Fixed or variable noise in contrast discrimination? The jury's still out

The ability to distinguish one visual stimulus from another slightly different one depends on the variability of their internal representations. In a recent paper on human visual-contrast discrimination, Kontsevich et al (2002 Vision Research 42 1771 - 1784) re-considered the long-standing question whether the internal noise that limits discrimination is fixed (contrast-invariant) or variable (contrast-dependent). They tested discrimination performance for 3 cycles deg-1 gratings over a wide range of incremental contrast levels at three masking contrasts, and showed that a simple model with an expansive response function and response-dependent noise could fit the data very well. Their conclusion - that noise in visual-discrimination tasks increases markedly with contrast - has profound implications for our understanding and modelling of vision. Here, however, we re-analyse their data, and report that a standard gain-control model with a compressive response function and fixed additive noise can also fit the data remarkably well. Thus these experimental data do not allow us to decide between the two models. The question remains open. [Supported by EPSRC grant GR/S74515/01]

Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.