"Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 4, How does each node discover and infer causes?, covers questions about the internal operations of nodes that were raised or partly covered in earlier sections.
Basically, each node simulataneously does both learning and recognition of spatial and temporal patterns. The output is information about the patterns that can be sent up and down the hierarchy of nodes.
Spatial patterns do not necessarilly mean space as in space-time continuum, although the example used in the essay is of a two dimensional visual space. Space is used in the mathematical sense. The data can be anything quantifiable. The space could be any number of dimensions. For instance the maximum daily surface temperature of the earth would consitute a space within a certain range of degrees Centigrade, to whatever desired level of precision, on a spherical 2D grid representing the surface of the earth to any desired degree of precision. The time sequence in this example would be daily samples. In a digital audio example the time sequence intervals might be something on the order of .0001 seconds.
The node has a significant number of "quantization points" available to categorize the spatial data. Only the most common data patterns, up to the number of quantization points, will be learned. Anything that is not one of the learned patterns will be assigned a probability that it is one of the learned patterns plus some noise.
Having leaned the quantization points, the node can start looking for common temporal sequences of them. Again, a limited number of points or memory units are allocated for learned temporal patterns. I can't find where the authors give them a name, so at the risk of being corrected later, I'll call them temporal pattern points. Again, temporal pattern matches don't need to be exact; some noise is tolerated.
Once learning has taken place (learning can continue), the node can work to infer causes. The patterns held in the quantization points, as well as the patterns of these in time held in the temporal pattern point, can be causes (or call them objects, which is the more typical if less precise vocabulary.). As time passes the data changes and the causes output to the higher level node(s) of the hierarchy change.
Another very important idea to wrap your head around is that the node, and the HTM, need to deal with probabilities. You might get an exact match with 100% probability, you might even be able to design special situations where you don't need to deal with probability. But the whole point of HTMs (from an engineering standpoint) is to be able to deal with complex real world data, in a manner similar to the human brain. So whether dealing with matching a spatial pattern to the quantization points, or a temporal pattern to the temporal pattern points, you need to think in terms of probability. There is a 42% change that it matches point 7, an 18% change it matches point 42, and a 40% chance that it matches none of the quantization points. With the temporal pattern it gets more complicated, since you can't assume that just because a spatial pattern is most likely point 7, it is not in a temporal pattern that goes, say 49, 3, 7 instead of 49, 3, 42.
Hey, but that is what computers are handy for, figuring probabilities and keeping track of them.
The output to the higher-level nodes might be though of as: There is a 12% probability that we are seeing temporal pattern point 7, 35% it is point 16, 48% it is point 34, and 5% it is point 49. It seems to us to be messy, but it is exactly the sort of thing the next level up is looking for. We call it a vector output, but it also can be thought as a set of data pairing probabilities and points that are arbitrarilly assigned to spatial-temporal patterns.
Hey, I think I am beginning to understand this stuff.
Which brings me back to one of those basic science and philosophy questions that made me interested in machine understanding in the first place. If everything is abstract, how do we (the HTM or a living human brain) get the picture of the world that seems all so familiar to us? If all the world does it produce neuronal impulses in our bodies, what makes red different from blue, and the junk on my desk resolve easily into envelopes, pens, gadgets, fake wood patterns and a host of other things?
Next: Why is Time Necessary to Learn?
Monday, March 8, 2010
Saturday, March 6, 2010
Evaluating HTMs, Part 4: The Importance of Hierarchy
See also Part 1, Part 2, Part 3
"Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 3, Why is Hierarchy Important?, draws a detailed picture of the relationship between the structuring of the nodes of an HTM and real-world (or even virtual world) data. To stick closely to the subject of hierarchy, I'll cover subsections 1, 2, and 4, here, leaving subsection 3, Belief Propagation, to be treated as a separate topic.
If you don't understand the concept of hierarchy, try Hierarchy at Wikipedia.
I think it is best to start with "3.2 The hierarchy of the HTM matches the spatial and temporal hierarchies of the real world." Hierarchies are not always patterns humans impose upon the sensory data we receive from the external world. Each whole has its parts, as a face has eyes, ears, a mouth and nose as well as other features.
