What "ideas from his 2007 book" are those? I read the book and my conclusion was that there was nothing new in it. (Sorry if this bursts someone's bubble)
I don't think there was much new in it, but (intentionally or not) it was a pretty good layman's introduction to the preceding decade or so of thought about predictive behavior in neural systems. Of course, Hawkins tended to imply that it was all his own ideas, but if you ignore that it's a pretty good overview.
I'd say it is normal. Generally you wouldn't find equations describing some proposed model, instead you would find "equations" describing the statistical observations. This paper, however, isn't empirical. It instead proposes a theoretical framework, based on the earlier studies. It argues (hopefully soundly) from the premises of the quoted studies to the conclusions it reaches. The point of the research isn't to present this is exactly how this behaves in mathematical terms, or even suggest a mathematical model for how it could work. Instead it presents a semi-formal description of how it could work, so someone can come up with an experiment trying to establish if it really does work that way. Once some evidence is obtained, you go from there to the more mathematical models.
Its hard to formalise things especially in fields were you're far removed from the maths. So rather than spending a ton of time making a model that is probably fundamentally wrong, you make an approximation in informal language. Scientific discovery is in my mind is always a balancing act between verifying propositions (which don't really _mean_ anything) and sharing thoughts (which don't really _prove_ anything).
In cognitive neuroscience semi-formal descriptions are great. In comp-sci, give me the equation already!
Grid cells is, according a learned colleague of mine, an epiphenomenon. If so, this is not a viable path, as it is really just the grandmother cell theory in disguise.
I like Hawkin's work. I think he has good instincts, and he was probably the first to hammer home the point that all the brain does is make predictions and there are a small number of evolutionary mechanisms at work in the brain. Still, that doesn't make him right here.
I am not sure that he's the first to note that the brain is a predictive machine, or to notice that models of state or the environment can be formulated entirely in terms of predictions[0].
Personally, I find that idea very convincing, because we already know how to learn to predict (reinforcement learning), and we can use the same framework to optimize an agent's behavior to maximize against these predictions.
There is some evidence that the brain uses something like temporal difference methods to learn.
The hard parts are: how to do this in a stable and efficient matter, and how to build up our representation to go from relatively simple goals (e.g., survive and collect resources) to more abstract goals (e.g., translate a poem in such a way that the original's charm is preserved[1]).
That is, you want to have a system that is capable of climbing up Maslow's hierarchy (or something like it) and actually proceeds to do so based on emergent properties of the system itself.
Proposing and investigating new ways of constructing learning systems so that there is a continuum between primal drives and complex abstract goals is hard, and even if grid cells are an epiphenomena, then it is worth studying them to see how they might develop from simpler rules.
If Hawkins' team can make something useful, then that can still be beneficial by allowing for more powerful and flexible AI, even if it's not a theory of everything.
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0. See for example: http://web.eecs.umich.edu/~baveja/Papers/psr.pdf (Littman, Sutton, and Singh), which describes and analyzes the equivalence between belief-state based representations and state representation based on predictions.
You have a point that the grandmother cell theory appeared first. Got people thinking. Then the grandmother cell theory people themselves came out and said 'hey, we were wrong - we think it is sparse coding'
Something similar could happen here. But then, it won't be grid cells as they are. Will it be that location is coded in every sparse representation? I don't know...
In the grandmother cell theory people said - hey this cell only seems to fire when i show you a picture of your grandmother. Hence all the hierarchical features that make up your mental representation of your granny are found in the extraordinary binding properties of this one neuron.
Of course, if you know large sparse DNNs, you know that you have 50 input vectors and pick any neuron far from the input, it may only activate in response to one of the 50 input vectors. It doesn't mean that it is the input vector.
Similarly, Jeff has a theory that all representations in the brain include spatial representations. Now he claims the grid cell does that. But how would the grid cell have evolved to do provide the spatial coordinates? Could not the spatial coordinates be part of the sparse coding for the entity in question - why do they need the grid cells?
