Difference between revisions of "Residuals"

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[[File:W_sphere.png|thumb|The equations on this page correspond to the picture above. An input vector (yellow dot) is compared to many stored vectors (red dots). The red dot to which it is closest gets chosen. This leads to a motor output resulting in a new input. Over the course of [[Evolution|evolution]] the dimensionality of the sphere increases as does the length and complexity of the paths through this space. Here is  an [http://glennersterlab.com/wiki/W_sphere_slides.mov animated version] of the figure.]] Most of the discussion in these pages is about what could be done with a fixed store of sensory+motivational contexts ([[Notation|$\mathbf{W}$]]). In that case, what matters is that the current context, [[Notation|$\vec{r}$]], identifies a unique 'recognised context', [[Notation|$\mathbf{W(k,:)}$]]. Of course, the current context, will never be quite the same as the stored context; the difference, or residual, is important for learning and memory.
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[[File:resid.png|thumb|The current context (yellow dot) is not identical to the most similar stored context (red dot). The difference, or residual, is useful for learning and creating a new Voronoi cell (or recognised context), shown by the dotted line.]]
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Most of the discussion in these pages is about what could be done with a fixed store of sensory+motivational contexts ([[Notation|<math>\mathbf{W}</math>]]). In that case, what matters is that the current context, [[Notation|<math>\vec{r}</math>]], identifies a unique 'recognised context', [[Notation|<math>\mathbf{W(k,:)}</math>]]. Of course, the current context, will never be quite the same as the stored context; the difference, or residual, is important for learning and memory.
  
If a person carries out a familiar task, like walking to work, the current context will pass through a set of established [[Voronoi cells]]. If they get to work and remember something particular about that journey, they must have generated new Voronoi cells, as the figure illustrates. It is well established in neuroscience that contexts can trigger actions (e.g. heat leading to a withdrawal response, or mechanical resistance triggering a stretch reflex in the spinal cord) but then the signal of mismatch or error is passed up the chain (e.g. to the cerebellum) leading to an adjustment of the programming of subsequent movements, i.e. learning.
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If a person carries out a familiar task, like walking to work, the current context will pass through a set of established [[Voronoi cells]]. If they get to work and remember something particular about that journey, they must have generated new Voronoi cells, as the figure illustrates. It is well established in neuroscience that contexts can trigger actions (e.g. heat leading to a withdrawal response, or mechanical resistance triggering a stretch reflex in the spinal cord) but then the signal of mismatch or error is passed up the chain (e.g. to the cerebellum<ref>Ito, M. (2013). Error detection and representation in the olivo-cerebellar system. Frontiers in Neural Circuits, 7, 1. http://doi.org/10.3389/fncir.2013.00001</ref>) leading to an adjustment of the programming of subsequent movements, i.e. learning.
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==References==
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<references/>

Latest revision as of 13:26, 20 May 2018

The current context (yellow dot) is not identical to the most similar stored context (red dot). The difference, or residual, is useful for learning and creating a new Voronoi cell (or recognised context), shown by the dotted line.

Most of the discussion in these pages is about what could be done with a fixed store of sensory+motivational contexts ([math]\mathbf{W}[/math]). In that case, what matters is that the current context, [math]\vec{r}[/math], identifies a unique 'recognised context', [math]\mathbf{W(k,:)}[/math]. Of course, the current context, will never be quite the same as the stored context; the difference, or residual, is important for learning and memory.

If a person carries out a familiar task, like walking to work, the current context will pass through a set of established Voronoi cells. If they get to work and remember something particular about that journey, they must have generated new Voronoi cells, as the figure illustrates. It is well established in neuroscience that contexts can trigger actions (e.g. heat leading to a withdrawal response, or mechanical resistance triggering a stretch reflex in the spinal cord) but then the signal of mismatch or error is passed up the chain (e.g. to the cerebellum[1]) leading to an adjustment of the programming of subsequent movements, i.e. learning.

References

  1. Ito, M. (2013). Error detection and representation in the olivo-cerebellar system. Frontiers in Neural Circuits, 7, 1. http://doi.org/10.3389/fncir.2013.00001