The world itself embodies the principle of locality. Spatial and temporal closeness and distance can be interpreted as a hierarchy, if a more abstract one. One might define "close" as meaning within a nanometer and nano secord, with hierarchical levels covering distances and times grouped by factors of twos or tens, up to the size of the cosmos. Or whatever is convenient for the data you are learning about. The bottom layer of the HTM hierarchy learns from the smallest divisions, and passes its interpretations (beliefs) up the hierarchy. Thus in music if the data is already in the form of notes, the bottom layer might deal with two-note sequences, the next layer with 4 note sequences, then 8 notes, 16 notes, 32 notes, on up to the number of notes in a symphony.
Music offers a one-dimensional (or two, if you plot the frequency of the notes) example, but HTMs should be able to deal with higher numbers of dimensions as long as the causes have a hierarchical structure.
Note the design guidance at the end of the section. Our HTM designs should be targetted at problems have appropriate space-time structure. The designs need to capture local correlations first. And the hierarchical structure of nodes should be designed to efficiently model the problem space.
Now back to 3.1, "Shared representaions lead to generalization and storage efficiency." The belief is that HTMs are efficient at learning complex data and causes. In other words, HTMs scale well. This can be, in computer hardware terms, memory size and computing power. This is possible because the lower levels of the HTM break interpret the data into what might be called micro-causes. Or cause modules. These modules can be reused by any of the causes found much higher in the HTM. This mimics what we know of the human visual pathway, where at the lower levels nerves appear to respond to small features on the retina like spots, short lines at various angles, simple changes in contrast, etc. Using the human face as an example, the HTM might recognize eyes, lips, proportions, etc., and categories within these features. Almost all six billion human faces presently on earth would be interpretable in terms of these basic components and their spatial relationships. Two represent each of the faces you don't need 6 billion 10 megapixel bitmap pictures. You just need 6 billion summaries that could probably be represented with a few bytes of data. Recognition would resolve to summarizing the new picture of a face and then finding the closest summary already held by the HTM.
The authors point out that "the system cannot easily learn to recognize new objects that are not made up of previously learned sub-objects." Which we see in human behavior from the household chore level right up to big pictures like evolution and relativity staring large groups of scientists in the face for decades before a Darwin or Einstein said "I recognize a new, high-level causation here."
Within the section is a helpful explanation about "quantization points," which I said were left unclear in section 2. It gives the reason for having a much lower number of quantization points than there are possible events in the event space. It points out that in a 10 by 10 square of binary (black or white) pixels, there are 2 to the 100th different patterns. By limiting the number of quantization points you force the node to group every input image into a type of pattern (some examples could be lines with various orientations, spots that move in a particular direction, more black on the right or left, etc.). These would be "the most common patterns seen by the node during training."
In section 3.4 the authors give an introductory look at the idea that HTMs can pay attention to certain aspects of the data. In other words, just as you might focus on your newspaper while riding public transportation to work, an HTM can pick some level of the hierarchy of data to focus on. Suppose it is a facial recognition HTM and it thinks a face present to it could be George or Herbert. By focussing on a particular aspect of the face, say the nose-to-lips difference, it might become more certain that the face belongs to George. People can do this both consciously and unconsicously.
It an HTM could do that, it would be really cool.
Next: Evaluating HTMs, Part 5: Belief Propagation
"Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 3, Why is Hierarchy Important?, draws a detailed picture of the relationship between the structuring of the nodes of an HTM and real-world (or even virtual world) data. To stick closely to the subject of hierarchy, I'll cover subsections 1, 2, and 4, here, leaving subsection 3, Belief Propagation, to be treated as a separate topic.
If you don't understand the concept of hierarchy, try Hierarchy at Wikipedia.
I think it is best to start with "3.2 The hierarchy of the HTM matches the spatial and temporal hierarchies of the real world." Hierarchies are not always patterns humans impose upon the sensory data we receive from the external world. Each whole has its parts, as a face has eyes, ears, a mouth and nose as well as other features.
