I just read a New York Times article, From a Songbird, New Insights Into the Brain by Nicholas Wade, and it reminded me of a number of machine understanding issues. So I am going to take a break from my series on the Hierarchical Temporal Memory (HTM) model and muse on intelligence, understanding and song.
The article gives a minimum of information on how genes actually affect the ability of a bird to learn and sing a song. The key revelations of the article are that the zebra finch (Taeniopygia guttata), has had its genome decoded and that about 800 genes change their activity levels in neurons when the finch sings. The article implies that defects in these genes might interrupt singing ability, just as mutated FOXP2 genes in humans cause speech defects. In particular the bird version of FOXP2, if defective, prevents songbirds from singing.
This would seem to go against my basic understanding of how systems of neurons work, which I like to think I is up with the current scientific consensus. Once a basically functioning neural network is in place, I thought genetic activity becomes background activity. Of course the genes would function just like they do in any cell, releasing instructions for making proteins that regulate cell activity. And maybe some of the 800 genes mentioned in Wade's article are ones that would up-regulate or down-regulate any neural activity, not just songs, or learning. But according to David F. Clayton, "these transcripts don't result in the cells producing proteins in the usual way. Instead they seem to modulate the activity of other genes involved in listening."
My (learned from textbooks) model is: genes have blueprints for several types of neurons with varying synapses and neurotransmitters and receptor. Signals are conducted by reasonably well understood mechanisms involving membrane potentials along the neurons and either chemical or electrical transmission at synapses. Genes in the neuron are just caretakers once a system is set up. Learning results from a strengthening or weakening of synaptic thresholds. This is called Hebbian learning, and while there are some theories about how Hebbian learning works at the molecular level, at this point I don't take them as proven.
If the article is true as presented, then individual neurons are more complex than I thought. It is implied that many neurons can function just fine with a mutated FOXP2 genes (every gene would be in every neuron, in fact in every cell), but not neurons that are involved in learning songs. But other neurons learn just fine.
What would distinguish a song-learning neuron from a muscle-coordination learning neuron? I don't know.
As is typical with the New York Times, they want to keep you in their ad ghetto, so they provide no link to the research report, but they say it is in the current issue of Nature. Here is the link: The genome of a songbird
Tuesday, April 6, 2010
Monday, April 5, 2010
Bitworm HTM Example Program, Part 3: Spatial and Temporal Pool Overview
In Understanding Bitworm Part 2 I wrote: "Among the other parameters of CreateNode you can see spatialPoolerAlgorithm and temporalPoolerAlgorithm. I don't think I having used "pooling" yet. Remember I wrote about quantization points? [See How do HTMs Learn?] There are a number of available points both for spatial and temporal patterns in the unsupervised nodes. They need to be populated, and they may change during the learning phase. Pooling appears to be NuSpeak for this process; a pooler algorithm is the code that matches up incoming data to quantization points."
To learn about the pooling algorithms I went to the Numenta Node Algorithm Guide, which is not at the Numenta web site, but installs with NuPIC under \Program Files\Numenta\nupic-1.7.1\share\doc\NodeAlgorithmsGuide.pdf.
There are two node types implementa the NuPIC learning algorithms:
SpatialPoolerNode
TemporalPoolerNode
Some confusion might exist because in more general Numenta discusions a node is treated as a single entity, but both the spatial and the temporal node are needed to create a functioning general node. When the unsupervised node in Bitworm is created with CreateNode(Zeta1Node,...), in effect both a SpatialPoolerNode and a TemporalPoolerNode are created to get full functionality. They refer to both node types being in the same level of the HTM hierarchy. But with you can design more complicated patterns by arranging SpatialPoolerNode and TemporalPoolerNode in an HTM as needed, rather than always pairing them on a level.
"Spatial pooling can be thought of as a quantization process that maps a potentially infinite number of input patters to a finite number of quantization centers." Which in other lit Numenta calls quantization points. Data, in our HTM world, has a spatial aspect. This might not be change along a spatial dimension; space has a more general sense. For instance, the space might be a range of voltages, or sets of voltages from an EKG, for instance. Spatial data usually varies so complexly that we are only interested in the data that is created by objects, or causes. Spatial pooling groups the data into a limited number of causes (or guesses about causes).
Temporal pooling does the same thing with the patterns (objects) identified by the spatial pooler over time sequences. "If pattern A is frequently followed by pattern B, the temporal pooler can assign them to the same group."
A group of nodes forming an HTM level may be able to form invariant representations of objects by combining spatial and temporal pooling. If it can, it passes these representation up the hierarchy.
Once learning is achieved the nodes can be used for inference: they can identify new data as containing patterns that have already been learned.
For now I will focus on the learning phase, since the inference phase is relatively easy to understand if you understand how learning takes place.
