Deep Learning
Capacity of strong attractor patterns to model behavioural and cognitive prototypes
We solve the mean field equations for a stochastic Hopfield network with temperature (noise) in the presence of strong, i.e., multiply stored, patterns, and use this solution to obtain the storage capacity of such a network. Our result provides for the first time a rigorous solution of the mean filed equations for the standard Hopfield model and is in contrast to the mathematically unjustifiable replica technique that has been used hitherto for this derivation. We show that the critical temperature for stability of a strong pattern is equal to its degree or multiplicity, when the sum of the squares of degrees of the patterns is negligible compared to the network size. In the case of a single strong pattern, when the ratio of the number of all stored pattens and the network size is a positive constant, we obtain the distribution of the overlaps of the patterns with the mean field and deduce that the storage capacity for retrieving a strong pattern exceeds that for retrieving a simple pattern by a multiplicative factor equal to the square of the degree of the strong pattern. This square law property provides justification for using strong patterns to model attachment types and behavioural prototypes in psychology and psychotherapy.
'It's going to be really bad': Fears over AI bubble bursting grow in Silicon Valley
'It's going to be really bad': Fears over AI bubble bursting grow in Silicon Valley At OpenAI's DevDay this week, OpenAI boss Sam Altman did what American tech bosses rarely do these days: he actually answered questions from reporters. I know it's tempting to write the bubble story, Mr Altman told me as he sat flanked by his top lieutenants. In fact, there are many parts of AI that I think are kind of bubbly right now. In Silicon Valley, the debate over whether AI companies are overvalued has taken on a new urgency. Sceptics are privately - and some now publicly - asking whether the rapid rise in the value of AI tech companies may be, at least in part, the result of what they call financial engineering.