Perpendicular Component

Perpendicular Component (class Perpendicular Component Mecha Recipe) is the geometry node of the merge toolkit. Give it two vectors - it treats each tensor of model b as a vector - and it returns the component of b that's orthogonal to a: everything in b minus its projection onto a. It's the "give me what B contributes that A doesn't already cover" operation.

Why would you want that? Model merges are full of overlapping directions. If you're combining two deltas that both push in similar ways, a plain add double-counts the shared part. Taking the perpendicular component of one relative to the other strips away the overlap, so what you add to a is only the genuinely new information from b. It's a de-redundancy filter, and it's the heart of the pack's Add Perpendicular method (which subtracts a common base from two models, takes the perpendicular component, and adds it back).

How it works

Per tensor, the math is the standard vector projection removal:

res = b − a · (a / ‖a‖) · (b / ‖a‖)

i.e. subtract from b its projection onto the direction of a. If the result comes out NaN - which happens when a is (near) zero and the projection is undefined - the node returns a zero tensor for that key instead of crashing the merge.

The inputs that matter:

• a, b (both MECHA_RECIPE, required) - a defines the direction to remove; b is what gets orthogonalized. The output is a modified b.
• recipe (output, weight space) - the orthogonal component of b. Wire it into an Add Difference/Add Perpendicular step or combine it into a larger recipe.

A couple of framing notes so the math lands. This works on weight-space tensors and is generally used in delta-composition flows: you subtract a base from two fine-tunes, orthogonalize one delta against the other, then combine. It's also the operation that makes some "debias" merges work - removing what's shared with a reference direction leaves only what's unique to the model you care about.

Install

It's part of the Mecha Merge Node Pack (ljleb/comfy-mecha):

• ComfyUI Manager → Install Custom Nodes → search "mecha" → Mecha Merge Node Pack, or manually:

cd ComfyUI/custom_nodes
git clone https://github.com/ljleb/comfy-mecha.git
pip install -r comfy-mecha/requirements.txt

Restart, find it under mecha. The pack's only dependency is sd-mecha==1.1.7; no model downloads.

Common issues

• Zero tensors in a produce zeroed output. That's the designed NaN fallback, and it means "nothing to remove here." Usually harmless, occasionally worth knowing about when the whole output looks suspiciously empty.
• Input order flips the meaning. Orthogonalizing b against a is not the same as orthogonalizing a against b. If your merge suddenly has less of the model you wanted, check which direction you wired.
• It's weight-space math. If you feed it deltas expecting a delta out, you'll get whatever the tensor math produces - keep this node in the weight-space part of your graph unless you know exactly what you're doing.

Perpendicular Component is not a daily driver. It's the tool you reach for when two models are too similar and a plain add just smears them together - the one that turns "these two deltas overlap" from a problem into something you can actually subtract away.