Your number of quantization points is set by maxCoincidenceCount. "Storing too few coincidence patterns can result in loss of accuracy due to loss of information. Storing too many coincidence patterns can result in lower generalization and longer training times."
You can also set the sigma parameter. Here's another insight into the algorithm: "each input pattern is compared to the stroed patterns assuming that the stored patterns are centers of radial basis functions with Gaussian tuning. The sigma parameter specifies the standard deviation of the Gaussian [distribution]." So this would work, along with maxDistance, in matching incoming data patterns to existing quantization points.
The clonedNodes parameter allows a set of spatial nodes to use the same coincidence patterns. This allows all the nodes in a level to detect the same causes. In vision that could be moving lines, spots, etc.
The spatial pooler nodes take inputs with the bottomUpIn parameter. The spatial pattern outputs in inference mode are in bottomUpOut; outputs in learning mode go to a temporal pooler.
Your number of temporal groups, or time quantization points, is set by requentedGroupCount.
You can select a variety of algothims to use to compute output probabilities with the temporalPoolerAlgorithm parameter, but it has no impact on the learning algorithm.
There are a number of sequencer parameters that allow control of the of the algorithm. sequencerWindowCount allows for multiple stages of discovery (the default is 10). sequencerWindowLength allows segmentation of the input sequence to look for patterns. sequencerModelComplexity apparently allows you to adjust for how the recognizable patterns are balanced between the spatial and temporal dimensions. Some objects produce mainly spatial patterns, others mainly temporal, and most combine the two to a greater degree.
As with SpatialPoolerNode, you can clone the nodes if you desire. bottomUpIn takes the data in from one or more spatial pooler nodes. bottomUpOut is the resulting vector of real numbers representing "the likelihood that the input belongs to each of the temporal groups of this node."
In addition to parameters, TemporalPoolerNode takes a command: predict, but it works only in inference mode.
Conclusion
Despite not revealing the details of the algorithms, the Guide, plus the previous materials I read, gave me a good overview of what the algorithms need to achieve. I am pretty sure that I would write algorithms that do approximately what the Numenta pooling algorithms do, but since they have been playing with this for years, I would rather catch up by examinging the code inside the Numenta classes.
See also: More on Internal Operations of Nodes
To learn about the pooling algorithms I went to the Numenta Node Algorithm Guide, which is not at the Numenta web site, but installs with NuPIC under \Program Files\Numenta\nupic-1.7.1\share\doc\NodeAlgorithmsGuide.pdf.
There are two node types implementa the NuPIC learning algorithms:
SpatialPoolerNode
TemporalPoolerNode
Some confusion might exist because in more general Numenta discusions a node is treated as a single entity, but both the spatial and the temporal node are needed to create a functioning general node. When the unsupervised node in Bitworm is created with CreateNode(Zeta1Node,...), in effect both a SpatialPoolerNode and a TemporalPoolerNode are created to get full functionality. They refer to both node types being in the same level of the HTM hierarchy. But with you can design more complicated patterns by arranging SpatialPoolerNode and TemporalPoolerNode in an HTM as needed, rather than always pairing them on a level.
"Spatial pooling can be thought of as a quantization process that maps a potentially infinite number of input patters to a finite number of quantization centers." Which in other lit Numenta calls quantization points. Data, in our HTM world, has a spatial aspect. This might not be change along a spatial dimension; space has a more general sense. For instance, the space might be a range of voltages, or sets of voltages from an EKG, for instance. Spatial data usually varies so complexly that we are only interested in the data that is created by objects, or causes. Spatial pooling groups the data into a limited number of causes (or guesses about causes).
Temporal pooling does the same thing with the patterns (objects) identified by the spatial pooler over time sequences. "If pattern A is frequently followed by pattern B, the temporal pooler can assign them to the same group."
A group of nodes forming an HTM level may be able to form invariant representations of objects by combining spatial and temporal pooling. If it can, it passes these representation up the hierarchy.
Once learning is achieved the nodes can be used for inference: they can identify new data as containing patterns that have already been learned.
For now I will focus on the learning phase, since the inference phase is relatively easy to understand if you understand how learning takes place.
SpatialPoolerNode
I just realized the paper I am reading does not actually give the algorithms used. However, the key algorithm is probably related to the maxDistance parameter. Distance here could be ordinary distance, but it is more likely to be distance within a generalized, possible many-dimensional, heterogeneous pattern space. All kinds of problems leap to mind for writing such a generalized algorithm. I would bet that space/data specific algorithms would really help here (sound vs. sight vs. spatial orientation of human fingers), but perhaps if the quantification is always done before the data is fed in, it is just a matter of matching numbers. Anyway, if you have a distance function, you can group the spatial patterns as falling around a set of centers. These centers are your quantization points. As discussed elsewhere these points are flexible; if a lot of patterns fall close to each other, you might want to tighten up the distance parameter because otherwise you don't use all your allocation of quanization points. That should happen automatically, but either it doesn't, so you need to set the maxDistance parameter, or it does but you still have the option of disagreeing with the automatic or default settings.Your number of quantization points is set by maxCoincidenceCount. "Storing too few coincidence patterns can result in loss of accuracy due to loss of information. Storing too many coincidence patterns can result in lower generalization and longer training times."
