We present a new supervised learning procedure for systems composed of many separate networks, each of which learns to handle a subset of the complete set of training cases. The new procedure can be viewed either as a modular version of a multilayer supervised network, or as an associative version of competitive learning. It therefore provides a new link between these two apparently different approaches. We demonstrate that the learning procedure divides up a vowel discrimination task into appropriate subtasks, each of which can be solved by a very simple expert network.

One way of simplifying neural networks so they generalize better is to add an extra term to the error function that will penalize complexity. Simple versions of this approach include penalizing the sum of the squares of the weights or penalizing the number of nonzero weights. We propose a more complicated penalty term in which the distribution of weight values is modeled as a mixture of multiple gaussians. A set of weights is simple if the weights have high probability density under the mixture model. This can be achieved by clustering the weights into subsets with the weights in each cluster having very similar values. Since we do not know the appropriate means or variances of the clusters in advance, we allow the parameters of the mixture model to adapt at the same time as the network learns. Simulations on two different problems demonstrate that this complexity term is more effective than previous complexity terms.

With a moment's thought, few of us would doubt that we move through our lives with preconceptions about physical and social causation. Few of us would doubt also that evidence via events which bear on these preconceptions sometimes results in knowledge change and sometimes has no effect. This being the case, it is crucial from the perspectives of both learning theory and educational practice to understand the processes of evidence-preconception coordination, and this is what motivated the study around which Strategies of Knowledge Acquisition revolves. The study involved ascertaining the preconceptions held by adults and children aged 8 to 10 regarding the causation of physical (speed of boats through water, speed of cars round racetracks) and social (school achievement of pupils, popularity of television programmes) phenomena. In particular, five variables were presented for each phenomenon, for instance water depth, boat size, boat weight, sail colour and sail size for speed of boats, and the participants were quizzed as to which variables they believed to be causal. They were then invited to determine empirically whether they were correct, the main interest being in whether they conducted appropriate tests and/or integrated results with expressed preconceptions. Since the participants worked with one physical phenomenon and one social for five weeks and then switched to the other physical and social phenomena for a further five weeks, the study provided evidence on changes over time within problem contexts and transfer of changes across problem contexts, in addition to the effects of age and (physical vs. social) domain.With each of the phenomena, some variables had been selected by the researchers to be relevant to outcome, and some to be irrelevant. Some variables were relevant in a simple linear fashion while others were more complex, being relevant for example at a single level of an alternative variable. Finally, the relevance or irrelevance of some variables typically concurred with the participants' preconceptions, whereas the relevance or irrelevance of others was usually discordant. These considerations made a difference: all participants had the greatest difficulties with non-linear variables and with variables which did not operate as expected. However, within this overarching pattern, there were differences as a function of time, age and domain. Over time, participants' beliefs usually became more accurate, and their approach to testing more appropriate. For instance, there was increasing reference to test results when discussing beliefs, and these references were increasingly valid. Importantly, gains made during the first five weeks were not compromised by the introduction of new material at the beginning of the sixth. Without doubt though, the adults started from a higher baseline than the children, and profited more from the experience. Most adults used a mixture of valid and invalid test strategies from the outset, shifting the balance over time towards the former. Only one child displayed val...

We present a new approach to computing from image sequences the two-dimensional velocities of moving objects that are occluded and transparent. The new motion model does not attempt to provide an accurate representation of the velocity flow field at fine resolutions but coarsely segments an image into regions of coherent motion, provides an estimate of velocity in each region, and actively selects the most reliable estimates. The model uses motion-energy filters in the first stage of processing and computes, in parallel, two different sets of retinotopically organized spatial arrays of unit responses: one set of units estimates the local velocity, and the second set selects from these local estimates those that support global velocities. Only the subset of local-velocity measurements that are the most reliable is included in estimation of the velocity of objects. The model is in agreement with many of the constraints imposed by the physiological response properties of cells in primate visual cortex, and its performance is similar to that of primates on motion transparency.