The world itself embodies the principle of locality. Spatial and temporal closeness and distance can be interpreted as a hierarchy, if a more abstract one. One might define "close" as meaning within a nanometer and nano secord, with hierarchical levels covering distances and times grouped by factors of twos or tens, up to the size of the cosmos. Or whatever is convenient for the data you are learning about. The bottom layer of the HTM hierarchy learns from the smallest divisions, and passes its interpretations (beliefs) up the hierarchy. Thus in music if the data is already in the form of notes, the bottom layer might deal with two-note sequences, the next layer with 4 note sequences, then 8 notes, 16 notes, 32 notes, on up to the number of notes in a symphony.
Music offers a one-dimensional (or two, if you plot the frequency of the notes) example, but HTMs should be able to deal with higher numbers of dimensions as long as the causes have a hierarchical structure.
Note the design guidance at the end of the section. Our HTM designs should be targetted at problems have appropriate space-time structure. The designs need to capture local correlations first. And the hierarchical structure of nodes should be designed to efficiently model the problem space.
Now back to 3.1, "Shared representaions lead to generalization and storage efficiency." The belief is that HTMs are efficient at learning complex data and causes. In other words, HTMs scale well. This can be, in computer hardware terms, memory size and computing power. This is possible because the lower levels of the HTM break interpret the data into what might be called micro-causes. Or cause modules. These modules can be reused by any of the causes found much higher in the HTM. This mimics what we know of the human visual pathway, where at the lower levels nerves appear to respond to small features on the retina like spots, short lines at various angles, simple changes in contrast, etc. Using the human face as an example, the HTM might recognize eyes, lips, proportions, etc., and categories within these features. Almost all six billion human faces presently on earth would be interpretable in terms of these basic components and their spatial relationships. Two represent each of the faces you don't need 6 billion 10 megapixel bitmap pictures. You just need 6 billion summaries that could probably be represented with a few bytes of data. Recognition would resolve to summarizing the new picture of a face and then finding the closest summary already held by the HTM.
The authors point out that "the system cannot easily learn to recognize new objects that are not made up of previously learned sub-objects." Which we see in human behavior from the household chore level right up to big pictures like evolution and relativity staring large groups of scientists in the face for decades before a Darwin or Einstein said "I recognize a new, high-level causation here."
Within the section is a helpful explanation about "quantization points," which I said were left unclear in section 2. It gives the reason for having a much lower number of quantization points than there are possible events in the event space. It points out that in a 10 by 10 square of binary (black or white) pixels, there are 2 to the 100th different patterns. By limiting the number of quantization points you force the node to group every input image into a type of pattern (some examples could be lines with various orientations, spots that move in a particular direction, more black on the right or left, etc.). These would be "the most common patterns seen by the node during training."
In section 3.4 the authors give an introductory look at the idea that HTMs can pay attention to certain aspects of the data. In other words, just as you might focus on your newspaper while riding public transportation to work, an HTM can pick some level of the hierarchy of data to focus on. Suppose it is a facial recognition HTM and it thinks a face present to it could be George or Herbert. By focussing on a particular aspect of the face, say the nose-to-lips difference, it might become more certain that the face belongs to George. People can do this both consciously and unconsicously.
It an HTM could do that, it would be really cool.
Next: Evaluating HTMs, Part 5: Belief Propagation
Thursday, March 4, 2010
How Do HTMs Learn?
Evaluating HTMs, Part 3: How do HTMs Learn?
"Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 2, "How Do HTMs Discover and Infer Causes", gives an overview of the internal mechanisms of HTMs.
Specifically, it gives an a overview of how HTMs learn. This prompted me to think about the difference between learning and discovery. They could be the same thing, but learning for humans often implies a teacher presenting information to be learned to a student. Discovery implies coming upon something new (perhaps a relationship between already known objects) and realizing that it is new and should be remembered.
Each node in an HTM uses the same algorithm. The nodes are arranged hiearchically, with representations typically showing a row of nodes at the bottom that take input. Each row above the bottom has progressively fewer nodes. The top node is a single node. Its output is a vector that represents a cause, or object related to the data in a causal fashion. In fact each node does this, passing its output vector to the next higher row of nodes. So causes are built up hierarchically. All data and discoveries include a time element. In a visual field, for instance, the time element could be no change in a part of the field, or changing color with time, or following a spot of color from one part of the visual field to another over a course of time.