You can also set the sigma parameter. Here's another insight into the algorithm: "each input pattern is compared to the stroed patterns assuming that the stored patterns are centers of radial basis functions with Gaussian tuning. The sigma parameter specifies the standard deviation of the Gaussian [distribution]." So this would work, along with maxDistance, in matching incoming data patterns to existing quantization points.
The clonedNodes parameter allows a set of spatial nodes to use the same coincidence patterns. This allows all the nodes in a level to detect the same causes. In vision that could be moving lines, spots, etc.
The spatial pooler nodes take inputs with the bottomUpIn parameter. The spatial pattern outputs in inference mode are in bottomUpOut; outputs in learning mode go to a temporal pooler.
TemporalPoolerNode
Temporal pooling has more options than spatial pooling, in particular offering parameters for both first-order and higher-order learning.Your number of temporal groups, or time quantization points, is set by requentedGroupCount.
You can select a variety of algothims to use to compute output probabilities with the temporalPoolerAlgorithm parameter, but it has no impact on the learning algorithm.
There are a number of sequencer parameters that allow control of the of the algorithm. sequencerWindowCount allows for multiple stages of discovery (the default is 10). sequencerWindowLength allows segmentation of the input sequence to look for patterns. sequencerModelComplexity apparently allows you to adjust for how the recognizable patterns are balanced between the spatial and temporal dimensions. Some objects produce mainly spatial patterns, others mainly temporal, and most combine the two to a greater degree.
As with SpatialPoolerNode, you can clone the nodes if you desire. bottomUpIn takes the data in from one or more spatial pooler nodes. bottomUpOut is the resulting vector of real numbers representing "the likelihood that the input belongs to each of the temporal groups of this node."
In addition to parameters, TemporalPoolerNode takes a command: predict, but it works only in inference mode.
Conclusion
Despite not revealing the details of the algorithms, the Guide, plus the previous materials I read, gave me a good overview of what the algorithms need to achieve. I am pretty sure that I would write algorithms that do approximately what the Numenta pooling algorithms do, but since they have been playing with this for years, I would rather catch up by examinging the code inside the Numenta classes.
See also: More on Internal Operations of Nodes
Wednesday, March 31, 2010
Understanding the Bitworm NuPIC HTM Example Program, Part 2: Network Creation Overview
Now that Bitworm is running (See Bitworm Part 1), there are a variety of options. In the Getting Started document the next steps are funning Bitworm with "temporally incoherent data" and then with noisy data. We could go to the data generation functions and play with them, then see how Bitworm reacts. I am more interested in how the network is created, and how it functions internally. An overview of this is covered in "Creating the Untrained HTM Network File," (starting page 21 of Getting Started).
One thing I found helpful is looking at the set of programs in \Numenta\nupic-1.71\share\projects\bitworm\runtimeNetwork\. These include what appears to be an older version of RunOnce.py that uses CreateNetwork.py for network creation. In the "plain" version of RunOnce the network creation segment has just four lines of code:
bitNet = Network()
AddSensor(bitNet, featureVectorLength = inputSize)
AddZeta1Level(bitNet, numNodes = 1)
AddClassifierNode(bitNet, numCategories = 2)
AddSensor(), AddZeta1Level(), and AddClassifier() are imported functions from nupic.network.helpers. They don't seem to be used other than for Bitworm, so they are worth discussing only in the context of understanding the node structure of Bitworm. This network appears to have 4 nodes in the Getting Started (page 22) illustration, but in CreateNetwork.py we find five listed: the sensor node, the category sensor node, an unsupervised node, a supervised node, and an effector node. Getting Started calls 3 of the nodes the same, but instead of supervised and unsupervised, refers to bottom-level and top-level nodes.
Jumping ahead in Getting Started, we find that bitNet = Network() does indeed create an HTM instance that nodes can be added to and arranged in.
The runtime version replaces these with a single command (but a lot more parameters):
createNetwork(untrainedNetwork = untrainedNetwork,
inputSize = inputSize,
maxDistance = maxDistance,
topNeighbors = topNeighbors,
maxGroups = maxGroups) CreateNetwork.py can also be found in the runtime directory. Open it and the first thing you see
CreateNetwork starts by importing nupic.network. So there is a set of one or more functions or classes we can use to get an overview; we'll look inside them later, if necessary. The following line of code gives us our function parameters, some of which are set specifically for Bitworm. So CreateNetwork.py is not a general-purpose HTM creation function.
def createNetwork(untrainedNetwork,
inputSize = 16,
maxDistance = 0.0,
topNeighbors = 3,
maxGroups = 8):
Next we have some agreement with the plain RunOnce.py:
net = Network()
Network() is an imported function that creates the overall data structure for the HTM.
