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EMNLP 2026 Tutorial · Causal Foundations for Interpretability
Steering along a mixed axis moves two concepts
A mixed axis: steering along it moves both concepts.
rotate the axes
63° on the slide
63°
steering strength
0.0
position
colour
blue, left
pink, right
grey, centre
learned axis 1
the steered ball, as a picture
left
centre
right
Position moved
0.00
Colour moved
0.00
Balls:
three pictures of a ball, each placed where the encoder puts it.
Grey lines:
the true axes, position (across) and colour (up).
Steering:
moving the grey ball’s encoding along learned axis 1, as far as the strength says.
Mixed axis:
at any angle but 0° or 90°, learned axis 1 is part position, part colour.
Numbers
are in the toy’s units: the blue ball sits at (−13, −7), the pink at (13, 7).