Can I imagine the difference between the model of the grandma neuron and the model of interconnected neuron network so that the information isn't primarily stored in the neurons (respectively in their states) but in the connections between them.
Is the information in the Brain stored in the connections rather than in the neurons ?
It depends on what information you are referring to.
The brain does not just store one type of information,the model of a grandmother cell and the model of an interconnected neuron network are 2 subsystems of a greater system working together perhaps in a competitive or complementary arrangement. The purpose of this system is to extract information from the environment and identify it again for the organisms benefit. 1.
So let's say we see something that will benefit us in the future or that we might want to avoid. This is a simplification, but as you see that something, neurons in your neocortex light up specifically in region V1 in the back of your head, they arrive there after a lot of computations along the way from your retina, but also project to other parts of your brain where they are perhaps processed consciously,they fire in an orderly fashion, in a map, this bouncing around of electrical signals represents your conscious, and unconscious processing of the image, so the information exists as a network of electrical signals. 2.
During recollection, ( there are different types of memories so the structure in charge could be the neocortex,basal ganglia, hippocampus or even a muscle)3. this same map ( or a smaller subset ) gets replayed. The mechanism(s) by which this information is first encoded and later retrieved is still not entirely understood, but it involves a map and a getaway or switchboard.4. This switchboard ties together different percepts ( a smaller network of electrical signals), so in a way the information is represented at the switchboard level, if you disable this switchboard, you can't make new memories or lose previous ones.
A grandmother cell in the scheme of what I just explained, is the result of another subsystem that helps recognize something. Once you successfully encode a percept ( thing we want to remember seeing) you might want to associate it with something ( good,bad,delicious,etc), at the top of a series of associations lies a grandmother cell, which in turn is a handy evolutionary way of signaling back to other systems when some previous information has been experienced. So in this way the information of whether a subset of relationships in between networks of electrical signals has been experienced and encoded lies here.
The idea of grandmother cells and object recognition in general is summarized in the Object Recognition chapter of ( Cognitive Neuroscience,Gazzinga-3rd ed 222-225) along with the problems a grandmother cell introduces in object recognition (ie if you lose the grandmother cell you would lose all the information about your grandmother)
Koch( Quest for Consciousness-2004) chapters on vision provide a very readable account of how the information goes from retina to v1. Vision Science (Palmer) is a more thorough account.
The chapter on learning and memory (Cognitive Neuroscience) gives an overview.
(Gluck -2001-Gateway to memory) presents different models of this arrangement.
The physiology of memory is still poorly understood, but there are some generalizations we can work with:
There are four "types" of memory which the human brain works with.
Sensory memory is very short-term (milliseconds), cannot be consciously accessed (it's used by the sensory processing centers of the brain for things like tracking moving objects), and is stored in the activation state of neurons (ie. which neurons are firing at any given time).
Working memory is short-term (it lasts up to 30 minutes), and stores "what you're thinking about now". It is not yet fully understood exactly how it works. However, we know that drugs which interrupt neuron state can "delete" working memory to some degree; this suggests that working memory is stored at least partially in the activation state of neurons.
Long-term memory is persistent and lasts, in theory, until the end of a person's life. It has been well established that long-term memory is stored in the connections between neurons.
Intermediate memory is a relatively new theory of memory which operates somewhere between working memory and long-term memory. As far as I'm aware, we don't yet understand many of the mechanisms behind it.
Grandmother Cells vs Distributed Representations
The idea of a "grandmother cell" is effectively the ultimate in sparse representations: that there is one, single neuron in your brain that represents your grandmother, and that everything you know about your grandmother is associated with that cell through connections.
At the other end of the spectrum is a "distributed representation," where a network of simultaneously active cells represents a concept, and that these cells are connected to each other and to related concepts (see here, here, and here). These networks could be highly overlapping, and could potentially overlap more when you are talking about related concepts: i.e., "dog" and "cat" might overlap more than "fish" and "squirrel" because the former are both 4-legged animals that live on land and are kept as pets - lots of similarity.
Realistically, no one in modern neuroscience is truly arguing for the existence of "grandmother cells" but there are certainly arguments about sparse vs. distributed representations, and now large or small the cell assemblies or networks are that reflect particular concepts, and what the importance of context is. The main arguments you will see today concern the extent of distribution across brain areas: that is, are there brain areas that contain somewhat-distributed representations of abstract concepts, or are those concepts distributed across modalities (where your concept of 'baseball' includes a synthesized visual representation in visual cortex, the texture of the seams in somatosensory cortex, the sound of ball-on-bat in auditory cortex, the motor plan for throwing the ball in motor cortex, etc).
Evidence for Grandmother cells?
Despite what I just said, there were some interesting papers from human subjects published several years ago, especially this one. These papers showed neurons in a particular area of the brain that had invariant responses to particular concepts, perhaps most famously "Jennifer Aniston" cells and "Halle Berry" cells that responded not only to various pictures of each actress but also to other more abstract representations such as their written name. Clearly, these are not the cells typically described in the primary visual cortex that respond to stimuli like bars and edges.
These papers were reported in the lay science and general press as evidence or proof of the "grandmother cell" theory. Some were more responsible and included some of the authors own words (see also here): essentially, what the authors are arguing is that cell assemblies might be pretty small (but not too small - the authors only recorded from a few cells yet found dozens that responded to Jennifer Aniston, not just one, for example).
Information in cells or connections
To get back to your original question: you asked about whether the difference between a grandmother cell and a neuronal network is whether the information is stored in the cells vs. the connections. I would argue that, although in the "grandmother cell" model there is a lot of importance placed on individual cells, in both cases the information is stored in the connections.
Even if you assume the extreme case of the "grandmother cell", where one cell is the hub that alone represents your grandmother, the information isn't stored as "grandma", it's stored as the associations you have with her: maybe smells of cookies, the shape of her face, her name signed on a birthday card. If you pulled someone's grandmother cell out of their brain network and interrogated it, you wouldn't be able to learn anything at all about their grandmother.
The difference between the "grandmother cell" and a more distributed network is that in the "grandmother cell" case, we would expect to find another cell that represented specifically the cookie smell, yet another that represented the shape of her face (and only her face), and so on. In a more distributed network, each of those related concepts would be encoded by their own network, and those networks might overlap somewhat where the concepts are closely related: that is, part of your representation of "grandmother" is the smell of her cookies.
From what I can gather, the short answer is that we don't have the full picture of how biological neural networks store information.
If you are willing to relax the constraints of your question to extent to artificial neural networks, then your answer becomes significantly easier to answer in part because we understand them much better. Artificial neural networks do store information as synaptic weights which is the only part that changes during the training of a network. The rest of the network such as the topology and the activation function remains unchanged.
Image classifiers are a convenient example of information as synaptic weights since we can see what the neural network 'sees' by maximal activation of neurons. It is immediately obvious that there is a lot of information stored in the weights of a network. The image below is taken from Understanding Neural Networks Through Deep Visualization