# Residuals

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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 the dimensionality of the sphere increases as does the length and complexity of the paths through this space. Here is an 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 ($\mathbf{W}$). In that case, what matters is that the current context, $\vec{r}$, identifies a unique 'recognised context', $\mathbf{W(k,:)}$. 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.

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.