Nodes are created with the CreateNode() function. The type of node - sensor, category sensor, unsupervised (Zeta1Nodes), supervised (Zeta1TopNodes), and effectors - is chosen with the first parameter of CreateNode(). Among the other parameters of CreateNode you can see spatialPoolerAlgorithm and temporalPoolerAlgorithm. I don't think I having used "pooling" yet. Remember I wrote about quantization points? [See How do HTMs Learn?] There are a number of available points both for spatial and temporal patterns in the unsupervised nodes. They need to be populated, and they may change during the learning phase. Pooling appears to be NuSpeak for this process; a pooler algorithm is the code that matches up incoming data to quantization points.
I did not get as far as I would have liked today, but I am beginning to see some structure, and dinner is calling. Instead of calling this entry HTM Creation Classes and Functions, I'll call it an Overview.
One thing I found helpful is looking at the set of programs in \Numenta\nupic-1.71\share\projects\bitworm\runtimeNetwork\. These include what appears to be an older version of RunOnce.py that uses CreateNetwork.py for network creation. In the "plain" version of RunOnce the network creation segment has just four lines of code:
bitNet = Network()
AddSensor(bitNet, featureVectorLength = inputSize)
AddZeta1Level(bitNet, numNodes = 1)
AddClassifierNode(bitNet, numCategories = 2)
AddSensor(), AddZeta1Level(), and AddClassifier() are imported functions from nupic.network.helpers. They don't seem to be used other than for Bitworm, so they are worth discussing only in the context of understanding the node structure of Bitworm. This network appears to have 4 nodes in the Getting Started (page 22) illustration, but in CreateNetwork.py we find five listed: the sensor node, the category sensor node, an unsupervised node, a supervised node, and an effector node. Getting Started calls 3 of the nodes the same, but instead of supervised and unsupervised, refers to bottom-level and top-level nodes.
Jumping ahead in Getting Started, we find that bitNet = Network() does indeed create an HTM instance that nodes can be added to and arranged in.
The runtime version replaces these with a single command (but a lot more parameters):
createNetwork(untrainedNetwork = untrainedNetwork,
inputSize = inputSize,
maxDistance = maxDistance,
topNeighbors = topNeighbors,
maxGroups = maxGroups) CreateNetwork.py can also be found in the runtime directory. Open it and the first thing you see
CreateNetwork starts by importing nupic.network. So there is a set of one or more functions or classes we can use to get an overview; we'll look inside them later, if necessary. The following line of code gives us our function parameters, some of which are set specifically for Bitworm. So CreateNetwork.py is not a general-purpose HTM creation function.
def createNetwork(untrainedNetwork,
inputSize = 16,
maxDistance = 0.0,
topNeighbors = 3,
maxGroups = 8):
Next we have some agreement with the plain RunOnce.py:
net = Network()
Network() is an imported function that creates the overall data structure for the HTM.
Nodes are created with the CreateNode() function. The type of node - sensor, category sensor, unsupervised (Zeta1Nodes), supervised (Zeta1TopNodes), and effectors - is chosen with the first parameter of CreateNode(). Among the other parameters of CreateNode you can see spatialPoolerAlgorithm and temporalPoolerAlgorithm. I don't think I having used "pooling" yet. Remember I wrote about quantization points? [See How do HTMs Learn?] There are a number of available points both for spatial and temporal patterns in the unsupervised nodes. They need to be populated, and they may change during the learning phase. Pooling appears to be NuSpeak for this process; a pooler algorithm is the code that matches up incoming data to quantization points.
I did not get as far as I would have liked today, but I am beginning to see some structure, and dinner is calling. Instead of calling this entry HTM Creation Classes and Functions, I'll call it an Overview.
Monday, March 29, 2010
Understanding the Bitworm NuPIC HTM Example Program , Part 1
Now for my least favorite part of intellectual projects, figuring out someone else's computer code.
When I installed the NuPIC package, a program called Bitworm was run to show that NuPIC installed correctly. Bitworm's main program, RunOnce.py is written in Python script and might be characterized as a simplest meaningul example program, which makes it considerably more complicated than your typical Hello World one liner.
The explanation of, and instructions for running and playing with Bitworm can be found in Getting Started With NuPIC (see pages 14-23). If you open RunOnce.py (mine conveniently opened in IDLE, "Python's Integrated Development Environment") there is a good outline of the process too.
The point is to test an HTM (Hierarchical Temporal Memory) with a simple data set. If you got here without knowing about HTMs, see www.numenta.com or my glosss starting with Evaluating HTMs, Part 1.
