic tangent (tanh) of that sum:
hidden = tanh( (8.0)(-0.49) + (3.0)(0.99) + 1.04) ) = tanh( -3.92 + 2.98 + 1.04 ) = tanh( 0.1058 ) = 0.1054
The tanh function is called the hidden layer activation function. Neural networks can use one of several different activation functions. In addition to tanh, the other two most common are logistic sigmoid (usually shortened to just “sigmoid”) and rectified linear.
After all the hidden node values are calculated, the next step is calculating the output nodes. First, the sum of the products of connected hidden nodes and their associated weights plus the bias value is computed. For example, output for this step is 1.0653, calculated as:
output = (1.0000)(-2.24) + (-0.1253)(1.18) + (0.1054)(0.55) + (-0.1905)(1.83) + (-1.0000)(-1.23) + 2.51 = (-2.2400) + (-0.1478) + (0.0580) + (-0.3486) + (1.2300) + 2.51 = 1.0653
In the same way, output is calculated to be -2.9547 and output is 1.8619.
Next, the three preliminary output values are scaled so they sum to 1.0, using what’s called the softmax function:
output = e^1.0653 / (e^1.0653 + e^-2.9547 + e^1.8619) = 0.3090 output = e^-2.9547 / (e^1.0653 + e^-2.9547 + e^1.8619) = 0.0055 output = e^1.8619 / (e^1.0653 + e^-2.9547 + e^1.8619) = 0.6854
These three values are interpreted as probabilities. So, for inputs of (8.0, 3.0) and the given weights and bias values, the outputs are (0.3090, 0.0055, 0.6854). The highest probability is the third value so the prediction is the third class, “green,” in this case.
Another way of interpreting the output values is to map them so the highest probability is one and all others are zero. For this example you’d get (0, 0, 1), which maps to the encoded value of “green.”
The process of determining the values of the weights and the biases is called training the network, and that’s what CNTK does.
Creating the Configuration File
Figure 1 gives you an idea of how CNTK is used. In an ordinary command shell, I navigated to the project root directory at C:\Data\SimpleNeuralNet. The project root directory contains files TrainData.txt and TestData.txt and a MakeModel.cntk configuration file. The CNTK tool was invoked by executing the command:
> cntk.exe configFile=MakeModel.cntk makeMode=false
Recall that the system PATH variable knows the location of the cntk.exe program, so it doesn’t have to be fully qualified. The .cntk configuration file has a lot of information. The makeMode=false parameter means to run the program and overwrite any previous results. CNTK command-line arguments are not case-sensitive.
Figure 6 shows the overall structure of the configuration file. The complete listing for the configuration file is presented in Figure 7.
Figure 6 The Structure of the Configuration File
# MakeModel.cntk command=Train:WriteProbs:DumpWeights:Test # system parameters go here Train = [ action="train" BrainScriptNetworkBuilder = [ # define network here ] ] Test = [ # training commands here ] WriteProbs = [ # output commands here ] DumpWeights = [ # output commands here ]
Figure 7 The Training Configuration File
# MakeModel.cntk command=Train:WriteProbs:DumpWeights:Test modelPath = "Model\SimpleNet.snn" deviceId = -1 dimension = 2 labelDimension = 3 precision = "float" # ===== Train = [ action="train" # network description BrainScriptNetworkBuilder = [ FDim = $dimension$ HDim = 5 LDim = $labelDimension$ # define the neural network neuralDef (ftrs) = [ W0 = Parameter (HDim, FDim) b0 = Parameter (HDim, 1) W1 = Parameter (LDim, HDim) b1 = Parameter (LDim, 1) hn = Tanh (W0 * ftrs + b0) zn = W1 * hn + b1 ].zn # specify inputs features = Input (FDim) labels = Input (LDim) # create network myNet = neuralDef (features) # define training criteria and output(s) ce = CrossEntropyWithSoftmax (labels, myNet) err = ErrorPrediction (labels, myNet) pn = Softmax (myNet) # connect to the NDL system. featureNodes = (features) inputNodes = (labels) criterionNodes = (ce) evaluationNodes = (err) outputNodes = (pn) ] # stochastic gradient descent SGD = [ epochSize = 0 minibatchSize = 1 learningRatesPerSample = 0.04 maxEpochs = 500 momentumPerMB = 0.90 ] # configuration for reading data reader = [ readerType = "CNTKTextFormatReader" file = "TrainData.txt" input = [ features = [ dim = $dimension$ format = "dense" ] labels = [ dim = $labelDimension$ format = "dense" ] ] ] ] # test Test = [ action = "test" reader = [ readerType = "CNTKTextFormatReader" file="TestData.txt" randomize = "false" input = [ features = [ dim = $dimension$ format = "dense" ] labels = [ dim = $labelDimension$ format = "dense" ] ] ] ] # log the output node values WriteProbs = [ action="write" reader=[ readerType="CNTKTextFormatReader" file="TestData.txt" input = [ features = [ dim = $dimension$ format = "dense" ] labels = [ dim = $labelDimension$ format = "dense" ] ] ] outputPath = "TestProbs_txt" ] # dump weight and bias values DumpWeights = [ action = "dumpNode" printValues = "true" ]
You can name a CNTK configuration file however you wish, but using a .cntk extension is standard practice. You can use the # character or // token for comments, which don’t span lines. At the top of the configuration file you give a colon-delimited list of modules to run, four in this case:
Notice that the order in which modules are executed doesn’t have to match the order in which they’re defined. Module names (in this example: Train, WriteProbs, DumpWeights, Test) aren’t keywords so you can name modules as you wish. Notice the Train module has an instruction action=“train.” Here, both words are keywords.
The Train module uses a training data file to create the prediction model, so most CNTK configuration files will have a module, usually named Train, that contains an action=“train” command. The Train module will write the resulting model information to disk in a binary format.
The Test module is optional but is usually included when creating a model. The Test module will use the newly created prediction model to evaluate the overall prediction accuracy and prediction error on the training data.
The WriteProbs module is optional. The module will write the actual prediction values for the test data items to a text file in the project root directory. This allows you to see exactly which test cases were correctly predicted and which were not.
The DumpWeights module will write a text file that contains the neural network weights and biases that define the prediction model. You can use this information to uncover trouble spots, and to make predictions on new, previously unseen data.
The MakeModel.cntk configuration file sets up five system parameters:
modelPath = "Model\SimpleNet.snn" deviceId = -1 dimension = 2 labelDimension = 3 precision = "float"
The modelPath variable specifies where to put the resulting binary model and what to call the model. Here, “snn” stands for simple neural network but you can use any extension. The deviceId variable tells CNTK whether to use the CPU (-1) or the GPU (0).
The dimension variable specifies the number of values in an input vector. The labelDimension specifies the number of possible output values. The precision variable can take values of float or double. In most cases float is preferable because it makes training much faster than double.
The Training Module
The demo Train module in the configuration file has three major sub-sections: BrainScriptNetworkBuilder, SGD and reader. These sub-sections define the neural network architecture, how to train the network and how to read training data.
The training module definition begins as:
Train = [ action="train" BrainScriptNetworkBuilder = [ FDim = $dimension$ HDim = 5 LDim = $labelDimension$ ...
The BrainScriptNetworkBuilder section of the Train module uses a special scripting language called BrainScript. Variables FDim, HDim, and LDim hold the number of features, hidden nodes, and label nodes for the neural network. These names aren’t required, so you could use names like NumInput, NumHidden and NumOutput if you wish. The number of input and output nodes is determined by the problem data, but the number of hidden nodes is a free parameter and must be determined by trial and error. The $ token is a substitution operator. The Train module definition continues with:
neuralDef (ftrs) = [ W0 = Parameter (HDim, FDim) b0 = Parameter (HDim, 1) W1 = Parameter (LDim, HDim) b1 = Parameter (LDim, 1) hn = Tanh (W0 * ftrs + b0) zn = W1 * hn + b1 ].zn ...
This is a BrainScript function. Variable W0 is a matrix that holds the input-to-hidden weights. The Parameter function means “construct a matrix.” Variable b0 holds the hidden node bias values. All calculations in BrainScript are performed on matrices, so b0 is a matrix with one column rather than an array.