Get used to the technical use of the term "belief" if you want to follow discussions about HTMs. This term is used extensively in probabilistic reasoning theory. "A belief is an internal state of each node," but it does correspond to a probability that there is a causal relationship in the data. "I believe the lion must have escaped from the zoo," is a sentence that conveys to us that a person lives where lions do not live in the wild; it differs from "I know ..." because the speaker is admitting there are other possible causes. In a simple HTM, in a lower node, a belief might be something like "28% probability that this is a horizontal line, 16% that this is two animal eyes, etc." Again, beliefs are represented in software by vectors, but they are not generally identical to the output vectors of the nodes.
In training or learning, the HTM forms new beliefs at the bottom of the hierarchy of nodes first. More complex beliefs can only be created once lower level beliefs exist, but the entire process is flexible. If a lower level node alters its belief, it tends to effect higher level nodes. So learning is not just memorization.
So how does a node do all this? Nodes are given a set number of "quantization points." Here the authors are not very clear. The input pattern is assigned to one of the quantization points. And/or "the node decides how close (spacially) the current input is to each of the quantization points and assigns a probablity to each quantization point." How it decides is presumably an algorithm. With enough quantization points, each input data set could be matched exactly to a point. Would that set up cause the node to fail? To do as the authors say, the assumption is there are less quantization points than there are possible inputs.
Step two is "the node looks for common sequences of these quantization points" and "represents each sequence with a variable." So you have to ask, why assign probabilities, why not just assign closest fits? In any case the output variable represents a sequence of quantization points based on the sequence of input data.
Admitting that the authors are introducing the topic, and its vocabulary, still I would have liked more than two short paragraphs on the internal operations of HTM nodes.
Interestingly (and copying what is known about the cortex of mammal brains) information can move both up and down the hierarchy of nodes. As just described, data moving up the hierarchy is temporal variables. Data going down the hierarchy represents the "distribution over the quantization points." That would be a probability distribution.
What I suspect the authors mean is that there is a mechanism to alter the quantization points themselves. Points with long-term zero percent probabilities don't help resolve ambiguity. The set of point probabilities being sent down the hierarchy allows the (lower) node to "take a relatively stable pattern from its parent node(s)" and "turn it into a sequence of spatial patterns."
The claim is that over time "patterns move from the bottom of the hierarchy to the top." In effect rather than sending the raw data up the hierarchy, the nodes send "names" of data sequences up the hierarchy.
That would be pretty cool, and I'd like to know exactly how it happens, but this is, afterall, only an introduction.
Next: Why is a hierarchy important?
Wednesday, March 3, 2010
Evaluating HTMs, Part 2: What HTMs Do
For the introduction See Evaluating HTMs, Part 1
"Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 1, What Do HTMs Do?, asserts that HTMs can discover causal relationships in data presented to them. Once the causality is established, they can infer the cause of a new input. They can predict (with some accuracy) future data sets, and they can use the above three abilities to direct (choose) behavior.
It should be pointed out immediately that each of these 4 abilities have been demonstrated by other computational systems. Neural network software that could discover certain types of relationships from raw data was available at least as early as the 1980's. Many mathematical forms of analysis can find causal relationships within data, for instance regression analysis. In any system, once a relationship is established, recognizing it should present no great difficulty. Nor should making predictions, or using the system to control behavior.
What is interesting about the set of claims for HTMs is that they work together holistically (like the human brain) and should be stackable. That is, the HTM systems should be able to deal with external relationships of increasing complexity by stacking HTM subsystems into an appropriate system. In addition, the HTMs can find relationships in time (sequential or temporal relationships).
In fact, if we call some of the data "objects," for an HTM the objects "have a persistent structure; they exist over time." The authors call the objects "causes." In theory an HTM system could deal with multiple forms of data coming in directly from the world, but usually (for now) the HTM deals with a specific subset of data (much as when a human, say, concentrates on music, or on reading). The data could be a computer file, or a stream of data from input devices.
