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Aaron Leiby
Joined: 18 Apr 2005
Posts: 3
Location: Seattle, WA
04-20-05, 11:30 am |
 Post subject: Invariant Representation |
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Great book, though I'm left a bit confused.
| Quote: | | (from the top of page 78) However, the problem of understanding how your cortex forms invariant representations remains one of the biggest mysteries in all of science. [...] So much so that no one, not even using the most powerful computers in the world, has been able to solve it. And it isn't for a lack of trying. |
So much of the theory rides upon figuring out how invariant representations work, I was hoping for a bit more.
Later, toward the end of chapter six (p.154), a simple example using musical intervals is given to explain how specific predictions are created from invariant memories.
| Quote: | | The columns of your region represent all possible specific intervals such as C-E, C-G, D-A, etc. |
Okay, fine... there exist columns for each interval I've learned to recognize.
| Quote: | | When the region above tells you to expect a fifth, it causes layer 2 cells to fire in all the columns that are fifths, such as C-G, D-A, and E-B. |
Whoa, slow down there. So I can only recognize specific fifths if I've heard those specific fifths before? This from the section that starts out asking, "How do we make predictions about events we have never seen before?"
I can train a child to learn a minor third from middle C, and then play a low G out of key on a different instrument and have her hum a minor third relative to that in her own voice range. What's going on here?
I'm sure in reality, it's all a lot fuzzier. A single column is unlikely to represent one specific thing. It's more likely to be spread out over many columns, each column contributing a bit here, a bit there. Holographic if you will. It seems unlikely that we'd have a single column dedicated to fifths, or to any one element (monad?) that'd we could give a name to.
So, if the example as presented was stripped down to aid the reader, that's fine. It would be pretty neat if specific predictions were just table lookups (see the rest of the paragraph quoted, fig 11, etc). But how are those predictions novel? How do we make specific predictions that aren't already "in the database"?
It still seems to me we need a difference engine. I hear a C followed by an E-flat, and its difference gets stored. Eventually, I'm able to label this a minor third. Later, when I hear an out of tune G, I can take that, add the difference and get an equally out of tune B-flat. It seems that this is the mechanism we should be looking for. And maybe that just brings us back to the original quote - the biggest mystery yet unsolved: invariant representation.
Or am I just missing something? I really just want to start writing some code. :) |
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Mark
Joined: 31 Mar 2005
Posts: 29
Location: Palo Alto, CA
04-21-05, 12:32 pm |
| Post subject: Tough Nut |
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Yeah, that “invariant representation” notion is one tough nut. There must be a fairly simple invariant representation for the concept expressed by “What goes up must come down.” Now assume that Italians have the same expression. The invariant representation should be exactly the same in both languages. If you could crack that nut you could converse fluently with anybody on earth. Lotsa luck.
The “biggest mystery”? Perhaps. It’s certainly a contender. Then again, that’s like discussing the biggest infinity. The Mainard direction “Can’t get there from here” comes to mind. |
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diogenes
Joined: 20 Nov 2004
Posts: 9
Location: Williamstown Massachusetts
05-10-05, 10:32 am |
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Memory seems to be encoded in the modification of synapses, connections, and neurons (and possibly attrition and generation).
Whether the "representation" is encoded in one or a few cells or connections or whether it is distributed "holonomically" among many is less important. In either case the "information" is stored in the form of a potentially active combination of neurons and processes. The activation of part of the pattern stimulates the entire pattern (auto-associative memory). Loritz (below) refers to it as "Adaptive Resonance Theory".
Sing a note to a piano with the loud petal depressed; when you stop suddenly, the piano will be "singing" that note back. Push a child on a swing; short swings return quicker. They only work at their own particular (resonant) frequency. Tune a radio to one station (feed in a frequency). The selected carrier frequency picks one and excludes all others (usually), but the hardware is unchanged, only it's (resonant) frequency patterns change.
Invariant representation seems to be a fundamental neurological capability of the brain. It appears to be implemented with the columnar organization in the cortex featuring an "on center, off surround" architecture. For details see "How the Brain Evolved Language" by Donald Loritz. Such architecture is capable of picking out features in the input. With successive hierarchical connections via the parallel fibers, more and more abstract notions can be learned. The "grandmother cell hypothesis" is apparently still argued.
Essentially everything is stored in the same "invariant" representation using neurons, patterns of activation, synapses, neurotransmitters, etc.. We really build internal models of our external world, models that include all the actions we were taking, the proprioceptive and enteroceptive state at the time, the chemical balance, etc.. Integrating these depends strongly on the (dynamic and evolving) wiring diagram.