Variables W1 and b1 hold the hidden-to-output weights and the output node bias values. The values of the hidden nodes are calculated into a variable named hn using a sum of products and the tanh function, as explained earlier. Variable zn holds the pre-softmax output values. The closing bracket-dot-variable notation is how a BrainScript function returns a value. The Train definition continues with:
features = Input (FDim) labels = Input (LDim) myNet = neuralDef (features) ...
Here, the input features and output labels are defined. Variable names “features” and “labels” aren’t keywords, but they must match the strings used in the training and test data files. The neural network is created by calling the neuralDef function. Next, the module defines information that will be used during training:
ce = CrossEntropyWithSoftmax (labels, myNet) err = ErrorPrediction (labels, myNet) pn = Softmax (myNet) ...
The CrossEntropyWithSoftmax function specifies that cross-entropy error should be used when calculating how close calculated output values are to actual output values in the training data. Cross-entropy error is the standard metric but squared error is an alternative.
The ErrorPrediction function instructs CNTK to compute and display the prediction model accuracy (percentage of correct predictions on the training data) and cross-entropy error and perplexity, which are measures of error between calculated outputs and actual outputs.
The Softmax function instructs CNTK to normalize computed output values so they sum to 1.0 and can be interpreted as probabilities. For a neural network classifier, Softmax is used except in extremely rare situations. The training module definition concludes with:
... featureNodes = (features) inputNodes = (labels) criterionNodes = (ce) evaluationNodes = (err) outputNodes = (pn) ]
Here, the required system variables of featureNodes, inputNodes, criterionNodes, and outputNodes, and the optional evaluationNodes, are associated with the user-defined variables.
The stochastic gradient descent (SGD) sub-section defines how CNTK will train the neural network. In the context of a neural network, SGD is usually called back-propagation. The sub-section definition is:
SGD = [ epochSize = 0 minibatchSize = 1 learningRatesPerSample = 0.04 maxEpochs = 500 momentumPerMB = 0.90 ]
The epochSize variable specifies how much of the training data to use. A special value of zero means to use all available training data. The minibatchSize variable specifies how much of the training data to process in each training iteration. A value of one means update the weights and biases after each training item is processed. This is often called “online” or “stochastic” training.
If the value of minibatchSize is set to the number of training items (24 in the case of the demo), then all 24 items would be processed and the results aggregated, and only then would the weights and biases be updated. This is sometimes called “full-batch” or “batch” training. Using a value between one and the training set size is called “mini-batch” training.
The learningRatesPerSample variable specifies how much to adjust the weights and biases on each iteration. The value of the learning rate, along with the other parameters in the SGD sub-section, must be determined by trial and error. Neural networks are typically extremely sensitive to the value of the learning rate—for example, using 0.04 might give you a very accurate prediction system but using 0.039 or 0.041 could give you a very poor system.
The maxEpochs variable specifies how many iterations to perform for training. Too small a value will result in a poor model (“model under-fit”), but too many iterations will over-fit the training data. This leads to a model that predicts the training data very well but predicts new data very poorly.
The momentumPerMB (momentum per mini-batch, not per megabyte as you might assume) is a factor that increases or decreases the amount by which weights and biases are updated. Just like the learning rate, a momentum value must be determined by trial and error, and neural network training is typically extremely sensitive to the value of momentum. The value of 0.90 used by the demo is the default value so the momentumPerMB parameter could have been omitted.
The training module of the demo configuration file concludes by setting the values of the parameters of the reader sub-section:
... reader = [ readerType = "CNTKTextFormatReader" file = "TrainData.txt" input = [ features = [ dim = $dimension$; format = "dense" ] labels = [ dim = $labelDimension$; format = "dense" ] ] ] ] # end Train
The CNTK tool has many different types of readers for use with different types of input data. The meaning of the parameters in the demo reader sub-section should be clear. Notice that I put multiple statements on a single line by using the semicolon delimiter.
The Test Module
To recap to this point, the MakeModel.cntk configuration file has some global system parameters (such as modelPath) plus four modules: Train, Test, WriteProbs, DumpWeights. The Train module has three sub-sections: BrainScriptNetworkBuilder, SGD, reader.
The Test module is mercifully very simple, as you can see in Figure 8.
