Thermometer Encoding

[georgwiese]

Depends on #20

This PR adds two gadgets:

• GreaterThanChip: Computes x > y
• EncodeImageChip: Maps an image to a binary vector by comparing each pixel to multiple binarization thresholds

The WnnChip then wires everything together and now proves the entire prediction, starting from the intensity values of the image! 🎉 The most involved part here was writing a test which asserts the right outputs all the way from the pixel values.

Other Changes:

• The HashChip no longer needs to range-check its inputs, because they are now comping from the Bits2NumChip, which guarantees that they can be represented by a certain number of bits.
• I got rid of warnings by allowing dead code in the (currently unused) "Single Bit Bloomfilter" gadget.

These are the benchmark results (including the changes from #20):

benches/proof_generation
                        time:   [1.6548 s 1.6812 s 1.7049 s]
                        change: [+28.771% +31.727% +34.625%] (p = 0.00 < 0.05)
                        Performance has regressed.
benches/key_generation  time:   [888.46 ms 905.16 ms 924.79 ms]
                        change: [+7.9176% +10.317% +13.273%] (p = 0.00 < 0.05)
                        Performance has regressed.
benches/verification    time:   [14.755 ms 15.330 ms 15.743 ms]
                        change: [+3.5830% +11.686% +20.987%] (p = 0.01 < 0.05)
                        Performance has regressed.

Fixes #6

[ElusAegis]

Good job. We can merge it as it is, but in general I feel like we should make the image as an Instance Column so that we would known on which image we actually got the result

[ElusAegis]

Should the image be as a public input in Advice? As now we are proving that some image was converted into a valid representation

[georgwiese]

Thanks for the review!

I think both use cases are valid, with public and private input. For private input, you'd probably want to additionally validate the image in the circuit (e.g. by checking the signature of an attested sensor). So then, you'd use this codebase as a library.

I think we should support both and opened #21 to track it.