I think you misunderstood the paper. Grid cells don't encode location, a set of grid cell modules do. So there isn't a grandmother cell here at all. He's simply proposing this theory because of the noted presence of grid cells in the neocortex.
His new theory, if I understand it correctly, is pretty basic. It is simply saying every sparse encoding of sensory inputs is also tied to a spatial encoding by sets of grid cell modules within the same cortical column. For deep learning practitioners, it would be like saying every embedding comes with it's own spatial encoding, or placed into the same embedding space, however you want to look at it.
These spatial encodings are then related to other spatial encodings of other sensory inputs on different cortical column stacks (by displacement cells?), to firstly build up representations of objects, and then, he surmises further, the relationships of these objects with each other (part to whole).
I think the last part is probably what Jeff will need to substantiate a bit more.
I think Numenta is basing their claim on other studies that suggest there are grid cell like signatures in the neocortex, thus leading to the rampant speculation.
This is way beyond what I can understand, but got me thinking: if a complex neocortex finally gets emulated and trained (current ML techniques) to a human level, how hard do you think it would be to implant primary directives?
Robot brains in Asimov's SF stories were designed mathematically, and they were mathematically proved incapable of defying the three laws. Our robots would be less certain, as its design would include too much randomness to manipulate with absolute certainty. OTOH, even Asimovian robots could defy the three laws if they knew enough philosophy.
I think we would have to understand better how instinctive behavior ends up affecting this kind of cognitive processes, but I think it would be possible. Examples that immediately come to mind would be some cats' aversion to cucumbers due to resemblance to snakes, or superprecociality [1] in newborn animals who can walk within minutes of being born or fly on the same day they hatch.
Dude, every sci-fi story about robots and the three laws is about robots defying these laws. It's a narrative trope, it has nothing to do with an actual AI design.
If you're interested in the subject - check out "Rationality: From AI to Zombies" by Eliezer Yudkowsky and "Superintelligence: Paths, Dangers, Strategies" by Nick Bostrom.
I highly recommend checking out "On Intelligence" by Jeff Hawkins [1] - an amazing book where the author of this paper elaborates on his theory (as of 2004).
Also, I'm currently reading "I Am a Strange Loop" by Douglas Hofstadter [2], it's relevant to this topic and super fascinating. I bet you'll enjoy reading it!
Despite being mentioned everywhere, the term "object" is never really formally defined at all.
What does the brain even consider an "object"? The paper is fundamentally flawed by missing this definition, since their idea is entirely reliant on the definition of an object.
Are there some common things in the physical world that constitute the basic atomic building blocks of objects according to the brain? If so, this needs to specified, otherwise all of this theory is totally vague...
How is the statement that "the cortex is capturing the relative positions of objects" in the slightest bit novel at all? Obviously mammals are capable of navigation, hunting, etc etc. Basically any interaction with your environment requires immediately knowing where all objects are, so obviously this is critically encoded within our learned representations of the world.
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[ 0.85 ms ] story [ 861 ms ] threadThanks, OP this will be Sunday morning reading at its finest.
The ideas from his 2007 book have stuck with me and it will be very interesting to see where the state of their art is.
Its hard to formalise things especially in fields were you're far removed from the maths. So rather than spending a ton of time making a model that is probably fundamentally wrong, you make an approximation in informal language. Scientific discovery is in my mind is always a balancing act between verifying propositions (which don't really _mean_ anything) and sharing thoughts (which don't really _prove_ anything).
In cognitive neuroscience semi-formal descriptions are great. In comp-sci, give me the equation already!
I like Hawkin's work. I think he has good instincts, and he was probably the first to hammer home the point that all the brain does is make predictions and there are a small number of evolutionary mechanisms at work in the brain. Still, that doesn't make him right here.