Figure 8 The Test Module
Test = [ action = "test" reader = [ readerType="CNTKTextFormatReader" file = "TestData.txt" randomize = "false" input = [ features = [ dim = $dimension$ format = "dense" ] labels = [ dim = $labelDimension$ format = "dense" ] ] ] ]
The reader sub-section of the test module should match the reader sub-section of the training module except for the file parameter value and the addition of the randomize parameter. When training with SGD, it’s extremely important that the data items be processed in random order, and true is the default value for randomize. But when walking through the test data there’s no need to randomize the order of the data items.
The test module emits one accuracy metric and two error metrics to the shell. If you refer back to Figure 1, just before the “Action test complete” message, you’ll see:
err = 0.11111111 * 9 ce = 0.33729280 * 9 perplexity = 1.40114927
The err = 0.1111 * 9 means that 11 percent of the nine test data items were incorrectly predicted using the model. In other words, eight out of nine test items were correctly predicted. The training output doesn’t, however, tell you which data items were correctly and incorrectly predicted.
The ce = 0.3372 * 9 means that the average cross-entropy error is 0.3372. For this introduction to CNTK, just think of cross entropy as an error term, so smaller values are better.
The perplexity = 1.4011 is a minor metric. You can think of perplexity as a measure of how strong the predictions are, where smaller values are better. For example, for three possible output values as in the demo, if the prediction is (0.33, 0.33, 0.33) ,you don’t have a strong prediction at all. The perplexity in this case would be 3.0, which is a maximum for three output values.
The WriteProbs Module
The third module in the demo CNTK configuration file is WriteProbs. This module is optional but very useful because it gives you additional information about the predictions made on the test data. The module is defined in Figure 9.
Figure 9 The WriteProbs Module
WriteProbs = [ action="write" reader=[ readerType="CNTKTextFormatReader" file="TestData.txt" input = [ features = [ dim = $dimension$ format = "dense" ] labels = [ dim = $labelDimension$ format = "dense" ] ] ] outputPath = "TestProbs_txt" ]
The WriteProbs module is the same as the test module except for three changes. First, the action parameter is set to “write” instead of “test.” Second, the randomize parameter has been removed (because false is the default). Third, an outputPath parameter has been added.
When the WriteProbs module executes, it will write the exact output values for the test data to the specified file. In this case the file name will have “.pn” appended because that was the variable name used for the output nodes in the training module.
For the nine demo test items, the contents of file TestProbs_txt.pn are:
0.837386 0.162606 0.000008 0.990331 0.009669 0.000000 0.275697 0.724260 0.000042 0.271172 0.728788 0.000040 0.264680 0.735279 0.000041 0.427661 0.572313 0.000026 0.309024 0.005548 0.685428 0.000134 0.000006 0.999860 0.000190 0.000008 0.999801
The first three probability vectors go with the first three test items, which map to the correct output of (1, 0, 0), so the first two test items were predicted correctly. But the third probability vector of (0.27, 0.74, 0.00) maps to (0, 1, 0), so it’s an incorrect prediction.
The next three probability vectors go with test items that have output (0, 1, 0), so all three predictions are correct. Similarly, the last three probability vectors go with (0, 0, 1), so they’re also correct predictions.
To recap, the Test module will emit accuracy and error metrics to the shell, but not tell you which individual test items are correct or give you their error. The WriteProbs module writes exact output values to file and you can use them to determine which test items are incorrectly predicted.
The DumpWeights Module
The last of the four modules in the demo configuration file is DumpWeights, which is defined as:
DumpWeights = [ action = "dumpNode" printValues = "true" ]
When executed, this module will save the trained model’s weights and bias values to file. By default, the filename will be the same as the binary model (SimpleNet.snn in the demo), with “.__AllNodes__.txt” appended, and the file will be saved in the directory specified by the modelPath parameter (“Model” in the demo).
