Neuralink Compression Submission

Problem Statement

See Problem.

Software Used

7Zip:

$ 7z

7-Zip 24.05 (x64) : Copyright (c) 1999-2024 Igor Pavlov : 2024-05-14

FFMpeg:

$ ffmpeg
ffmpeg version 6.0-full_build-www.gyan.dev Copyright (c) 2000-2023 the FFmpeg developers
  built with gcc 12.2.0 (Rev10, Built by MSYS2 project)
  configuration: --enable-gpl --enable-version3 --enable-shared --disable-w32threads --disable-autodetect
                 --enable-fontconfig --enable-iconv --enable-gnutls --enable-libxml2 --enable-gmp
                 --enable-bzlib --enable-lzma --enable-libsnappy --enable-zlib --enable-librist --enable-libsrt
                 --enable-libssh --enable-libzmq --enable-avisynth --enable-libbluray --enable-libcaca --enable-sdl2
                 --enable-libaribb24 --enable-libdav1d --enable-libdavs2 --enable-libuavs3d --enable-libzvbi 
                 --enable-librav1e --enable-libsvtav1 --enable-libwebp --enable-libx264 --enable-libx265
                 --enable-libxavs2 --enable-libxvid --enable-libaom --enable-libjxl --enable-libopenjpeg
                 --enable-libvpx --enable-mediafoundation --enable-libass --enable-frei0r --enable-libfreetype
                 --enable-libfribidi --enable-liblensfun --enable-libvidstab --enable-libvmaf --enable-libzimg
                 --enable-amf --enable-cuda-llvm --enable-cuvid --enable-ffnvcodec --enable-nvdec --enable-nvenc
                 --enable-d3d11va --enable-dxva2 --enable-libvpl --enable-libshaderc --enable-vulkan --enable-libplacebo
                 --enable-opencl --enable-libcdio --enable-libgme --enable-libmodplug --enable-libopenmpt
                 --enable-libopencore-amrwb --enable-libmp3lame --enable-libshine --enable-libtheora --enable-libtwolame
                 --enable-libvo-amrwbenc --enable-libilbc --enable-libgsm --enable-libopencore-amrnb --enable-libopus
                 --enable-libspeex --enable-libvorbis --enable-ladspa --enable-libbs2b --enable-libflite --enable-libmysofa
                 --enable-librubberband --enable-libsoxr --enable-chromaprint
  libavutil      58.  2.100 / 58.  2.100
  libavcodec     60.  3.100 / 60.  3.100
  libavformat    60.  3.100 / 60.  3.100
  libavdevice    60.  1.100 / 60.  1.100
  libavfilter     9.  3.100 /  9.  3.100
  libswscale      7.  1.100 /  7.  1.100
  libswresample   4. 10.100 /  4. 10.100
  libpostproc    57.  1.100 / 57.  1.100

Python:

$ python --version
Python 3.12.3

SciPy/NumPy:

$ pip install -U scipy
Requirement already satisfied: scipy in python312\lib\site-packages (1.13.1)
Requirement already satisfied: numpy<2.3,>=1.22.4 in python312\lib\site-packages (from scipy) (1.26.4)

GoldWave:

v6.80

Basic Data Analysis

An analysis of the file in data.zip reveals a ton of .wav files. First, we want to find out what are these files, what is the size of metadata in all these files.

We prepare the Data folder by simply unzipping:

$ 7z x data.zip

and we basically try to look at what the data is:

$ file data/00d4f842-fc92-45f5-8cae-3effdc2245f5.wav
data/00d4f842-fc92-45f5-8cae-3effdc2245f5.wav: RIFF (little-endian) data, WAVE audio, Microsoft PCM, 16 bit, mono 19531 Hz

Audio File Entropy

First, I converted manually to ALAC to see how it fared, and removed all metadata.

$ du -hs data/00d4f842-fc92-45f5-8cae-3effdc2245f5.wav
196K    data/00d4f842-fc92-45f5-8cae-3effdc2245f5.wav

$ ffmpeg -i data/00d4f842-fc92-45f5-8cae-3effdc2245f5.wav -map_metadata -1 -acodec alac data/00d4f842-fc92-45f5-8cae-3effdc2245f5.m4a

$ du -hs data/00d4f842-fc92-45f5-8cae-3effdc2245f5.m4a
132K    data/00d4f842-fc92-45f5-8cae-3effdc2245f5.m4a

I also tried compressing the file individually, and saw that zip and 7z formats did just as badly. What is to be remembered is that a streaming format is optimized for lower latencies, and few good streaming libraries exist for archival formats.

$ cd data
$ 7z a -tzip -mx9 00d4f842-fc92-45f5-8cae-3effdc2245f5.zip 00d4f842-fc92-45f5-8cae-3effdc2245f5.wav
$ 7z a -t7z -mx9 00d4f842-fc92-45f5-8cae-3effdc2245f5.7z 00d4f842-fc92-45f5-8cae-3effdc2245f5.wav

$ du -hs 00d4f842-fc92-45f5-8cae-3effdc2245f5.zip
$ 75K    00d4f842-fc92-45f5-8cae-3effdc2245f5.zip

$ du -hs 00d4f842-fc92-45f5-8cae-3effdc2245f5.7z
$ 75K    00d4f842-fc92-45f5-8cae-3effdc2245f5.7z
$ cd ..