For the HTM to work the causes should be relatively stable, but should generate data that changes over time, as a horse moving across a visual field, or a conversation between two people. Causes are typically multiple.
The discovery of the causal relationships is a learning process. During learning the HTM builds representations of causes in the form of vectors. The relationship is expressed as a set of probabilities for causes; this set is called a "belief." The causes, relationships, and beliefs can be quite complex if the HTM is complex enough. In particular, hierarchies of causes and beliefs can be learned.
The authors say an HTM, once it has gone through learning, can "infer causes of a novel input." This means that if it is presented with new data, it will try to match the data up to one of the causes it knows about. This is basically pattern recognition, and there are other systems, including certain neural networks, that do this well in certain situations. A good point made by is that if a million pixel visual field (of a scene with motion) is used as the input, it would be rare that an exact pattern would be input twice. So inference, matching a set of data to the closest cause, is a necessity. In the older neural networks causes were typically static; adding a time dimension to the data usually makes it easier for an HTM to learn and infer. I should point out, however, that "infer causes of novel input," to me can mean something more than is claimed by an HTM. For humans, it can mean a deduction, or even a deep set of deductions, rather than just recognizing a pattern or its degree of ambiguity. Then again, perhaps a sufficiently complete HTM system could do even that.
The ability to predict is the third leg of what HTMs do. In other words, given a sequence already encountered, an HTM will predict that sequence is happening again. This sounds like not much, but it is an ability that is crucial to machine understanding. In particular the authors point to priming. Given the latest data, the HTM makes a prediction and notes differences between what is predicted and what happens. If data is ambiguous or noisy, the HTM may fill in with the predicted data. If a prediction is fed back into the HTM as data, this is akin to thinking or imagining. Thus the machine could plan for the future. The authors claim "HTMs can do this well." Imagine a sheep-herding dog application. The better it can predict the behavior of the sheep, the less energy it should need to herd them.
Finally, HTMs can direct behavior. Of course almost any device, even simple mechanical ones, can direct behavior. A mouse trap, given a certain type of input, will engage in a known set behavior. Still, mentioning this for HTMs is important because that is exactly what we would expect artificial intelligence or machine understanding to be used for: behavior. An important point is that "From the HTM's perspective, the [output] system it is connected to is just another object in the world." In other words, an HTM can learn about how its own outputs act is causes in the world.
If you want to get an idea of the potential power of HTMs, before wading through a lot of other materials, section 1.4 of the paper "Direct Behavior", is a great starting point.
I'm excited after reading this part.
Possible Acronym: LIPD (learn, infer, predict, direct)
Next: How do HTMs discover and infer causes?
"Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George, Section 1, What Do HTMs Do?, asserts that HTMs can discover causal relationships in data presented to them. Once the causality is established, they can infer the cause of a new input. They can predict (with some accuracy) future data sets, and they can use the above three abilities to direct (choose) behavior.
It should be pointed out immediately that each of these 4 abilities have been demonstrated by other computational systems. Neural network software that could discover certain types of relationships from raw data was available at least as early as the 1980's. Many mathematical forms of analysis can find causal relationships within data, for instance regression analysis. In any system, once a relationship is established, recognizing it should present no great difficulty. Nor should making predictions, or using the system to control behavior.
What is interesting about the set of claims for HTMs is that they work together holistically (like the human brain) and should be stackable. That is, the HTM systems should be able to deal with external relationships of increasing complexity by stacking HTM subsystems into an appropriate system. In addition, the HTMs can find relationships in time (sequential or temporal relationships).
In fact, if we call some of the data "objects," for an HTM the objects "have a persistent structure; they exist over time." The authors call the objects "causes." In theory an HTM system could deal with multiple forms of data coming in directly from the world, but usually (for now) the HTM deals with a specific subset of data (much as when a human, say, concentrates on music, or on reading). The data could be a computer file, or a stream of data from input devices.
For the HTM to work the causes should be relatively stable, but should generate data that changes over time, as a horse moving across a visual field, or a conversation between two people. Causes are typically multiple.
