{"title": "Plasticity-Mediated Competitive Learning", "book": "Advances in Neural Information Processing Systems", "page_first": 475, "page_last": 480, "abstract": null, "full_text": "Plasticity-Mediated Competitive Learning \n\nNicol N. Schraudolph \nnici@salk.edu \n\nTerrence J. Sejnowski \nterry@salk.edu \n\nComputational Neurobiology Laboratory \nThe Salk Institute for Biological Studies \n\nSan Diego, CA 92186-5800 \n\nand \n\nComputer Science & Engineering Department \n\nUniversity of California, San Diego \n\nLa Jolla, CA 92093-0114 \n\nAbstract \n\nDifferentiation between the nodes of a competitive learning net(cid:173)\nwork is conventionally achieved through competition on the ba(cid:173)\nsis of neural activity. Simple inhibitory mechanisms are limited \nto sparse representations, while decorrelation and factorization \nschemes that support distributed representations are computation(cid:173)\nally unattractive. By letting neural plasticity mediate the compet(cid:173)\nitive interaction instead, we obtain diffuse, nonadaptive alterna(cid:173)\ntives for fully distributed representations. We use this technique \nto Simplify and improve our binary information gain optimiza(cid:173)\ntion algorithm for feature extraction (Schraudolph and Sejnowski, \n1993); the same approach could be used to improve other learning \nalgorithms. \n\n1 \n\nINTRODUCTION \n\nUnsupervised neural networks frequently employ sets of nodes or subnetworks \nwith identical architecture and objective function. Some form of competitive inter(cid:173)\naction is then needed for these nodes to differentiate and efficiently complement \neach other in their task. \n\n\f476 \n\nNicol Schraudolph, Terrence 1. Sejnowski \n\n1.00 -\n\n0.50 -\n\n0.00 -\n\nj ................................. '.' \n\n-\n\nf(y) \n\u00b74r(y)' .... \n\n.......... / / .... \u00b7\u00b71 \n\n= ... = ... :::. ... :::: ... :j:. ... :..... ... -.. -~ \n\n'.:! ' .... \"\u00b7\u00b7,,\u00b7\u00b7.,, . .. \n\n' .. 1 \u2022\u2022\u2022\u2022 \u2022\u2022\u2022\u2022\u2022\u2022 \u2022\u2022 \u2022 \n\n-4.00 \n\n-2.00 \n\n0.00 \n\n2.00 \n\n4.00 \n\ny \n\nFigure 1: Activity f and plasticity f' of a logistic node as a function of its net input \ny. Vertical lines indicate those values of y whose pre-images in input space are \ndepicted in Figure 2. \n\nInhibition is the simplest competitive mechanism: the most active nodes suppress \nthe ability of their peers to learn, either directly or by depressing their activity. \nSince inhibition can be implemented by diffuse, nonadaptive mechanisms, it is an \nattractive solution from both neurobiological and computational points of view. \nHowever, inhibition can only form either localized (unary) or sparse distributed \nrepresentations, in which each output has only one state with significant informa(cid:173)\ntion content. \nFor fully distributed representations, schemes to decorrelate (Barlow and Foldiak, \n1989; Leen, 1991) and even factorize (Schmidhuber, 1992; Bell and Sejnowski, 1995) \nnode activities do exist. Unfortunately these require specific, weighted lateral \nconnections whose adaptation is computationally expensive and may interfere \nwith feedforward learning. While they certainly have their place as competitive \nlearning algorithms, the capability of biological neurons to implement them seems \nquestionable. \nIn this paper, we suggest an alternative approach: we extend the advantages of \nsimple inhibition to distributed representations by decoupling the competition \nfrom the activation vector. In particular, we use neural plasticity -\nthe derivative \nof a logistic activation function - as a medium for competition. \nPlasticity is low for both high and low activation values but high for intermediate \nones (Figure 1); distributed patterns of activity may therefore have localized plastic(cid:173)\nity. If competition is controlled by plasticity then, simple competitive mechanisms \nwill constrain us to localized plasticity but allow representations with distributed \nactivity. \nThe next section reintroduces the binary information gain optimization (BINGO) \nalgorithm for a single node; we then discuss how plasticity-mediated competition \nimproves upon the decorrelation mechanism used in our original extension to \nmultiple nodes. Finally, we establish a close relationship between the plasticity \nand the entropy of a logistiC node that provides an intuitive interpretation of \nplasticity-mediated competitive learning in this context. \n\n\fPlasticity-Med;ated Competitive Learning \n\n477 \n\n2 BINARY INFORMATION GAIN OPTIMIZATION \n\nIn (Schraudolph and Sejnowski, 1993), we proposed an unsupervised learning rule \nthat uses logistic nodes to seek out binary features in its input. The output \n\nz = f(y), where f(y) = 1 + e- Y and y = tV \u00b7 x \n\n1 \n\n(1) \n\nof each node is interpreted stochastically as the probability that a given feature is \npresent. We then search for informative directions in weight space by maximizing \nthe information gained about an unknown binary feature through observation of \nz. This binary infonnation gain is given by \n\nD.H(z) = H(Z) - H(z) , \n\n(2) \nwhere H(z) is the entropy of a binary random variable with probability z, and z \nis a prediction of z based on prior knowledge. Gradient ascent in this objective \nresults in the learning rule \n\nD.w