4 ms·

At first I thought this had something to do with the classic "breadth vs. depth" notion on learning stuff -- if you're preparing for the MCAT it is better to ha

by sova 5y ago

At first I thought this had something to do with the classic "breadth vs. depth" notion on learning stuff -- if you're preparing for the MCAT it is better to have breadth that covers all the topics than depth in one or two particulars for the exam, but this is actually just about the dimensions of the neural network used to create representations. Naturally, one would expect a "sweet spot" or series of "sweet spots." From the paper at https://arxiv.org/pdf/2010.15327.pdf https://arxiv.org/pdf/2010.15327.pdf > As the model gets wider or deeper, we seethe emergence of a distinctive block structure— a considerable range of hidden layers that have very high representation similarity (seen as a yellow square on the heatmap). This block structure mostly appears in the later layers (the last two stages) of the network. I wonder if we could do similar analysis on the human brain and find "high representational similarity" for people who do the same task over and over again, such as play chess. Also, I don't really know what sort of data they are analyzing or looking at with these NN, maybe someone with better scansion can let me know?

andersource 5y ago
Haven't read thoroughly but it seems they are investigating ResNet models [0] trained for image classification. > We apply CKA to a family of ResNets of varying depths and widths, trained on common benchmark datasets (CIFAR-10, CIFAR-100 and ImageNet) [0] https://arxiv.org/abs/1512.03385 https://arxiv.org/abs/1512.03385
verdverm 5y ago
iirc, the human neocortex is only 6 layers deep with some interesting vertical connection structures, perhaps similar to skip connections in NN. It would be interesting to see where the deep vs wide analysis ends up when many problem types are used. Can a single network be trained on multiple problems at once and perform well on all?
- ubercore 5y ago
  That sounds fascinating. When talking about something as complex and interconnected as a human neocortex, what does "only 6 layers deep" mean?
  - mattkrause 5y ago
    If you look at a slice of cortex under the microscope, there appear to be six physical layers (like a cake), owing to the different types, numbers, and arrangement of neurons in each. Canonically, the cortex is built out of columns, each of which repeat the same motif. Within a cortical column, signals enter a cortical region through layer IV, 'ascend' to other cortical areas via Layers II and III, and project elsewhere in the brain via Layer V/VI. Layer I mostly contains passing fibers going elsewhere. There are also "horizontal" or lateral connections between and within columns. This is sort of an abstraction though. It's often hard to clearly delineate the boundary between Layer II and III. Layer IV of primary visual cortex has many small sublayers (4C alpha), but it's very very small in others.
- Buttons840 5y ago
  I'm not sure what skip connections are, but I think I have a good guess as to what they are. I've wanted to try a neural network where the output of every layer goes into every subsequent layer. Each layer would thus provide a different perspective to subsequent layers. Anyone know if this has been tried?
  - verdverm 5y ago
    Have a look at AlphaStar, it's a pretty interesting network of networks that has some skip functionality. The DeepMind lecture series on YouTube is pretty great. You'd likely overdue it with skips everywhere, too many connections to learn and backprop on that learning would likely be difficult
  - nomad225 5y ago
    Densely Connected Convolutional Networks (https://arxiv.org/abs/1608.06993 https://arxiv.org/abs/1608.06993) use the idea you're talking about quite effectively.
    - Buttons840 5y ago
      Yeah. That seems like exactly what I was describing. Thanks.
- mattkrause 5y ago
  Each cortical area has six layers, but most behaviors require interactions between many cortical areas, so "input" passes through many more than six layers before it produces an output. Felleman and Van Essen is a classic paper on the organization of the visual system. Figure 2 (p. 4) might give you good sense for how much of the brain it occupies and Figure 4 (p. 30) is the well-known "wiring diagram. In the 30 years since that paper was written, we've found a few more boxes and a lot more wires! We've also come to appreciate that there are lots of recurrent loops. V1 -> V2 is one of the biggest connections in the brain, V2 -> V1 is a near runner up. https://cogsci.ucsd.edu/~sereno/201/readings/04.03-MacaqueAreas.pdf https://cogsci.ucsd.edu/~sereno/201/readings/04.03-MacaqueAr...
  - verdverm 5y ago
    Indeed, there are many "horizontal" and recurrent connections and simply thinking of it as a 6 layer feed forward network is a gross oversimplification. It's more like a complex network of complex networks... of the spiking variety
    - mattkrause 5y ago
      Yup, and that’s just the “classical” synaptic transmission. Mixed in with that, there is also slower signaling via neuromodulators (dopamine, norepinephrine etc), neuroendocrine system, and God only knows whatever the astrocytes are doing. Every neuron has its own internal dynamics too, over scales ranging from milliseconds (channel inactivation) to hours or days (receptor internalization). There’s even the possibility of “ephaptic coupling”, wherein the electric fields produced by some neurons affect the activity of others, without making any sort of direct contact. We’ve collected some of the stronger data in favor of that possibility and yet I remain firmly in denial because it would make the brain so absurdly complicated.
      - verdverm 5y ago
        Did you see the FPGA which had an "ineffectual" circuit created while using Evolution Algo to optimize design for calculating integrals? Turns out it wasn't ineffectual but had EM effects between circuits that the calculation required! I would not be surprised if the brain did similar things, especially given that light and magnets are causing effects in various studies.
- dimatura 5y ago
  There's a lot of differences between the mainstream CNNs and biological NNs though. For one, inference in most CNNs is just feed-forward, whereas in the brain the information flow is a lot more complex, modulated by all sorts of feedback loops as well as a dynamic state given by memory, expectation, attention, etc. Biological neurons are also a lot more complicated (and diverse) than the artificial ones. So those six layers aren't really very comparable to six layers in a typical modern CNN. Of course, I'm talking about just the typical current day CNN. There's a lot of ongoing work in recurrent neural nets, memory for neural nets, attention (though the idea of "attention" that is hot right now is quite simplified compared to what we usually call attention), etc.