Personally, I find that idea very convincing, because we already know how to learn to predict (reinforcement learning), and we can use the same framework to optimize an agent's behavior to maximize against these predictions. There is some evidence that the brain uses something like temporal difference methods to learn.
The hard parts are: how to do this in a stable and efficient matter, and how to build up our representation to go from relatively simple goals (e.g., survive and collect resources) to more abstract goals (e.g., translate a poem in such a way that the original's charm is preserved[1]). That is, you want to have a system that is capable of climbing up Maslow's hierarchy (or something like it) and actually proceeds to do so based on emergent properties of the system itself.
Proposing and investigating new ways of constructing learning systems so that there is a continuum between primal drives and complex abstract goals is hard, and even if grid cells are an epiphenomena, then it is worth studying them to see how they might develop from simpler rules. If Hawkins' team can make something useful, then that can still be beneficial by allowing for more powerful and flexible AI, even if it's not a theory of everything.
---
0. See for example: http://web.eecs.umich.edu/~baveja/Papers/psr.pdf (Littman, Sutton, and Singh), which describes and analyzes the equivalence between belief-state based representations and state representation based on predictions.
https://en.wikipedia.org/wiki/Alternative_explanations_of_th...
Something similar could happen here. But then, it won't be grid cells as they are. Will it be that location is coded in every sparse representation? I don't know...
Similarly, Jeff has a theory that all representations in the brain include spatial representations. Now he claims the grid cell does that. But how would the grid cell have evolved to do provide the spatial coordinates? Could not the spatial coordinates be part of the sparse coding for the entity in question - why do they need the grid cells?
His new theory, if I understand it correctly, is pretty basic. It is simply saying every sparse encoding of sensory inputs is also tied to a spatial encoding by sets of grid cell modules within the same cortical column. For deep learning practitioners, it would be like saying every embedding comes with it's own spatial encoding, or placed into the same embedding space, however you want to look at it.
These spatial encodings are then related to other spatial encodings of other sensory inputs on different cortical column stacks (by displacement cells?), to firstly build up representations of objects, and then, he surmises further, the relationships of these objects with each other (part to whole).
I think the last part is probably what Jeff will need to substantiate a bit more.
I think Numenta is basing their claim on other studies that suggest there are grid cell like signatures in the neocortex, thus leading to the rampant speculation.
Robot brains in Asimov's SF stories were designed mathematically, and they were mathematically proved incapable of defying the three laws. Our robots would be less certain, as its design would include too much randomness to manipulate with absolute certainty. OTOH, even Asimovian robots could defy the three laws if they knew enough philosophy.
[1] https://en.wikipedia.org/wiki/Precociality
If you're interested in the subject - check out "Rationality: From AI to Zombies" by Eliezer Yudkowsky and "Superintelligence: Paths, Dangers, Strategies" by Nick Bostrom.
"Emulating" or "training" neocortex has nothing to do with current ML techniques.
The three laws are an interesting thought experiment, but not an interesting solution.
Also, I'm currently reading "I Am a Strange Loop" by Douglas Hofstadter [2], it's relevant to this topic and super fascinating. I bet you'll enjoy reading it!
[1] https://www.audible.com/pd/On-Intelligence-Audiobook/B002V8L...
[2] https://www.audible.com/pd/I-Am-a-Strange-Loop-Audiobook/B07...
I’ve been waiting for it to be released on Audible for years. They just added it
What does the brain even consider an "object"? The paper is fundamentally flawed by missing this definition, since their idea is entirely reliant on the definition of an object.
Are there some common things in the physical world that constitute the basic atomic building blocks of objects according to the brain? If so, this needs to specified, otherwise all of this theory is totally vague...
How is the statement that "the cortex is capturing the relative positions of objects" in the slightest bit novel at all? Obviously mammals are capable of navigation, hunting, etc etc. Basically any interaction with your environment requires immediately knowing where all objects are, so obviously this is critically encoded within our learned representations of the world.