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The notion of manifolds as mechanism for behavioral or cognitive control is not new; much work has been done in the field of movement science e.g. juggling and

The notion of manifolds as mechanism for behavioral or cognitive control is not new; much work has been done in the field of movement science e.g. juggling and other forms of dynamic pattern generation. See for example JAS Scott Kelso's Dynamic Patterns or Spivey's Continuity of Mind or the newish field of Radical Embodied Cognition. This is fairly systems neuroscience oriented approach much welcome, but not ground breaking.

kzrdude 7y ago
Which sense of 'manifold' is used here? I vaguely know the locally flat object with an atlas of maps, but I'm not sure that's what they mean.
- marmaduke 7y ago
  Manifold in the sense of a low dimensional locally flat object, in a high dime sional space. An autoencoder has a manifold at the bottleneck layer, for example.
- joeyo 7y ago
  That's what it means here, too. The idea is that if you take the N-dimensional state-space of neural activity --- each dimension being the activity of a neuron or electrode or voxel or whatever --- and look at how the state evolves through time, you discover that it "lives" in a manifold, k, of much smaller dimension than the full space, N. This is, I think, simply a restatement of the fact that neurons exhibit correlations in their activity patterns. That is, not all vectors of activity are "allowed". Still, it has implications for everything from learning to brain-machine interfaces.
  - The_rationalist 7y ago
    This is ridiculously obvious. How is that a discovery? If they had accurately quantified the frequency of correlations now that would be a news.
    - bonoboTP 7y ago
      A meta comment: in academia, for an outsider a specific paper's contribution is usually hard to decipher. Many papers will sound fairly similar. Popular articles like TFA will essentially have to resort to describing a whole branch of research or even a whole subfield. Authors of the academic paper often don't even recognize their work from just reading the PR summary produced by the marketing department of the university (although this one is written by the original authors). Hardly any work is ground breaking in science nowadays. There are incremental advances most of the time.
      - deleted 7y ago
        [deleted]
  - joe_the_user 7y ago
    This reminds of locality-preserving hashes, which also are based on mapping a high dimensional space onto a low dimensional space.

kzrdude 7y ago

Which sense of 'manifold' is used here? I vaguely know the locally flat object with an atlas of maps, but I'm not sure that's what they mean.

marmaduke 7y ago
Manifold in the sense of a low dimensional locally flat object, in a high dime sional space. An autoencoder has a manifold at the bottleneck layer, for example.
joeyo 7y ago
That's what it means here, too. The idea is that if you take the N-dimensional state-space of neural activity --- each dimension being the activity of a neuron or electrode or voxel or whatever --- and look at how the state evolves through time, you discover that it "lives" in a manifold, k, of much smaller dimension than the full space, N. This is, I think, simply a restatement of the fact that neurons exhibit correlations in their activity patterns. That is, not all vectors of activity are "allowed". Still, it has implications for everything from learning to brain-machine interfaces.
- The_rationalist 7y ago
  This is ridiculously obvious. How is that a discovery? If they had accurately quantified the frequency of correlations now that would be a news.
  - bonoboTP 7y ago
    A meta comment: in academia, for an outsider a specific paper's contribution is usually hard to decipher. Many papers will sound fairly similar. Popular articles like TFA will essentially have to resort to describing a whole branch of research or even a whole subfield. Authors of the academic paper often don't even recognize their work from just reading the PR summary produced by the marketing department of the university (although this one is written by the original authors). Hardly any work is ground breaking in science nowadays. There are incremental advances most of the time.
    - deleted 7y ago
      [deleted]
- joe_the_user 7y ago
  This reminds of locality-preserving hashes, which also are based on mapping a high dimensional space onto a low dimensional space.