Mỗi ô đại diện cho một giá trị khác nhau, và các giá trị của b được biểu diễn trong hộp bởi vị trí đầu vào tương ứng. Trọng lượng được thể hiện bằng mức độ màu xám quy mô với 0 màu xám | 22 Representational Learning A B projective field receptive field - dots receptive field - gratings Figure Projective and receptive fields for a sparse coding network with Nu Nv 144. A Projective fields Gab with a indexing representational units the components of v and b indexing input units u ona12 X 12 pixel grid. Each box represents a different a value and the b values are represented within the box by the corresponding input location. Weights are represented by the gray-scale level with gray indicating 0. B The relationship between projective and receptive fields. The left panel shows the projective field of one of the units in A. The middle and right panels show its receptive field mapped using inputs generated by dots and gratings respectively. Adapted from Olshausen and Field 1997. Peter Dayan and . Abbott Draft December 17 2000 Causal Models for Density Estimation 23 Projective fields for the Olshausen and Field model trained on natural scenes are shown in figure with one picture for each component of v. In this case the projective field for va is simply the matrix elements Gab plotted for all b values. In figure the index b is plotted over a two-dimensional grid representing the location of the input ub within the visual field. The projective fields form a Gabor-like representation for images covering a variety of spatial scales and orientations. The resemblance of this representation to the receptive fields of simple cells in primary visual cortex is quite striking although these are the projective not the receptive fields of the model. Unfortunately there is no simple form for the receptive fields of the v units. Figure compares the projective field of one unit to receptive fields determined by presenting either dots or gratings as inputs and recording the responses. The responses to the dots directly determine the receptive field while responses to the gratings directly determine the Fourier transform of the receptive .
