a=b write

Remap prompt a so its velocity behaves like concept b. One loss. It does not turn b up everywhere.

Category: velocity · Identity: write

Syntax

a=b
a=b:0.8
a=b:guidance=2
=b
b=

The target b is required. A bare = raises DSLError. =b and b= both write b into the empty prompt (a="").

Velocity target

In b's sampling context. When a is non-empty the GPU trainer wraps a and b in one shared template from WRITE_TEMPLATES. The 2-D fixture and loss_game pin that list to "{}".

v0 = v_f("")
vb = v_f(b)
v_t(a) → v0 + g (vb − v0)
loss = MSE

g is options["guidance"] if set, otherwise OpDefaults.write_guidance.

Defaults

Knob	Trainer OpDefaults	2-D fixture and loss_game
alpha	1	1
guidance	2 (overshoot past an exact copy)	1 (exact remap)

The game uses the fixture pin on purpose. It does not invent a third guidance. GPU training still constructs OpDefaults() unless a script overrides it, so a DiT run of red=blue uses guidance 2 unless you set :guidance=.

Composition

= does not boost b on prompts that never said a. The swap recipe that also exaggerates b and lightly aligns is a~b (replace), or the same three rules written out.

Mix on this fixture is red=red stripe (write toward the concatenated embedding). Isolate is red stripe=stripe. Both are writes. A + glyph would be a synonym here; it is not a separate op. See ../../dsl.md.

2-D verdict

../../dsl.md: right for red=blue. Trained red aligns with frozen blue; stripe hold stays high.

Uncond =b cannot move this fixture: e("") is the zero vector, so the shared LoRA has nothing to grab. That is a fixture limit, not a parser bug. Worked phrase: ../examples/remap.md.

Failure modes

• Expecting cat=dog to boost dogs that were never cats. It will not. Use ~ or add dog++.
• guidance left at the trainer default (2) is a stronger write than the 2-D pictures, which use 1.
• Prompts that contain =, :, |, #, %, ^, or ~ must go through sanitize_prompt before they are pasted into a rule.

Example

from conceptmod.dsl import parse_phrase
rule = parse_phrase("red=blue")[0]
assert (rule.op, rule.a, rule.b) == ("write", "red", "blue")
assert parse_phrase("=blue")[0].a == ""