Bitworm, or RunOnce, starts by creating a minimal HTM. It does this by importing nodes and components using functions that are part of the NuPIC package. It also sets some parameters which have already been built elsewhere. Then the HTM is trained using another already-created data set of bitworms, which are essentially short binary strings easily visualized if 1's as interpreted as black and 0's as white (or whatever colors you like). Later I'll want to look inside the nodes, and at how nodes are interconnected, in order to understand why this works, but for now I'll keep to the top-level-view.
To test if the NuPIC HTM network learned to distinguish 2 types of bitworms, the training data set is again presented to see what outputs the HTM gives. This is also known as pattern recognition, but in temporal memory talk we prefer the term inference. The bitworms are examples of causes (objects in most other systems), and the HTM infers, from the data, which causes are being presented to it.
That seems like too easy of a trick, infering causes based on the training set, so RunOnce also sees how the trained network does trying to infer cuases from a somewhat different set of data.
As output RunOnce gives us the percentages of correct inferences for the training set and second data set, plus some information about the network itself.
Presuming that you are using Windows and downloaded and setup the NuPIC package (see prior blog entry), to run Bitworm with RunOnce.py, open a command prompt (press Start, in the search box type Command. This should show Command Prompt at the top of the program list. Click it once. Since you will need Command Prompt often, you might also return to Start, right-click on Command Prompt, and Pin to Start Menu. Then it is always in your Start Menu. Or create a shortcut).
Type:
cd %NTA%\share\projects\bitworm
and hit Enter. That will get you in the right directory.
Then run RunOnce by typing the following and hitting Enter:
python RunOnce.py
If you get errors, you need to run the Command Prompt as an Administrator. Close the window, then right click on Command Prompt and choose Run As Administrator. Click through security warnings.
The output says there were two sets off 420 data vectors written. Inference with the training set as input data was 100% accurate. Inference with the 2nd data set was 97.85...% accurate.
As it says, you can also open report.txt. Here's what mine says:
General network statistics:
Network has 5 nodes.
Node names are:
category
fileWriter
level1
sensor
topNode
Node Level1 has 40 coincidences and 7 groups.
Node Level2 has 8 coincidences.
------------------------------
Performance statistics:
Comparing: training_results.txt with training_categories.txt
Performance on training set: 100.00%, 420 correct out of 420 vectors
Comparing: test_results.txt with test_categories.txt
Performance on test set: 97.86%, 411 correct out of 420 vectors
------------------------------
Getting groups and coincidences from the node Level1 in network ' trained_bitworm.xml
====> Group = 0
1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0
0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0
0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0
0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0
0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1
When I installed the NuPIC package, a program called Bitworm was run to show that NuPIC installed correctly. Bitworm's main program, RunOnce.py is written in Python script and might be characterized as a simplest meaningul example program, which makes it considerably more complicated than your typical Hello World one liner.
The explanation of, and instructions for running and playing with Bitworm can be found in Getting Started With NuPIC (see pages 14-23). If you open RunOnce.py (mine conveniently opened in IDLE, "Python's Integrated Development Environment") there is a good outline of the process too.
The point is to test an HTM (Hierarchical Temporal Memory) with a simple data set. If you got here without knowing about HTMs, see www.numenta.com or my glosss starting with Evaluating HTMs, Part 1.
Bitworm, or RunOnce, starts by creating a minimal HTM. It does this by importing nodes and components using functions that are part of the NuPIC package. It also sets some parameters which have already been built elsewhere. Then the HTM is trained using another already-created data set of bitworms, which are essentially short binary strings easily visualized if 1's as interpreted as black and 0's as white (or whatever colors you like). Later I'll want to look inside the nodes, and at how nodes are interconnected, in order to understand why this works, but for now I'll keep to the top-level-view.
To test if the NuPIC HTM network learned to distinguish 2 types of bitworms, the training data set is again presented to see what outputs the HTM gives. This is also known as pattern recognition, but in temporal memory talk we prefer the term inference. The bitworms are examples of causes (objects in most other systems), and the HTM infers, from the data, which causes are being presented to it.
That seems like too easy of a trick, infering causes based on the training set, so RunOnce also sees how the trained network does trying to infer cuases from a somewhat different set of data.
As output RunOnce gives us the percentages of correct inferences for the training set and second data set, plus some information about the network itself.
Presuming that you are using Windows and downloaded and setup the NuPIC package (see prior blog entry), to run Bitworm with RunOnce.py, open a command prompt (press Start, in the search box type Command. This should show Command Prompt at the top of the program list. Click it once. Since you will need Command Prompt often, you might also return to Start, right-click on Command Prompt, and Pin to Start Menu. Then it is always in your Start Menu. Or create a shortcut).
Type:
cd %NTA%\share\projects\bitworm
and hit Enter. That will get you in the right directory.
