Heart Rate not accurate in "Yoga" activity (reported HR too low) but fine in "Cardio" activity.

The first image is the HIIT workout as "cardio" and the second one is the same workout one day later as "yoga". The difference here is huge.

Is this the difference the watsch SHOULD be causing?

even when I actually do yoga I get a higher average heart rate.

I would say that the difference is as expected with the current technology. You would probably see similar results with other watches. Hopefully the hardware and software will improve over the next few years, to make the readings more trustworthy.

When you say that 10 percent variance would make sense, is that from a user point of view, or a technical point of view? Are you familiar with algorithms for Fourier transformations and Laplace transformations / Z-transformations?

I'm well aware of the equations and how they have little to no relevance here. All of that fancy underlying mathematics (and engineering) is to use a photo sensor and an led in the evaluation of the skin to determine "was there a heart beat".  If you set the watch to yoga activity and go for a run, the watch will maintain a much better mechanical connection to the skin and you can crudely account for differences between modes. Better yet you can do what I did and have the watch under an old schoool cotton nike arm band which will block out light seeping in and further increase the contact which should result in more accuracy. It doesn't. It still registers 30bpm below when it is in "Cardio" or "Running" mode.

There are existing modes that are reasonably accurate. Yoga mode IS NOT.We want the heart rate accuracy from Running or Cardio mode to be reflected in the Yoga mode. This is an inherently reasonable ask because the accuracy can be achieved with the device but it is simply not implemented in the specific mode.

For me, the cardio mode is very inaccurate if I use it for anything but cardio, as the watch expects high heart rate and rapid changes. When lifting weights around 100 BPM, the watch will sometimes register around 200 BPM in cardio mode, which is over my maximum heart rate. If I do yoga, my heart rate is typically around 60-90, and changing slowly. The yoga mode is a lot more accurate for me than cardio in this situation, as this is the pattern the algorithm is optimized for.

Knowing the algorithms have relevance to understand why they are more likely to miss by 50 percent than by 10 percent.

If your heart rate is not typical for the event you are doing, it makes sense to try other activity types to get better accuracy.

I had this same issue. Was doing a tabata class and could barely catch my breath and my Garmin watch kept saying HR around 80. I only realised it was on yoga mode when I ended the workout and my data synched to the app on phone.