This is quite a neat research direction and I think the title undersells it? I thought it was “circle-days of the week” (which is so last year, pun unintended) geometry as opposed to “Some features change across longer sequence positions; most don’t. We use simple probes to show this.”, which is much cooler.
Renamed along the lines of your suggestion, thanks! For people reading later, the original title was “The Residual Stream has a Geometry of Time.”
How would you classify this research direction? I look at it as searching for axes to carve the residual stream, where my bet is that valuable axes are scarce. SAEs found one through sparsity, timescale could prove to be another.
There’s also the provenance axis, meaning which component wrote a direction. I already estimated it cheaply here (though this is just alignment, not necessarily provenance), and slow directions skew attention-aligned beyond what residual PCA alone explains. Any ideas on what the other axes could be?
This is quite a neat research direction and I think the title undersells it? I thought it was “circle-days of the week” (which is so last year, pun unintended) geometry as opposed to “Some features change across longer sequence positions; most don’t. We use simple probes to show this.”, which is much cooler.
Renamed along the lines of your suggestion, thanks! For people reading later, the original title was “The Residual Stream has a Geometry of Time.”
How would you classify this research direction? I look at it as searching for axes to carve the residual stream, where my bet is that valuable axes are scarce. SAEs found one through sparsity, timescale could prove to be another.
There’s also the provenance axis, meaning which component wrote a direction. I already estimated it cheaply here (though this is just alignment, not necessarily provenance), and slow directions skew attention-aligned beyond what residual PCA alone explains. Any ideas on what the other axes could be?