Then run RunOnce by typing the following and hitting Enter:
python RunOnce.py
If you get errors, you need to run the Command Prompt as an Administrator. Close the window, then right click on Command Prompt and choose Run As Administrator. Click through security warnings.
The output says there were two sets off 420 data vectors written. Inference with the training set as input data was 100% accurate. Inference with the 2nd data set was 97.85...% accurate.
As it says, you can also open report.txt. Here's what mine says:
General network statistics:
Network has 5 nodes.
Node names are:
category
fileWriter
level1
sensor
topNode
Node Level1 has 40 coincidences and 7 groups.
Node Level2 has 8 coincidences.
------------------------------
Performance statistics:
Comparing: training_results.txt with training_categories.txt
Performance on training set: 100.00%, 420 correct out of 420 vectors
Comparing: test_results.txt with test_categories.txt
Performance on test set: 97.86%, 411 correct out of 420 vectors
------------------------------
Getting groups and coincidences from the node Level1 in network ' trained_bitworm.xml
====> Group = 0
1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0
0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0
0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0
0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0
0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0
0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1
====> Group = 1
0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0
0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1
====> Group = 2
0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0
0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0
0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0
0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0
0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0
0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0
====> Group = 3
0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0
0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0
0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
====> Group = 4
0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0
0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0
0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0
0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0
0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0
0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1
====> Group = 5
0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0
0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0
0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0
0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0
0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1
====> Group = 6
0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1
Full set of Level 2 coincidences:
0 -> [ 0. 0. 1. 0. 0. 0. 0. 0.]
1 -> [ 1. 0. 0. 0. 0. 0. 0. 0.]
2 -> [ 0. 0. 0. 1. 0. 0. 0. 0.]
3 -> [ 0. 0. 0. 0. 0. 1. 0. 0.]
4 -> [ 0. 1. 0. 0. 0. 0. 0. 0.]
5 -> [ 0. 0. 0. 0. 0. 0. 1. 0.]
6 -> [ 0. 0. 0. 0. 0. 0. 0. 1.]
7 -> [ 0. 0. 0. 0. 1. 0. 0. 0.]
Monday, March 22, 2010
Downloading and Installing NuPIC on a Windows computer
At last it is time for me to start playing with NuPIC (Numenta Platform for Intelligent Computing). First I need to get a working copy onto my computer, which is running Windows Vista 32-bit Home Premium on an AMD Athlon dual-core processor.
The main Numenta page is http://www.numenta.com/. From there procede to the NuPIC downloads page. You need to log in, so register if you haven't already done so. The Windows version is 32 bit; there are also Mac and Linux (both 32 and 64 bit) versions available. The Windows version file size is 112 MB, which took my satelite Internet over 20 minutes to download. Then you need NuPIC installation instructions. If you are like me, go straight to Windows NuPIC installation instructions. You also need your license file, which is sent to your email address when you register and download NuPIC.
Oh boy, it come with a Python installer. Another programming language to learn (I hope not). Add it, in my case, to APL, Cobol, Fortran, PL1, Pascal, Basic, C, C++, PHP, Javascript ... I hope I have not forgotten anyone important.
After downloading and running the installation file, I did run into a hitch in the installation wizard. After the Python installation I got the old "not responding" error in the wizard window. Eventually, after closing some other application windows, I saw that a secondary Python window had popped up and needed to have its Continue buttons pressed. Once that was done the "not responding" error in the main install window went away and I completed the install successfully.
That leaves Python on my system at C:/Python25/
and NuPIC on my system at C:/Program Files/Numenta/nupic-1.7.1/
It also means the first example, BitWorm, ran successfully, although I did not learn anything from it yet.
Next up: the BitWorm example in detail
The main Numenta page is http://www.numenta.com/. From there procede to the NuPIC downloads page. You need to log in, so register if you haven't already done so. The Windows version is 32 bit; there are also Mac and Linux (both 32 and 64 bit) versions available. The Windows version file size is 112 MB, which took my satelite Internet over 20 minutes to download. Then you need NuPIC installation instructions. If you are like me, go straight to Windows NuPIC installation instructions. You also need your license file, which is sent to your email address when you register and download NuPIC.
Oh boy, it come with a Python installer. Another programming language to learn (I hope not). Add it, in my case, to APL, Cobol, Fortran, PL1, Pascal, Basic, C, C++, PHP, Javascript ... I hope I have not forgotten anyone important.
After downloading and running the installation file, I did run into a hitch in the installation wizard. After the Python installation I got the old "not responding" error in the wizard window. Eventually, after closing some other application windows, I saw that a secondary Python window had popped up and needed to have its Continue buttons pressed. Once that was done the "not responding" error in the main install window went away and I completed the install successfully.
