Exact Filters

Shared Filter, Same Weights

The same given filter is reused at two different windows, and both output sums are recomputed exactly from the visible patches.

highlighted = computed this step

Keep the filter unchanged

Use the same pinned 2 by 2 filter at two visible windows. The filter weights are not rewritten between landings.

same 2×2 filter at two windows\text{same }2\times2\text{ filter at two windows}
Shared Filter, Same WeightsThe same 2x2 filter is reused at two visible windows.shared-filter demo imagec1c2c3c4c51020301010201020101030201same 2x2 filterc1c21001unchanged for both windowsshared filter, same weightslandingvisible patchsame-filter arithmeticsumwindow 1 start (0,0)[1, 0; 0, 1]1*1 + 0*0 + 0*0 + 1*12window 2 start (0,2)[2, 0; 0, 1]1*2 + 0*0 + 0*0 + 1*13same filter weights reused; sums 2 and 3same 2x2 filter; two exact window sumsone exact shared-weight mechanic; head softmax is NAMEDNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT probability truthNOT feature quality; NOT model quality; NOT learned real CNN filter

First window sum

At start (0,0), the shared filter gives 1·1 + 0·0 + 0·0 + 1·1 = 2.

1⋅1+0⋅0+0⋅0+1⋅1=21\cdot1 + 0\cdot0 + 0\cdot0 + 1\cdot1 = 2
Shared Filter, Same WeightsThe same 2x2 filter is reused at two visible windows.shared-filter demo imagec1c2c3c4c51020301010201020101030201same 2x2 filterc1c21001unchanged for both windowsshared filter, same weightslandingvisible patchsame-filter arithmeticsumwindow 1 start (0,0)[1, 0; 0, 1]1*1 + 0*0 + 0*0 + 1*12window 2 start (0,2)[2, 0; 0, 1]1*2 + 0*0 + 0*0 + 1*13same filter weights reused; sums 2 and 3same 2x2 filter; two exact window sumsone exact shared-weight mechanic; head softmax is NAMEDNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT probability truthNOT feature quality; NOT model quality; NOT learned real CNN filter

Second window sum

At start (0,2), the filter is still the same. The exact sum is 1·2 + 0·0 + 0·0 + 1·1 = 3.

1⋅2+0⋅0+0⋅0+1⋅1=31\cdot2 + 0\cdot0 + 0\cdot0 + 1\cdot1 = 3
Shared Filter, Same WeightsThe same 2x2 filter is reused at two visible windows.shared-filter demo imagec1c2c3c4c51020301010201020101030201same 2x2 filterc1c21001unchanged for both windowsshared filter, same weightslandingvisible patchsame-filter arithmeticsumwindow 1 start (0,0)[1, 0; 0, 1]1*1 + 0*0 + 0*0 + 1*12window 2 start (0,2)[2, 0; 0, 1]1*2 + 0*0 + 0*0 + 1*13same filter weights reused; sums 2 and 3same 2x2 filter; two exact window sumsone exact shared-weight mechanic; head softmax is NAMEDNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT probability truthNOT feature quality; NOT model quality; NOT learned real CNN filter

What this mechanic says

This is one exact shared-weight convolution mechanic. It is NOT training, NOT learning, NOT generalization, NOT accuracy, NOT calibration, NOT probability truth, NOT feature quality, NOT model quality, and NOT a learned real CNN filter.

same filter; recomputed exact sums 2 and 3\text{same filter; recomputed exact sums }2\text{ and }3
Shared Filter, Same WeightsThe same 2x2 filter is reused at two visible windows.shared-filter demo imagec1c2c3c4c51020301010201020101030201same 2x2 filterc1c21001unchanged for both windowsshared filter, same weightslandingvisible patchsame-filter arithmeticsumwindow 1 start (0,0)[1, 0; 0, 1]1*1 + 0*0 + 0*0 + 1*12window 2 start (0,2)[2, 0; 0, 1]1*2 + 0*0 + 0*0 + 1*13same filter weights reused; sums 2 and 3same 2x2 filter; two exact window sumsone exact shared-weight mechanic; head softmax is NAMEDNOT training; NOT learning; NOT generalizationNOT accuracy; NOT calibration; NOT probability truthNOT feature quality; NOT model quality; NOT learned real CNN filter