by sova 5y ago

andersource 5y ago

Haven't read thoroughly but it seems they are investigating ResNet models [0] trained for image classification. > We apply CKA to a family of ResNets of varying depths and widths, trained on common benchmark datasets (CIFAR-10, CIFAR-100 and ImageNet) [0] https://arxiv.org/abs/1512.03385 https://arxiv.org/abs/1512.03385

verdverm 5y ago

iirc, the human neocortex is only 6 layers deep with some interesting vertical connection structures, perhaps similar to skip connections in NN. It would be interesting to see where the deep vs wide analysis ends up when many problem types are used. Can a single network be trained on multiple problems at once and perform well on all?

ubercore 5y ago
That sounds fascinating. When talking about something as complex and interconnected as a human neocortex, what does "only 6 layers deep" mean?
- mattkrause 5y ago
  If you look at a slice of cortex under the microscope, there appear to be six physical layers (like a cake), owing to the different types, numbers, and arrangement of neurons in each. Canonically, the cortex is built out of columns, each of which repeat the same motif. Within a cortical column, signals enter a cortical region through layer IV, 'ascend' to other cortical areas via Layers II and III, and project elsewhere in the brain via Layer V/VI. Layer I mostly contains passing fibers going elsewhere. There are also "horizontal" or lateral connections between and within columns. This is sort of an abstraction though. It's often hard to clearly delineate the boundary between Layer II and III. Layer IV of primary visual cortex has many small sublayers (4C alpha), but it's very very small in others.
Buttons840 5y ago
I'm not sure what skip connections are, but I think I have a good guess as to what they are. I've wanted to try a neural network where the output of every layer goes into every subsequent layer. Each layer would thus provide a different perspective to subsequent layers. Anyone know if this has been tried?
- verdverm 5y ago
  Have a look at AlphaStar, it's a pretty interesting network of networks that has some skip functionality. The DeepMind lecture series on YouTube is pretty great. You'd likely overdue it with skips everywhere, too many connections to learn and backprop on that learning would likely be difficult
- nomad225 5y ago
  Densely Connected Convolutional Networks (https://arxiv.org/abs/1608.06993 https://arxiv.org/abs/1608.06993) use the idea you're talking about quite effectively.
  - Buttons840 5y ago
    Yeah. That seems like exactly what I was describing. Thanks.
mattkrause 5y ago
Each cortical area has six layers, but most behaviors require interactions between many cortical areas, so "input" passes through many more than six layers before it produces an output. Felleman and Van Essen is a classic paper on the organization of the visual system. Figure 2 (p. 4) might give you good sense for how much of the brain it occupies and Figure 4 (p. 30) is the well-known "wiring diagram. In the 30 years since that paper was written, we've found a few more boxes and a lot more wires! We've also come to appreciate that there are lots of recurrent loops. V1 -> V2 is one of the biggest connections in the brain, V2 -> V1 is a near runner up. https://cogsci.ucsd.edu/~sereno/201/readings/04.03-MacaqueAreas.pdf https://cogsci.ucsd.edu/~sereno/201/readings/04.03-MacaqueAr...
- verdverm 5y ago
  Indeed, there are many "horizontal" and recurrent connections and simply thinking of it as a 6 layer feed forward network is a gross oversimplification. It's more like a complex network of complex networks... of the spiking variety
  - mattkrause 5y ago
    Yup, and that’s just the “classical” synaptic transmission. Mixed in with that, there is also slower signaling via neuromodulators (dopamine, norepinephrine etc), neuroendocrine system, and God only knows whatever the astrocytes are doing. Every neuron has its own internal dynamics too, over scales ranging from milliseconds (channel inactivation) to hours or days (receptor internalization). There’s even the possibility of “ephaptic coupling”, wherein the electric fields produced by some neurons affect the activity of others, without making any sort of direct contact. We’ve collected some of the stronger data in favor of that possibility and yet I remain firmly in denial because it would make the brain so absurdly complicated.
    - verdverm 5y ago
      Did you see the FPGA which had an "ineffectual" circuit created while using Evolution Algo to optimize design for calculating integrals? Turns out it wasn't ineffectual but had EM effects between circuits that the calculation required! I would not be surprised if the brain did similar things, especially given that light and magnets are causing effects in various studies.
dimatura 5y ago
There's a lot of differences between the mainstream CNNs and biological NNs though. For one, inference in most CNNs is just feed-forward, whereas in the brain the information flow is a lot more complex, modulated by all sorts of feedback loops as well as a dynamic state given by memory, expectation, attention, etc. Biological neurons are also a lot more complicated (and diverse) than the artificial ones. So those six layers aren't really very comparable to six layers in a typical modern CNN. Of course, I'm talking about just the typical current day CNN. There's a lot of ongoing work in recurrent neural nets, memory for neural nets, attention (though the idea of "attention" that is hot right now is quite simplified compared to what we usually call attention), etc.