The "ear" object is connected to the "eye" object, the eye object is connected to the "hand" object, the hand object is connected to the "taste" object, etc. Now, to add language, just change "object" to "word".
Because all inputs are stored in the same type of representation, comparing the representation of "apples" to the representation of "oranges" is, to use an electronic metaphor, simply a matter of installing a voltage comparator. We evolved these associative brain connections (wiring patterns) that served our survival needs, and that included mapping the inputs of one sense to the inputs to another sense and to our motor controls that resulted in changes to the inputs as we move around.
Note that since the motor controls and the sensory inputs for handling Italian and handling English are different, these must be recorded separately and associated. Some brain research shows that different areas of the brain light up during use of a later learned second language (compared to the primary language) while in subjects who learned both languages early the same area lights up for both languages.
While the internal representation is the same (the same type) it appears to be "recorded" in slightly different locations when the second language is learned later.
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Ralph E. Kenyon, Jr.
http://www.xenodochy.org/ralph.html
It's not that seeing is believing, believing is seeing,
and we're much better at believing than we are at seeing. |
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davros
Joined: 07 Jul 2005
Posts: 5
07-08-05, 08:41 pm |
| Post subject: How the brain forms invariant representations |
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It is probable that the brain forms invariant representations
by simply identifying obvious significant and persistent variations from pre-established,encoded information that is most similar to the events or objects currently under scrutiny.If the observed variations are preserved over time they are identified as hallmarks of the event or object.Once these significant variations are identified they are then assigned a link to the original representation to form a sub-branch or category.The variation could also be granted it's own new classification nexus to be utilized for future comparisons.
Very much like the distillation process the unique elements could be identified and encoded to construct a vast interlinked network.This network would be refined over time with repeated exposure to the stimulus and would explain the overwhelming reliance upon analogy or comparison that the book repeatedly mentions.Any future substantial,persistent deviation from this framework representation would be identified easily and added to a possible exception branch.
For example the invariant representation of an orange would be made up of all the encoded information that makes it unique yet similar to other event items in the brains information store.Any significantly sustained,derived peculiarities specific to said orange would form it's representation.
This in turn could be used in the future to quantify a portion of another event or item.(it smelled like orange but tasted like grape) |
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Orion
Joined: 10 Apr 2005
Posts: 42
Location: Reed City, Michigan, U.S.
07-14-05, 06:46 am |
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| Quote: | I can train a child to learn a minor third from middle C, and then play a low G out of key on a different instrument and have her hum a minor third relative to that in her own voice range. What's going on here?
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It's possible that the child already has basic representations for notes and the spaces between them, and is only learning names for these concepts (which allow the concepts to be sharpened). There is no proof that the hummed note is a new invention.
| Quote: | | It still seems to me we need a difference engine. |
Despite the fact that there is no proof, I definitely see the need for an ability to generalize as you outlined. If the memory-prediction framework truly lacks an explanation for this, then it is doomed (unless it can be fixed, of course). But does it really lack this? I'm reluctant to conclude something so devastating to the theory...
Because ideas are actually represented spatially in the brain, that is, spread out physically on the cortex, the ratio between the two notes actually (approxamately) represents their distance from eachother on the lowest processing area of the auditory heirarchy. "Generalizing" therefore, in this situation, means that some invariant column somewhere up the heirarchy activates whenever two notes are a certain distance apart. It also means that this column muat be trained to do this without actually being trained for every single ratio of that size; it must be trained with a subset of such ratios, and be able to somehow form a generalized connection to all such ratios. It sounds mentally possible, but is it physically possible? Physical connections must be made here, each with the same neural distance between two branches. These physical connections may involve several heirarchical layers, of course; but it seems that some part of such a heirarchy must form spontaneously, somehow. Is this so? The question confuses me.We MUST generalize; but how, precisely?
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eightwings
Joined: 07 Aug 2005
Posts: 29
Location: Miami, Florida
08-09-05, 06:43 am |
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| Quote: | | It still seems to me we need a difference engine. I hear a C followed by an E-flat, and its difference gets stored. Eventually, I'm able to label this a minor third. Later, when I hear an out of tune G, I can take that, add the difference and get an equally out of tune B-flat. It seems that this is the mechanism we should be looking for. |
I think we need a percentage engine rather than a difference engine. The way it works is that one interval predicts the others. That is, the predicted intervals are an exact percentage of the predictor.
| Quote: | | And maybe that just brings us back to the original quote - the biggest mystery yet unsolved: invariant representation. |
Invariant representation is more than just the ability to recognize a learned melody regardless of tempo. Learning temporal correlations is a minor problem, IMO. The more interesting problem is this: How does one recognize one's grandmother regardless of whether or not she's facing foward, to the left or right side, downward, or upward? Obviously, when grandma appears in view, a huge number of memory sequences wake up and start firing. The problem is, how does one associate these sequences with grandma? I have excellent reasons to believe that this is not a perceptual learning problem (as everyone supposes) but a motor learning problem. Related sequences can be harnessed into a coherent group by detecting motor conflicts. It's regrettable that Mr. Hawkins has little to say about the linkage between memory and motor control and coordination.
