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WOLFRAM NOTEBOOK
Machine Learning, Neural Networks, and LLMs in Wolfram Mathematica
Machine Learning, Neural Networks, and LLMs in Wolfram Mathematica
Retrieving and Shaping Data
Retrieving and Shaping Data
This data will be used a couple times throughout:
In[]:=
rawdata=EntityValue[FilteredEntityClass["Galaxy",EntityFunction[g,MemberQ[{"elliptical","spiral","barred spiral"},g["Shape"]]]],EntityFunction[e,e["Image"]->e["Shape"]]];
In[]:=
readydata=Select[rawdata,Information[First[#],"ImageDimensions"]==={150,150}&&Information[First[#],"ColorSpace"]==="RGB"&];
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rawimages=Map[First,readydata];
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cropped=Map[ImageCrop[#,{64,64}]&,rawimages];
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Take[cropped,10]
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Functions for Statistics and Built-In Machine Learning
Regression and Modeling
Regression and Modeling
Many methods here fall under “traditional” machine learning that pre-date neural networks
Create fitted models from data:
data=;model=LinearModelFit[data,{1,x,,,},x]
2
x
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x
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x
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FittedModel
Use computed properties of a fitted model:
mae=Mean[Abs[model["FitResiduals"]]]
Out[]=
0.696983
Visualize the model and original data:
ShowPlot{model[x],model[x]+2mae,model[x]-2mae},{x,0,10},,ListPlot[data,PlotStyle->Red]
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Create predictor functions using a variety of methods:
pf=Predict[data[[All,1]]->data[[All,2]]]
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PredictorFunction
Use computed properties of the predictor function:
σ[x_]:=StandardDeviation[pf[x,"Distribution"]];ShowPlot{pf[x],pf[x]+2σ[x],pf[x]-2σ[x]},{x,0,10},,ListPlot[data,PlotStyle->Red]
Out[]=
Cluster Analysis
Cluster Analysis
Find clusters in data:
ListPlotFindClusters
Out[]=
Specify method and other options for greater control:
ListPlotFindClusters,Method->"DBSCAN"
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Analyze clusters in the context of graphs:
CommunityGraphPlot[ExampleData[{"NetworkGraph","JazzMusicians"}]]
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Analyze components in images:
ClusteringComponents
,7//Colorize
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Dimensionality Reduction
Dimensionality Reduction
A color function shows that the structure of this data can be embedded in a lower dimension space:
Create a dimension reducing function for this dataset:
Apply the dimension reducing function to the data:
Detect Anomalous Data
Detect Anomalous Data
Retrieve information from a classic dataset:
Create an anomaly detection function:
Use the detector function to find anomalies in the dataset:
Visualize the data and decision boundary:
Impute Values for Missing Data
Impute Values for Missing Data
Simulate missing data by removing information from existing data:
Learn a distribution to predict missing values:
Synthesize missing values and plot the results:
Computer Vision
Computer Vision
Highlight objects in an image:
Import pre-trained semantic segmentation networks form the Wolfram Neural Net Repository:
Use the imported network to perform semantic segmentation and colorize the results:
Signal Processing
Signal Processing
Common transforms and signal processing techniques are also worth mentioning for this audience:
Apply common filters and transforms to clean a signal:
For those of you who are interested in audio signals specifically, these are also supported:
Import an audio file:
Detect activity specified by a particular parameter, in this case detecting a speaking voice:
Plot the active intervals with red rectangles:
Working with Neural Networks
This example builds up to the task of synthetic data generation. To read more about Generative Adversarial Networks, check out this blog post:
Generative Adversarial Networks (GANs) in the Wolfram Language
Generative Adversarial Networks (GANs) in the Wolfram Language
For many other applications of neural networks to astronomy, Smith and Geach (2023) have a great review article:
https://royalsocietypublishing.org/doi/10.1098/rsos.221454
https://royalsocietypublishing.org/doi/10.1098/rsos.221454
Building Blocks of Neural Networks
Building Blocks of Neural Networks
Neural networks are made of layers. Many different kinds of specialized layers exist for particular architectures.
With some restrictions on the functions supported, you can define (almost) any function that you like applied to the inputs:
Composing a Network
Composing a Network
In Wolfram Language, layers are composed into either a NetChain or NetGraph
Using a Generative Adversarial Network (GAN) for Synthetic Data
Using a Generative Adversarial Network (GAN) for Synthetic Data
Define a Generator network (creates synthetic data from noise)
Define a Discriminator network (decides if data is real or synthetic)
Combine the two into a GAN architecture
Training a Network
Training a Network
Using an autoencoder to get a reasonable mapping of data to a latent space:
Using an autoencoder to get a reasonable mapping of data to a latent space:
Define an autoencoder
Train it
Get the trained network:
This imports the autoencoder trained before the presentation. Remember to export your networks. ONNX or WLNET file formats are possibly the most convenient for this.
Note: For many purposes, you may want a variational autoencoder (VAE) instead
Note: For many purposes, you may want a variational autoencoder (VAE) instead
You can read more about implementing those in this community post:
https://community.wolfram.com/groups/-/m/t/1379189
https://community.wolfram.com/groups/-/m/t/1379189
Use the pre-trained autoencoder to give the GAN training a head start:
Define a series of functions for generating the training data. The training data must include the real images and latent data from a distribution:
In other words, each real image is paired with some noise from the latent space:
Finally, train the GAN. This mini-example took ~1 hour to train on a GPU.
Create a collage of synthetic galaxy images. Starting with a VAE, using larger networks, or more high quality training examples are next steps to improve a quick prototype to a part of a pipeline.
Remember you will want to export your trained network to save the weights and biases after all the training time has been spent:
Neural Net Repository and Net Surgery
Neural Net Repository and Net Surgery
Rather than training networks from scratch or redesigning your own architecture, it is often helpful to leverage a pre-trained network.
You can find many pre-trained networks for various tasks in the Wolfram Neural Net Repository:
https://resources.wolframcloud.com/NeuralNetRepository
You can find many pre-trained networks for various tasks in the Wolfram Neural Net Repository:
https://resources.wolframcloud.com/NeuralNetRepository
See if the learned representations of another network can be used for a new task
See if the learned representations of another network can be used for a new task
Replace only the last layers to change the number of classes represented by the network from 1000 down to 3:
Split the data into test and training sets for this supervised learning task:
Train only the new layers of the network to keep all the previously learned representations
Remember to Export and then Import the previously trained network between sessions:
See how the classifier performed:
Notice how with this very small training run, transfer learning failed to capture the difference between spiral and barred spiral galaxies; however it did capture the difference between elliptical and all types of spiral structure reasonably well:
Tools for Use with Large Language Models
Last but not least, LLMs can be a helpful part of workflows:
LLMs for Code Assistance
LLMs for Code Assistance
Have the LLM act as a code assistant to work through an existing example.
Please explain the code above to a student new to Wolfram Language. Be concise.
Using this example, what would the student do fix the right end of the beam as well as the left end? Make this adjustment to the code and use only gamma to represent the boundary condition. Reproduce all the code with these adjustments.
Data Retrieval
Data Retrieval
Write code to create a dataset that contains the "Image" entity property and "HubbleType" entity property for 20 randomly selected galaxies using RandomEntity. Use DocumentationLookup tool if needed.