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@bayesianbrain | |||||
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Finally, we are all on Twitter to exchange ideas and not one-up each other so I hope everyone feels free to share their perspective. :)
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Aidan Rocke
@bayesianbrain
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1. velj |
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Physical interpretation of the Manifold Hypothesis mathoverflow.net/q/351368/56328…
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Aidan Rocke
@bayesianbrain
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1. velj |
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I think this question might interest @KordingLab, @xaqlab, @benlansdell, @antoniocbscosta, @rbhar90, @Aras121, @a_tschantz, @NoahGuzman14
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Aidan Rocke
@bayesianbrain
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1. velj |
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Aidan Rocke
@bayesianbrain
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1. velj |
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@NatashaMhatre I think this is also related to our previous discussion on the controllability and stability of complex dynamical systems.
Instead of framing the question in the abstract I think we can connect it to an existing hypothesis in machine learning. :)
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Aidan Rocke
@bayesianbrain
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1. velj |
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I haven't seen this question properly formulated anywhere so this represents my attempt. From my discussions with an applied topologist it has yet to be properly addressed.
I also highly doubt that this is one of those problems where there will be a single ‘eureka’ moment. ;)
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xaq
@xaqlab
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1. velj |
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I don't understand the question yet.
But one straightforward thought on neural manifold: Bottleneck-then-expansion strongly favors low-D representations in high-D space (though not guaranteed because of possible temporal multiplexing).
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Aidan Rocke
@bayesianbrain
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1. velj |
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Here's the problem in two parts:
In order to do ML we need to collect a lot of data from a data-generating process so this process must be stable. Empirically we observe that the intrinsic dimension d of the data is generally much smaller than the ambient dimension D.
1/2
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Aidan Rocke
@bayesianbrain
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1. velj |
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Note: I think this might be one of the most interesting open problems in machine learning and neural information processing, unless a theoretical neuroscientist has already adequately addressed this question in a slightly different setting.
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