The discovery of the causal relationships is a learning process. During learning the HTM builds representations of causes in the form of vectors. The relationship is expressed as a set of probabilities for causes; this set is called a "belief." The causes, relationships, and beliefs can be quite complex if the HTM is complex enough. In particular, hierarchies of causes and beliefs can be learned.
The authors say an HTM, once it has gone through learning, can "infer causes of a novel input." This means that if it is presented with new data, it will try to match the data up to one of the causes it knows about. This is basically pattern recognition, and there are other systems, including certain neural networks, that do this well in certain situations. A good point made by is that if a million pixel visual field (of a scene with motion) is used as the input, it would be rare that an exact pattern would be input twice. So inference, matching a set of data to the closest cause, is a necessity. In the older neural networks causes were typically static; adding a time dimension to the data usually makes it easier for an HTM to learn and infer. I should point out, however, that "infer causes of novel input," to me can mean something more than is claimed by an HTM. For humans, it can mean a deduction, or even a deep set of deductions, rather than just recognizing a pattern or its degree of ambiguity. Then again, perhaps a sufficiently complete HTM system could do even that.
The ability to predict is the third leg of what HTMs do. In other words, given a sequence already encountered, an HTM will predict that sequence is happening again. This sounds like not much, but it is an ability that is crucial to machine understanding. In particular the authors point to priming. Given the latest data, the HTM makes a prediction and notes differences between what is predicted and what happens. If data is ambiguous or noisy, the HTM may fill in with the predicted data. If a prediction is fed back into the HTM as data, this is akin to thinking or imagining. Thus the machine could plan for the future. The authors claim "HTMs can do this well." Imagine a sheep-herding dog application. The better it can predict the behavior of the sheep, the less energy it should need to herd them.
Finally, HTMs can direct behavior. Of course almost any device, even simple mechanical ones, can direct behavior. A mouse trap, given a certain type of input, will engage in a known set behavior. Still, mentioning this for HTMs is important because that is exactly what we would expect artificial intelligence or machine understanding to be used for: behavior. An important point is that "From the HTM's perspective, the [output] system it is connected to is just another object in the world." In other words, an HTM can learn about how its own outputs act is causes in the world.
If you want to get an idea of the potential power of HTMs, before wading through a lot of other materials, section 1.4 of the paper "Direct Behavior", is a great starting point.
I'm excited after reading this part.
Possible Acronym: LIPD (learn, infer, predict, direct)
Next: How do HTMs discover and infer causes?
Tuesday, March 2, 2010
Evaluating HTMs, Part 1
I am now going to evaluate the particular model of Hierarchical Temporal Memory (HTM) developed by Jeff Hawkins, Dileep George, and members of their team at Numenta, NuPIC. My key question will be: could HTMs serve as a basis for machine understanding (MU)? Since there are many subgoals on the way to true MU, I will be evaluating HTM capabilities on a number of issues that are usually within the realm of AI (artificial intelligence).
This will be a long project. The current plan is to read and critically summarize "Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George; read and comment on the "Getting Started with NuPIC Guide;" downloading and trying NuPIC, and then assessing what whether to continue on the project.
In preparation I have previously read On Intelligence by Jeff Hawkins twice; read and commented on Towards a Mathematical Theory of Cortical Micro-circuits by George and Hawkins [see early entries of this blog]; took a course in neural networks at SDSU long ago; and read From Neuron to Brain to get detailed information on biological neurons. I know how to write software and I am fairly good at math.
Still, my head hurts just thinking about it, but here we go (into "HTM Concepts, Theory, and Terminology'):
In the Introduction the authors remind us that the human mind/brain has capabilities that computers have so far been unable to duplicate. HTMs are a memory system that can learn to solve certain problems. They are organized as hierarchical systems of nodes. HTMs are currently implemented as software on traditional computer hardware. "The learning curve can be steep."
That is all ground I have already covered in this blog. My learning curve is probably going to be steeper than that of most students who would be interested in this topic, but hopefully watching me struggle will be helpful to at least a few people.
This will be a long project. The current plan is to read and critically summarize "Hierarchical Temporary Memory, Concepts, Theory, and Terminology " by Hawkins and George; read and comment on the "Getting Started with NuPIC Guide;" downloading and trying NuPIC, and then assessing what whether to continue on the project.
