 This interpretation puts the useful mathematical resources of dynamical systems into the hands of computational neuroscientists. Vector spaces are an example. Learning can then be characterized fruitfully in terms of changes in synaptic weights in the network and subsequent reduction of error in network output. (This approach to learning goes back to Hebb 1949, although the vector-space interpretation was not part of Hebb’s account.) A useful representation of this account uses a synaptic weight-error space. One dimension represents the global error in the network’s output to a given task, and all other dimensions represent the weight values of individual synapses in the network. Consider  Figure 2.  Points in this multi-dimensional state space represent the global performance error correlated with each possible collection of synaptic weights in the network. As the weights change with each performance, in accordance with a biologically-inspired learning algorithm, the global error of network performance continually decreases. The changing synaptic weights across the network with each training episode reduces the total error of the network’s output vector, compared to the desired output vector for the input vector. Learning is represented as synaptic weight changes correlated with a descent along the error dimension in the space (Churchland and Sejnowski 1992). Representations (concepts) can be portrayed as partitions in multi-dimensional vector spaces. One example is a neuron activation vector space. See  Figure 3.  A graph of such a space contains one dimension for the activation value of each neuron in the network (or some specific subset of the network’s neurons, such as those in a specific layer). A point in this space represents one possible pattern of activity in all neurons in the network. Activity patterns generated by input vectors that the network has learned to group together will cluster around a (hyper-) point or subvolume in the activity vector space. Any input pattern sufficiently similar to this group will produce an activity pattern lying in geometrical proximity to this point or subvolume. Paul Churchland (1989) argued that this interpretation of network activity provided a quantitative, neurally-inspired basis for prototype theories of concepts developed in late-twentieth century cognitive psychology.