So, 7z still seems to do better in compression ratio. However, there is a lot of unncessary information stored (file, bytes etc.) in the Zip, and metadata information is redundant and significant, so what is the impact of eliminating all of that, assuming the textual data can be moved to a side-channel and encoded much better.

$ python Scripts/ConcatenateWav.py
$ 7z a -tzip -mx9 Output.zip Output.wav
$ 7z a -tzip -mx9 OutputSide.zip Output.txt

$ du -hs Output.zip
57M     Output.zip

$ du -hs OutputSide.zip
20K     Output.zip

We just saved 6MB excluding the list of files and all the extraneous metadata alone.

The SideCar data is only a mere 20KB. If we only emitted the frames information and the filename had no relevance (seems to be a random UUID), the whole thing is 1374 bytes only even when compressed as text.

What about 7z?

$ 7z a -t7z -mx9 Output.7z Output.wav
$ 7z a -t7z -mx9 OutputSide.7z Output.txt

$ du -hs Output.7z
50M     Output.7z

$ du -hs OutputSide.7z
16K     OutputSide.7z

We already improved the baseline by 12MB, a 20% saving. With extremely time-taking compression, but it gets us very close to the entropy of this file. Sidecar sizes are similar.

This isn't great but it already confirms my suspicions about the file.

Audio/Perception based Entropy

One of the better approaches to compress this kind of data is based on Fourier transforms. If we can visualize this file better, we can see if it's random noise or smooth stuff.

It's not random noise, when I concatenated the whole damn thing and opened in GoldWave. What I saw was this:

So, it looks like it can be compressed lossily, and we can print the PSNR. This is outside the scope of the assignment, but I want it looked at carefully.

This is how MP3 fares:

$ ffmpeg -i Output.wav -c:a mp3 Output.mp3

$ du -hs Output.mp3
15M    Output.mp3

and 64 kbps Opus:

$ ffmpeg -i Output.wav -c:a libopus Output.opus

$ du -hs Output.opus
30M     Output.opus

and 32 kbps Opus:

$ ffmpeg -i Output.wav -b:a 32k -c:a libopus Output.opus

$ du -hs Output.opus
14M     Output.opus

and back:

$ ffmpeg -i Output.opus -ar 19531 Lossy.wav

$ du -hs Lossy.wav
140M    Lossy.wav

Already at a further 40-80% reduction in size. What is the perceptual difference between these files?

For MP3:

$shell Scripts/SNR.py
Output.wav => 0.30912332921100283
Lossy.wav => 0.3086850807150957

For 64 kbps Opus:

$ python Scripts/SNR.py
Output.wav => 0.30912332921100283
Lossy.wav => 0.0002217705736148185

For 32 kbps Opus:

$ python Scripts/SNR.py
Output.wav => 0.30912332921100283
Lossy.wav => -2.963617756168254e-05

MP3 seems to be Viable?!! The WaveForm Image Comparison does not appear to be bad at all! Of course it's not lossless, but it's already 1/4th of the Zip file size to begin with.

If Neuralink Scientists are interested, they should give this a try and see how it fares in lab tests.

Conclusion

I first looked at the data, tried to separate the signal data and the metadata. That gave us a good way to get rid of extraneous attributes quickly.

Some basic findings there:

• Individual signal data entropy is not same as Individual file entropy.
• Combined file entropy is not the same as packing individual data together in a Zip file.
• Use the Wave Combiner then run compression on the Output.wav. Compress the Sidecar separately.
• Their per file compression has a lower ratio than combined.
• If Neuralink had shipped a zip file for each wav it would be much larger.
• If Neuralink need all these files separately and yet they wish to compress better, they need a side car to store segment information efficiently.
• Individual file entropy is meaningless if a collection of wav files together plus their sidecar has lower entropy.

Next, I checked out the feasibility of the lossless audio algorithms available today. They did not perform better than the textual algorithms.

There are a lot of Hutter Prize algorithms to compress this data losslessly at high ratios, they do not work well today to meet the latency nor compression ratio constraints. Even the best ones. Assuming you wanted to develop a low cost low power chip to do that algorithm, there isn't one to compress as fast today to meet the latency challenges. Not at 10mW with a latency of <1ms at 200x ratios, with humanly available technology in 2024. If there is amazing alien level technology available today in a secret government lab, I'd say bring it on and solve for the world.

If there is a good signal generator (or an encoder) available already which can mimic the behavior of the real world, that would indeed be the ideal scenario, then all you need to do is send the command stream across and play it on the other side. Then you don't start with generic audio files like this, you just go digital already!

Another thing is how important each electrode's data is. This can only come from empirical experimentation, and since I am not a Neuroscientist yet I cannot tell how to get rid of extraneous signal entropy any more. I am also assuming this signal data will be noisy, the real world needs to tell me if this assumption is correct or not.

Next, I actually analyzed the signal data for what we can do with it today. What I found was that lossy compression is actually reasonably better than LZ based file compression. We can get roughly 15MB of audio data for an hour tops and has excellent SNR ratios similar to the original. If we do not need higher fidelity, we do not need to overengineer for it. Adequate is what I am aiming for.

I think lossy compression might have a bright future if a good SNR value can be determined. In all seriousness, Engineering is about making things happen today with what's available today to shape a better tomorrow. Innovation is great yet there needs to be more talk about what is good enough for a variety of usecases, so that it helps us embrace and design for real-world constraints.

Feedback

All feedback welcome!

• Author: Karthik Kumar Viswanathan
• Web : http://karthikkumar.org
• Email : [email protected]