That leaves Python on my system at C:/Python25/
and NuPIC on my system at C:/Program Files/Numenta/nupic-1.7.1/
It also means the first example, BitWorm, ran successfully, although I did not learn anything from it yet.
Next up: the BitWorm example in detail
Thursday, March 18, 2010
Evaluating HTMs: CPT details; specific memories
This is the last essay on "Hierarchical Temporary Memory, Concepts, Theory, and Terminology" by Hawkins and George. Here I review two issues raised in Section 6, Questions: details on how conditional probability tables (CPTs) work with HTMs, and why humans can have specific memories of events, but HTMs as currently described do not. The first is very technical, the second has more interesting implications.
CPTs are used in Bayesian networks to allow the belief (a set of probabilities about causes) of one node to modify another node. They can be create from algorithms using probability theory in conjunction with known data, the beliefs already established in the two nodes. In HTMs they are learned. As the quantization points are learned, the CPTs are the same as the learned quantization function that links the points to the temporal variables. There are two separate algorithms, but they run in parallel, creating an output to send up the hierarchy to the next node. This will probably because more transparent when we look at the actual algorithms used by the HTM nodes.
It is claimed that humans can remember specific details and events, as well as model the world, whereas HTMs don't keep specific memories. The authors talk about how the human brain might accomplish this feat, and how the capability might be added to HTMs. I instead wonder whether they are right about humans remembering specific details of specific events.
It certainly is the naive view, and since I subscribe to the common sense school of philosophy (with my own updates), assailing the view is mainly just an exercise at this point. But consider this: numerous studies have shown that eye witnesses are unreliable. I suspect that a visual memory is not like a photograph, nor is the memory of a song like a recording, nor is the memory of an event a sort of whole sensory record of a period of time. I believe humans do remember things, and can train their memories to be more like recorders, and in particular can memorize speeches, poems, sequences of numbers, etc. But I think the HTM model actually is at least approximately the way that the brain works. Different levels of the neurological system remember, or become capable of recognizing, different levels of details about things. There are mechanisms in the brain that allow recall of these memories on different levels. But I would be careful about assuming that because we can recall an event (or picture, etc.) in more or less detail we must be calling up a recording. We seldom learn anything of any length in detail by simply hearing or seeing it. If you have memorized that the first digits of pi are 3.14159, what is that a recording of? The words for the number sequence as sounded out in English, a visual memory of seeing this number in a particular typeface in a particular paragraph on paper of a particular tone, or an abstract memory corresponding to abstract groups of abstract units? Typically we must be exposed to something many times to be able to remember it or recognize it, just like an HTM.
I think we are so good at reconstructing certain types of memories that we think we have photograph or video-like recordings of them. That is why eye witnesses think they are telling the truth, when they often substitute details from other events into a "memory" [notably, a face from a lineup that actually was not present at a crime scene]. That is why our memories are so often mistaken (I could have sworn I turned off that burner!) and why we can recall so much without having a roomful of DVDs in our brains. Our memories are largely indistinguishable from our intelligence, and are both fragmented in detail and yet easily molded into a whole as necessary. This is why recognition is usually much better than recall.
The more I study HTMs, the more curious I get. I don't know what the next step will be in my investigations, but hopefully I'll let you know soon.
CPTs are used in Bayesian networks to allow the belief (a set of probabilities about causes) of one node to modify another node. They can be create from algorithms using probability theory in conjunction with known data, the beliefs already established in the two nodes. In HTMs they are learned. As the quantization points are learned, the CPTs are the same as the learned quantization function that links the points to the temporal variables. There are two separate algorithms, but they run in parallel, creating an output to send up the hierarchy to the next node. This will probably because more transparent when we look at the actual algorithms used by the HTM nodes.
It is claimed that humans can remember specific details and events, as well as model the world, whereas HTMs don't keep specific memories. The authors talk about how the human brain might accomplish this feat, and how the capability might be added to HTMs. I instead wonder whether they are right about humans remembering specific details of specific events.
It certainly is the naive view, and since I subscribe to the common sense school of philosophy (with my own updates), assailing the view is mainly just an exercise at this point. But consider this: numerous studies have shown that eye witnesses are unreliable. I suspect that a visual memory is not like a photograph, nor is the memory of a song like a recording, nor is the memory of an event a sort of whole sensory record of a period of time. I believe humans do remember things, and can train their memories to be more like recorders, and in particular can memorize speeches, poems, sequences of numbers, etc. But I think the HTM model actually is at least approximately the way that the brain works. Different levels of the neurological system remember, or become capable of recognizing, different levels of details about things. There are mechanisms in the brain that allow recall of these memories on different levels. But I would be careful about assuming that because we can recall an event (or picture, etc.) in more or less detail we must be calling up a recording. We seldom learn anything of any length in detail by simply hearing or seeing it. If you have memorized that the first digits of pi are 3.14159, what is that a recording of? The words for the number sequence as sounded out in English, a visual memory of seeing this number in a particular typeface in a particular paragraph on paper of a particular tone, or an abstract memory corresponding to abstract groups of abstract units? Typically we must be exposed to something many times to be able to remember it or recognize it, just like an HTM.