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Louis Savain
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Orion
Joined: 10 Apr 2005
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Location: Reed City, Michigan, U.S.
08-10-05, 11:57 am |
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| Quote: | | I have excellent reasons to believe that this is not a perceptual learning problem (as everyone supposes) but a motor learning problem. |
How so? I don't understand the connection. I do agree, though, that the motor connection needs to be stronger; the explanation that "the motor cortex is also based on memory-prediction" is much insufficient.
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eightwings
Joined: 07 Aug 2005
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Location: Miami, Florida
08-11-05, 12:41 pm |
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I apologize for the length of this response.
| Orion wrote: | | Quote: | | I have excellent reasons to believe that this is not a perceptual learning problem (as everyone supposes) but a motor learning problem. |
How so? I don't understand the connection. I do agree, though, that the motor connection needs to be stronger; the explanation that "the motor cortex is also based on memory-prediction" is much insufficient. |
In my opinion, memory sequences exist for one reason only, and that is to generate motor behavior (speech, eye movements, locomotion, etc...). I believe that the notion that a grandmother cell is the end point of a perceptual learning pyramid is fallacious. As I pointed out in another article, the psychological data on stimulus response timings refutes the pyramid hypothesis. And as Rodney Brooks once said, the connectivity diameter of the brain is only about five or six neurons. The slow processing nature of biological neurons precludes a perceptual pyramid of more than six levels as would certainly be required to generate a grandmother cell.
It is better to think of a grandmother cell as a control cell (an invariant concept cell, if you wish) for a group of sequences related to a given concept, in this case, grandma. Here's my grandmother cell hypothesis in a nutshell  :
Group Control and Attention
There is no longer any doubt that there are such things as "grandmother" cells in the brain. A couple of months ago, Rodrigo Quiroga and his colleagues at the University of Leicester, UK, located and identified grandmother-like cells (source: http://www.newscientist.com/article.ns?id=dn7567 New Scientist) in the hippocampus of their patients. In my opinion, these neurons should be called invariant concept cells because they fire continually while a subject is focusing on a particular concept. Most AI researchers assume that a concept cell is the end point of a multi-level perceptual pyramid that is rooted in sensory data. There is at least one problem with this model: what does a brain do with a firing concept cell? In other words, what complex motor task can it perform with a single firing cell? Not much. Certainly, if it could be built, one could use a perceptual pyramid to create an invariant recognition engine but there is a wide gulf between recognition and motor behavior.
Canalization
In my model, a concept cell is an attention cell. That is, as long as it continues to fire, it keeps the system focused on a particular concept and the behavior and sensory channels associated with it. This is corroborated by psychological research http://www.univie.ac.at/constructivism/people/riegler/papers/riegler01anticipation.pdf[pdf] that shows the existence of a canalization of sensory and motor activity while performing a particular task. Canalization is only possible if the intelligent system has the ability to activate a group of related memory cells while deactivating all others. Two questions arise: a) what are memory cells and b) how does an intelligent system determine which memory cells are related so as to group them as a single coherent concept?
Bottom-up Perceptual Learning
In my model, memory consists of a huge number of seven-node sequences. These store intervals in such a way that the recording of the first interval is enough to predict the other six (dynamic pattern completion). The purpose of sequences is to anticipate the arrival of sensory signals so as to compensate for missing information. The nodes receive signals from the sensory cortices and send output signals directly to effectors to execute motor actions. Sensory learning and memory sequence formation is part of what I call bottom-up perceptual learning.
Top-down Concept Formation
It is virtually impossible to generate an invariant concept cell from perceptual learning alone. Consider the grandmother cell example. We are able to recognize grandma even if she's facing away from us, by observing her gait or silhouette or by hearing her voice. We are somehow able to associate a myriad disparate patterns with a single concept. How is that possible? In my opinion, we form concepts by finding and grouping related memory sequences using a trial and error process based on motor learning. This is because only related signals can be used to generate coordinated or non-conflicting motor commands. Motor behavior runs the gamut from speech generation to walking, grasping, turning one's head, moving one's eyes, etc... But behavior is not always observable, at least in humans. Thinking is a form of behavior. We can all speak to ourselves or play back a melody without actually making any sound.