After running the MakeModel.cntk demo, if you open a file explorer and point it to directory \SimpleNeuralNet\Model, you’ll see 503 files:
SimpleNet.snn SimpleNet.snn.__AllNodes__.txt SimpleNet.snn.0 ... SimpleNet.snn.499 SimpleNet.ckp
The SimpleNet.snn is the trained model saved in binary format for use by CNTK. The 500 files that have names that end with a digit, and the one file that ends with a “.ckp” extension, are binary checkpoint files. The idea here is that training a complex neural network can take hours or even days. Recall that the demo set a maxEpochs parameter to 500. The CNTK tool saves training information periodically so in case of a system failure, you don’t have to restart training from scratch.
The first half of the contents of the AllNodes__.txt file for the demo (with a few lines removed) is:
myNet.b0=LearnableParameter [5,1] -1.42185283 1.84464693 1.04422486 2.57946277 1.65035748 ################################################ myNet.b1=LearnableParameter [3,1] 2.51937032 -1.5136646 -1.03768802
These are the values of the hidden node biases (b0) and the output node biases (b1). If you refer back to the neural network diagram in Figure 4, you’ll see where these values are truncated to two decimals. The second half of the AllNodes__.txt file looks like:
myNet.W0=LearnableParameter [5,2] 2.41520381 -0.806418538 -0.561291218 0.839902222 -0.490522146 0.995252371 -0.740959883 1.05180109 -2.72802472 2.81985259 ################################################# myNet.W1=LearnableParameter [3,5] -2.246624 1.186315 0.557211 1.837152 -1.232379 0.739416 0.814771 1.095480 0.386835 2.120146 1.549207 -1.959648 -1.627967 -2.235190 -0.850726
Recall that the demo network has two input values, five hidden nodes and three output nodes. Therefore, there are 2 * 5 = 10 input-to-hidden weights in W0, and there are 5 * 3 = 15 hidden-to-output weights in W1.
Making a Prediction
Once you have a trained model, you can use it to make a prediction. One way to do this is to use the CNTK tool with an “eval” action module. The demo takes this approach. First, a new set of data with a single item is created and saved as file NewData.txt:
|features 4.0 7.0 |labels -1 -1 -1
Because this is new data, the output labels use dummy -1 values. Next, I created a configuration file named MakePrediction.cntk with two modules named Predict and WriteProbs. The complete file is presented in Figure 10.
Figure 10 Making a Prediction
# MakePrediction.cntk stderr = "Log" # write all messages to file command=Predict:WriteProbs modelPath = "Model\SimpleNet.snn" # where to find model deviceId = -1 dimension = 2 labelDimension = 3 precision = "float" Predict = [ action = "eval" reader = [ readerType="CNTKTextFormatReader" file="NewData.txt" input = [ features = [ dim = $dimension$; format = "dense" ] labels = [ dim = $labelDimension$; format = "dense" ] ] ] ] WriteProbs = [ action="write" reader=[ readerType="CNTKTextFormatReader" file="NewData.txt" input = [ features = [ dim = $dimension$; format = "dense" ] labels = [ dim = $labelDimension$; format = "dense" ] ] ] outputPath = "Prediction_txt" # dump with .pn extension ]
When run, the output probabilities are saved in a file named Prediction_txt.pn, which contains:
0.271139 0.728821 0.000040
This maps to output (0, 1, 0), which is “blue.” If you look at the training data in Figure 2, you can see that (4.0, 7.0) could easily be either “red” (1, 0, 0) or “blue” (0, 1, 0).
Two alternative techniques for using a trained model are to use a C# program with the CNTK model evaluation library, or to use a custom Python script that uses the model weights and bias values directly.
To the best of my knowledge, CNTK is the most powerful neural network system for Windows that is generally available to developers. This article has covered only a very small part of what CNTK can do, but it should be enough to get you up and running with simple neural networks and allow you to understand the documentation. The real power of CNTK comes from working with deep neural networks—networks that have two or more hidden layers and possibly complicated connections between nodes.
The CNTK tool is under active development, so some of the details may have changed by the time you read this article. However, the CNTK team tells me that changes will likely be minor and you should be able to modify the demo presented in this article without too much difficulty.
Dr. James McCaffrey works for Microsoft Research in Redmond, Wash. He has worked on several Microsoft products including Internet Explorer and Bing. Dr. McCaffrey can be reached at email@example.com.
Thanks to the following Microsoft technical experts who reviewed this article: Adam Eversole, John Krumm, Frank Seide and Adam Shirey