The Advanced Quantizer is a max for live device that allows you to quantize each track individually, quantize note ons and offs separately, move the halfway line in between quantization points, allowing for a bias before quantization, and move the actual quantization point back by a fraction of a beat or certain time, in ms.
How it works:
Note ons and offs can be quantized separately, or the length of the note can be preserved (how quantization works normally within Ableton). When note offs are quantized, you can effectively quantize notes to line up on the grid perfectly, as if drawn with the pen tool.
The "before" dial moves the halfway line in between two quantization points, and can be set in fractions of a beat or ms. This makes it possible to snap a note to the nearest quantization point behind where it was recorded and never quantize it forward, even if it is closer to the forward quantization marker.
The quantization drop down menu sets the quantization mode. All modes are an option, including triplets + 8th notes and triplets + 16th notes.
The "after" dial moves the points of quantization back/forward in beats or ms. This means you can quantize to an off-the-beat point. I personally find this useful for looping drums, and adding a more human feel for quantizing other synths, especially while live looping.
This device will disable itself if Ableton's quantization is enabled. This is because having it on can create a feedback loop, if 2 quantizers are fighting each other on where the note is placed.
This device works on the currently selected clip within the track the device is placed on. This allows you to have advanced quantization work differently across all tracks. This does mean that quantization will not work if a clip is not currently selected.
Any notes placed on the piano roll while recording will be quantized, even if drawn with the pen tool. There's no way to differentiate between this through the API