Editing Warren Sturgis McCulloch (section)

=== How we know universals ===
In the 1947 paper ''How we know universals'', they studied the problem of recognizing objects despite changes in representation. For example, recognizing a square under different viewing angles and lighting conditions, or recognizing a phoneme under different loudness and tones. That is, recognizing objects invariant under the [[Group action|action]] of some [[symmetry group]]. This problem was partly inspired by a practical problem in designing a machine for the blind to read (recounted in Wiener's ''Cybernetics'', see before).<ref>{{Citation |last=Masani |first=P. R. |title=McCulloch, Pitts and the Evolution of Wiener's Neurophysiological Ideas |date=1990 |work=Norbert Wiener 1894–1964 |pages=218–238 |url=http://link.springer.com/10.1007/978-3-0348-9252-0_16 |access-date=2024-10-13 |place=Basel |publisher=Birkhäuser Basel |language=en |doi=10.1007/978-3-0348-9252-0_16 |isbn=978-3-0348-9963-5}}</ref>

The paper proposed two solutions. The first is in computing an invariant by averaging over the symmetry group. Let the symmetry group be <math>G</math> and the object to be recognized be <math>x</math>. Let a neural network implement a function <math>T</math>. Then, the group-invariant representation would be <math>\frac{1}{|G|}\sum_{g \in G} T(g x)</math>, the group-action average. The second solution is in a negative feedback circuit that drives a canonical representation. Consider the problem of recognizing whether an object is a square. The circuit moves the eye so that the "center of gravity of brightness" of the object is moved to the middle of the visual field. This then effectively converts each object into a canonical representation, which can then be compared with a representation in the brain.<ref>{{Cite journal |last=Aizawa |first=Kenneth |date=September 2012 |title=Warren McCulloch's Turn to Cybernetics: What Walter Pitts Contributed |url=https://journals.sagepub.com/doi/full/10.1179/0308018812Z.00000000017 |journal=Interdisciplinary Science Reviews |language=en |volume=37 |issue=3 |pages=206–217 |doi=10.1179/0308018812Z.00000000017 |bibcode=2012ISRv...37..206A |issn=0308-0188}}</ref><ref>{{Citation |last=Masani |first=P. R. |title=McCulloch, Pitts and the Evolution of Wiener's Neurophysiological Ideas |date=1990 |work=Norbert Wiener 1894–1964 |pages=218–238 |url=http://link.springer.com/10.1007/978-3-0348-9252-0_16 |access-date=2024-10-14 |place=Basel |publisher=Birkhäuser Basel |language=en |doi=10.1007/978-3-0348-9252-0_16 |isbn=978-3-0348-9963-5}}</ref>