In preparation I have previously read On Intelligence by Jeff Hawkins twice; read and commented on Towards a Mathematical Theory of Cortical Micro-circuits by George and Hawkins [see early entries of this blog]; took a course in neural networks at SDSU long ago; and read From Neuron to Brain to get detailed information on biological neurons. I know how to write software and I am fairly good at math.
Still, my head hurts just thinking about it, but here we go (into "HTM Concepts, Theory, and Terminology'):
In the Introduction the authors remind us that the human mind/brain has capabilities that computers have so far been unable to duplicate. HTMs are a memory system that can learn to solve certain problems. They are organized as hierarchical systems of nodes. HTMs are currently implemented as software on traditional computer hardware. "The learning curve can be steep."
That is all ground I have already covered in this blog. My learning curve is probably going to be steeper than that of most students who would be interested in this topic, but hopefully watching me struggle will be helpful to at least a few people.
Wednesday, February 24, 2010
Neuron to Brain Finished
As a log, this has not worked out so far. I have finished reading From Neuron To Brain by Stephen Kuffler, John Nicholls, and Robert Martin. A number of topics in the book would have made good blog entries. I even started one on Mauthner cells, which are large, complex, very interesting neurons found in fish, but did not complete it.
Except the early chapter on the visual cortex and the last chapter, "Genetic and Environmental Influences in the Mammalian Visual System," there is not much in the book that is directly helpful with issues of machine understanding.
And yet it does give an appreciation of the neural system, including its biochemistry. It would be a wonder of nature even if it were not capable, in human form, of smashing atoms and writing poetry. I had been working with simplistic ideas about how individual neurons work. That is actually fine for computer models. The fact that there are many modes of operation of neurons shows that evolution can make good use of both true redundancy and the fine tunings that come from slight variations.
I uncovered a small, common salamander today when pulling wood from the pile to bring up to the woodstove. There is no pond near the wood pile, so this creature had to wander some distance to get to this shelter. It is a good shelter too, complete with insects and other arthropods that make life easy for a salamander. I would tend to say that a salamander does not offer much in the way of understanding capabilities. But salamanders have been navigating the world and keeping alive, so even if we want to think of them as not capable of thought, still they have the necessary degree of intelligence to get them through their generations of life.
I am looking at the general issue of putting neurons together in patterns that could be said to be capable of at least the rudiments of understanding. There is nothing worth reporting on yet, so I'll probably go back to reporting on what Numenta is doing. The geniuses there are working on the problem full time, and are claiming some progress.
Except the early chapter on the visual cortex and the last chapter, "Genetic and Environmental Influences in the Mammalian Visual System," there is not much in the book that is directly helpful with issues of machine understanding.
And yet it does give an appreciation of the neural system, including its biochemistry. It would be a wonder of nature even if it were not capable, in human form, of smashing atoms and writing poetry. I had been working with simplistic ideas about how individual neurons work. That is actually fine for computer models. The fact that there are many modes of operation of neurons shows that evolution can make good use of both true redundancy and the fine tunings that come from slight variations.
I uncovered a small, common salamander today when pulling wood from the pile to bring up to the woodstove. There is no pond near the wood pile, so this creature had to wander some distance to get to this shelter. It is a good shelter too, complete with insects and other arthropods that make life easy for a salamander. I would tend to say that a salamander does not offer much in the way of understanding capabilities. But salamanders have been navigating the world and keeping alive, so even if we want to think of them as not capable of thought, still they have the necessary degree of intelligence to get them through their generations of life.
I am looking at the general issue of putting neurons together in patterns that could be said to be capable of at least the rudiments of understanding. There is nothing worth reporting on yet, so I'll probably go back to reporting on what Numenta is doing. The geniuses there are working on the problem full time, and are claiming some progress.
Tuesday, January 12, 2010
Bayesian Wasteland?
Despite being overloaded with other concerns, I continue to slog through two books that may (or may not) be helpful with the Machine Understanding project. On the information technology front we have Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference by Judea Pearl. I'm at page 116 as of last night. On the biological front I continue From Neuron to Brain by Stephen W. Kuffler; I'm on page 386.