Motor Conflict Resolution
In order to understand what a motor conflict is, we must first specify what is meant by "motor action" and "motor command". A motor action is a physical effect on the system's environment which consists of the system's own actuators, i.e., muscles, motors, solenoids, etc... Every action has an associated effector which is a motor neuron that services a given actuator. Each effector has a unique intensity level and may receive multiple command connections from multiple sources. Likewise, an actuator may be controlled by multiple effectors. Every action has duration and thus a beginning and an end. As a result, every effector has two complementary types of motor commands: start and stop. That is, a command can be used to either start a motor action or stop it. There are two types of motor conflicts: out-of-step and multiple-activation.
Out-of-step Motor Conflict
An out-of-step conflict occurs when when an effector receives multiple concurrent start or stop commands or when a command tries to stop an action that is already stopped or start one that has already started.
Multiple-activation Motor Conflict
A multiple-activation conflict occurs when multiple effectors try to activate the same actuator concurrently.
This is all there is to motor conflicts. It is all about timing. Conflict resolution simply consists of detecting conflicts as they happen and disconnecting bad command connections (synapses). These connections all have an initial strength which is increased by a small amount every time a command signal is received. However, whenever a conflict is detected, guilty connections are strongly weakened. Eventually, only non-conflicting connections survive.
Behavior Group Formation
Group formation is based on the premise that related sequences produce signals that can be used to generate coordinated (non-conflicting) motor commands. Every group is under the control of a single control cell which I earlier called an invariant concept cell. Every control cell tries to harness as many non-conflicting sequences as possible and may have sequences in common with other control cells. Obviously, given the finite number of motor resources and the impossibility of doing more than one task at a time, not all memory sequences can be active concurrently. Therefore, only one control cell and its group can be active at a time. The beauty of having a control cell is that it solves both the behavior selection problem and the credit assignment problem (that's another subject).
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Louis Savain
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Orion
Joined: 10 Apr 2005
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Location: Reed City, Michigan, U.S.
08-12-05, 06:17 am |
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Is't it still a perceptual learning problem? It seems to me that since you apply the iea of motor behavior to thoughts as well (not a bad idea, but potentially confusing), you are merely using different language for the same things. "resolving motor conflict" could well mean "resolving pattern conflict".
| Quote: | | I believe that the notion that a grandmother cell is the end point of a perceptual learning pyramid is fallacious. [...] It is better to think of a grandmother cell as a control cell (an invariant concept cell, if you wish) for a group of sequences related to a given concept, in this case, grandma. |
This does not sound different than Hawking's layout; you even admit that invariant concepts, his central idea, are important. You do concentrate on different things, but that is all. (How does Hawkings suggest that they are an "end point"? He merely doesn't concentrate on what the brain does with patterns.)
I really liked what Hawkings said about Behaviorism: (I'll paraphrase, since it would take awhile to look up) "I can be intelligent when I'm sitting in the dark doing nothing". It is true that the purpose of intelligent pattern recognition is to cause intelligent behavior; but that is a double-edged statement: it also means that to generate intelligent behavior, we must have intelligent pattern recognition. To act on the fact that we see our grandmother, we must first recognize our grandmother; and, on recognizing her, we may not decide to act.
"Conflict resolution" DOES sound like an interesting learning model, though. How does it decide between two conflicting signals? Does the stronger one win?
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"The more numerous the laws, the more corrupt the state." --Tacitus |
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svendeswan
Joined: 12 Jul 2007
Posts: 1
07-12-07, 01:56 am |
| Post subject: Invariance a matter of representation? |
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I think invariance could be just a matter of representation. The brain's storage method only seems to be in the way, to just store invariant information and filter out the rest. Let me make an example to get things clear:
If you plan to create an (online) dictionary, for example english-german, you have at least 2 columns: The first column is the english word and the second is the german word. So if you lookup an english word, you look for the word in the left column and return the word in the right column. This representation works well as we all probably know.
If you plan to create a function like Google has: "Did you mean...." for the case that a word you look for is not in your lexicon then your representation of your left column might look different. You could encode the left column words as letter triples, so "growth" would be encoded as ("gro" "row" "owt" "wth"). If you now look for the word "growt" (you might have accidentally dropped the last letter) you can find a 75% match with growth: "growt"-> ("gro" "row" "owt"). In the first representation (as pure word) you would get a 0% match.
So to come to the conclusion: I don't think that it is neccessary to find out the way how the brain filters invariances. It's more like finding out how brain stores things in general, or to be more precise the representation that is used.
What do you think?
Best,
Sven |
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