I think we are so good at reconstructing certain types of memories that we think we have photograph or video-like recordings of them. That is why eye witnesses think they are telling the truth, when they often substitute details from other events into a "memory" [notably, a face from a lineup that actually was not present at a crime scene]. That is why our memories are so often mistaken (I could have sworn I turned off that burner!) and why we can recall so much without having a roomful of DVDs in our brains. Our memories are largely indistinguishable from our intelligence, and are both fragmented in detail and yet easily molded into a whole as necessary. This is why recognition is usually much better than recall.
The more I study HTMs, the more curious I get. I don't know what the next step will be in my investigations, but hopefully I'll let you know soon.
Tuesday, March 9, 2010
Why Time is Necessary for HTM's Learning
In "Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 5, Why is Time Necessary to Learn? clarifies the role of temporal sequences and temporal pattern points in both learning and recognition (inference) by HTMs.
The authors use a good example, a cut versus uncut watermelon, to distinguish between pattern matching algorithms, and how HTM's learn to recognize patterns that are created by objects (causes, in HTM vocabulary). Any real world animal, when viewed, presents an almost infinite number of different visual representations. If you use a type of animal, say horses instead of a particular horse, the data is even more divergent. Pattern matching does not work well. But allow an HTM to view an animal or set of animals over time, and it will build up the ability to recognize an animal from different viewpoints: front, back, profile, or against most sorts of backgrounds.To do that requires data presented over time. Data that is close sequentially should be similar but not identical. Early data might be of a horse, head on, far away, which gradually resolves to a horse viewed close up. So over time the HTM can capture the totality of the horse.
Combining recognition of causes with names given by an outside source is also considered. Thus no amount of viewing a horse will tell an HTMs that human's call the thing "horse." You can do "supervised learning" with an HTM, training it to associate a name with a cause by imposing states on the top level of the HTM hierarchy. But it should be a simple extension to have a vocabulary learning HTM and an object learning HTM in a hierarchy with a learn-to-name-the-object HTM on top.
Once an HTM has learned to recognize images (or other types of data) it can recognize static images (or data). The authors say "The Belief Propagation techniques of the hierarchy will try to resolve the ambiguity of which sequences are active." I am not clear on that. It seems to me that static temporal patterns happen often enough in the real world so that some temporal pattern points will represent static causes. If the horse stands still in the real world, it would generate such temporal patterns. As the data goes up the hierarchy it tends to filter out ambiguity and stabilize causes, so a leaping horse should still be the same as a frozen image of a leaping horse at some point high enough in the hierarchy.
Section 6 is a sort of frequently asked questions part of the paper. I'm not sure if I'll cover all the sections or in what order, and I do want to go back to section 3.3 on belief propagation before closing out this series.
The authors use a good example, a cut versus uncut watermelon, to distinguish between pattern matching algorithms, and how HTM's learn to recognize patterns that are created by objects (causes, in HTM vocabulary). Any real world animal, when viewed, presents an almost infinite number of different visual representations. If you use a type of animal, say horses instead of a particular horse, the data is even more divergent. Pattern matching does not work well. But allow an HTM to view an animal or set of animals over time, and it will build up the ability to recognize an animal from different viewpoints: front, back, profile, or against most sorts of backgrounds.To do that requires data presented over time. Data that is close sequentially should be similar but not identical. Early data might be of a horse, head on, far away, which gradually resolves to a horse viewed close up. So over time the HTM can capture the totality of the horse.
Combining recognition of causes with names given by an outside source is also considered. Thus no amount of viewing a horse will tell an HTMs that human's call the thing "horse." You can do "supervised learning" with an HTM, training it to associate a name with a cause by imposing states on the top level of the HTM hierarchy. But it should be a simple extension to have a vocabulary learning HTM and an object learning HTM in a hierarchy with a learn-to-name-the-object HTM on top.
Once an HTM has learned to recognize images (or other types of data) it can recognize static images (or data). The authors say "The Belief Propagation techniques of the hierarchy will try to resolve the ambiguity of which sequences are active." I am not clear on that. It seems to me that static temporal patterns happen often enough in the real world so that some temporal pattern points will represent static causes. If the horse stands still in the real world, it would generate such temporal patterns. As the data goes up the hierarchy it tends to filter out ambiguity and stabilize causes, so a leaping horse should still be the same as a frozen image of a leaping horse at some point high enough in the hierarchy.
Section 6 is a sort of frequently asked questions part of the paper. I'm not sure if I'll cover all the sections or in what order, and I do want to go back to section 3.3 on belief propagation before closing out this series.
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