Regarding Probabilistic Reasoning, so far I have seen a lot of interesting work on the problem of combining probability calculations with logic. I just finished the section on Markov Networks and am about to read up on Bayesian Networks. My problem so far is that I don't see any advantages to marrying anything I've seen of probabilistic reasoning to Jeff Hawkin's theory of predictive memory. Despite having read "Towards a Mathematical Theory of Cortical Micro-circuits," as reported in previous entries. Then again sometimes I have trouble taking up novel ideas. But my impression so far is that neural networks are not operating on a probability basis. The closest I can get, so far, to that kind of model is a signal-mixing basis, where analog functions might represent Pearl's probabilies. Nor do I see how the probability network models can cope with invariants. The word invariant is not found in the index to Probablistic Reasoning. I have higher hopes for a Tensor model, even though my own work on that is very preliminary. [I am reminded of the two seemingly totally different mathematical methods used in early quantum mechanics, which then were proven to be equivalants.]
In From Neuron, I have been reading astonishing details about how synapses and single nerve cells work, including how experiments were conducted, in mind-numbing detail. I am just getting to where how neurons and sets of neurons have been shown to operate, with the first example being neurons that sense the stretching of muscles. Again, I am pointed to tensors, which can be used to represent how multiple muscles representing various degrees of freedom of motion can lead to a coherent knowledge of where a body part is in three-dimensional, euclidean-modeled space.
More oddly, Neuron has basically nothing about Hebbian learning. True, the book is dated 1984. But did no one even try to find a physical basis for Hebbian learning as of that date? If you know of a definitive paper that appears to prove a biochemical mechanism for Hebbian learning, let me and my readers know.
I intended to explain what I was reading, in suitable chunks, in this blog. But it is easier to just keep reading at this point, rather than writing about details that I am not even sure are important yet. I keep finding I have to go back to basics. Today, worrying about tensors, muscles, feedback, and a neuron-level learning model, I am revisiting a two-neuron learning model that, oddly, I first worked on back in the 1980's. If anything comes of it, I'll let you know here.
Regarding Probabilistic Reasoning, so far I have seen a lot of interesting work on the problem of combining probability calculations with logic. I just finished the section on Markov Networks and am about to read up on Bayesian Networks. My problem so far is that I don't see any advantages to marrying anything I've seen of probabilistic reasoning to Jeff Hawkin's theory of predictive memory. Despite having read "Towards a Mathematical Theory of Cortical Micro-circuits," as reported in previous entries. Then again sometimes I have trouble taking up novel ideas. But my impression so far is that neural networks are not operating on a probability basis. The closest I can get, so far, to that kind of model is a signal-mixing basis, where analog functions might represent Pearl's probabilies. Nor do I see how the probability network models can cope with invariants. The word invariant is not found in the index to Probablistic Reasoning. I have higher hopes for a Tensor model, even though my own work on that is very preliminary. [I am reminded of the two seemingly totally different mathematical methods used in early quantum mechanics, which then were proven to be equivalants.]
In From Neuron, I have been reading astonishing details about how synapses and single nerve cells work, including how experiments were conducted, in mind-numbing detail. I am just getting to where how neurons and sets of neurons have been shown to operate, with the first example being neurons that sense the stretching of muscles. Again, I am pointed to tensors, which can be used to represent how multiple muscles representing various degrees of freedom of motion can lead to a coherent knowledge of where a body part is in three-dimensional, euclidean-modeled space.
More oddly, Neuron has basically nothing about Hebbian learning. True, the book is dated 1984. But did no one even try to find a physical basis for Hebbian learning as of that date? If you know of a definitive paper that appears to prove a biochemical mechanism for Hebbian learning, let me and my readers know.
I intended to explain what I was reading, in suitable chunks, in this blog. But it is easier to just keep reading at this point, rather than writing about details that I am not even sure are important yet. I keep finding I have to go back to basics. Today, worrying about tensors, muscles, feedback, and a neuron-level learning model, I am revisiting a two-neuron learning model that, oddly, I first worked on back in the 1980's. If anything comes of it, I'll let you know here.
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