a%b orthogonal

Decorrelate the trained concept direction of b from the frozen direction of a. Negative alpha aligns them (a blend). Only b is trained.

Category: velocity · Identity: orthogonal

Syntax

a%b
a%b:2
a%b:-0.1
a%b:--0.1

Both sides are required. The extra leading - on an alpha (--0.1) is accepted and means -0.1, matching the original parser.

{random_prompt} is legal on either side. materialize (and loss_game(..., random_prompt=)) substitutes it. The placeholder is not a loss by itself.

Velocity target

da = CFG_f(a) = v_f(a) − v_f("")
db = CFG_t(b) = v_t(b) − v_t("")
loss = orthogonal_scale * mean(|cos(da, db)|)

The value is non-negative. The trainer multiplies by rule.alpha, so a negative alpha maximizes |cos| (align) instead of minimizing it. The loss does not flip its own sign.

Defaults

Knob	Trainer OpDefaults	2-D fixture and loss_game
alpha	1 (decorrelate)	1
orthogonal_scale	0.01	1

The fixture scale is larger so a non-zero cosine would actually move the tiny field. On this field the cosine starts at 0, so the scale does not matter: the gradient is zero either way. The game copies the fixture pin. It does not define a third scale.

Composition

% is one-directional. A mutual blend is two rules:

red%stripe:-1|stripe%red:-1

A small negative % next to a write is a regularizer, not the remap:

#:0.4|human=robot:0.8|robot%human:-0.1

That composite is the original-repo phrase. The human/robot words are the historical example; the 2-D scoreboard uses color and pattern.

% does not project a mix onto one axis. red%red stripe inflates the perpendicular component. The isolate job is the write red stripe=stripe.

2-D verdict

../../dsl.md: right no-op. The color and pattern axes start orthogonal, so |cos| = 0 and the gradient vanishes. Negative % therefore cannot create a mix from a perpendicular pair. Use red=red stripe for that job.

The SANA proof anime%hyperrealistic:-3|hyperrealistic%anime:-3 is the same op on concepts that are already correlated. That is a different geometry from this fixture. Do not read the 2-D no-op as "blend is broken."

Failure modes

• Expecting % to subtract a concept the way a projection would. It minimizes absolute cosine, which can grow the part of b that was already perpendicular.
• Expecting negative % to mix red with stripe from a cold start on this fixture. It will not move.
• Leaving orthogonal_scale at 0.01 on a GPU run and wondering why a mild |cos| barely shows up. Raise alpha, or add a # anchor, before inventing a new glyph.

Example

from conceptmod.dsl import parse_phrase
rule = parse_phrase("red%stripe:-0.1")[0]
assert (rule.op, rule.a, rule.b, rule.alpha) == ("orthogonal", "red", "stripe", -0.1)