Nagare

Heider, Cartwright and Harary state it in one sentence: a cycle is balanced when the product of its signs is positive. "My friend’s friend is my friend; my enemy’s enemy is my friend." That is not a metaphor but a constraint — and where a network really obeys it, the sign of an unknown edge can be predicted from the cycles it lies in.

HSiKAN puts that constraint in the core of the network rather than in the loss. Nagare is the framework the model and its training live in; the CogInfoCom 2026 paper introduces HSiKAN and Gömb, built around a compact cycle core.

The test that says what it was reading

A good score on its own proves nothing: the model may have read balance, but it may equally have read leaked test signs or plain degree. The label-shuffle audit separates the two. Shuffle the signs of the training edges and leave everything else alone: the balance signal is destroyed, the rest is not. A model that reasons by balance must lose its accuracy here.

observed signs

0.8839

shuffled training signs

0.3703

Balanced synthetic graph, 400 vertices, 150 passes; held-out test AUROC. Chance is 0.5 — the shuffled run falls below it, because the shuffled training misclassifies consistently.

The model is not hidden

There are three models to choose from: HSiKAN with its spline layers; the fuzzy signature with Catmull-Rom memberships, cells folded by a T-norm and vertices folded by an S-norm; and the two together — spline layers whose vertex state a fuzzy signature reads. Whichever you pick, Nagare reads it from its own model file and shows it beside the run as a tree: which block, which layer, with which parameters. What stands there is what trains — not an illustration of it.

The tree’s header is editable. The sizes can be typed, the norms picked from a list, and the next run trains the edited model. An edit the model cannot take is refused in red and taken back — it does not silently accept a value that means nothing.

What runs in your browser

Nagare’s signed-link task, compiled to WebAssembly, on one thread of your CPU, in a Web Worker. Nothing is sent to any server. Where the browser offers WebGPU, Kawamirai — the HyMeKo simulator’s own renderer — fills the whole window and draws the run as it trains. The View select in the top ribbon holds ten drawings of the same run: the observed and the predicted signs, four hull views including the decision regions, and the network itself — its dataflow, its hyperedges, its factors, input to output. The panels float over it, translucent, and the H key hides them all at once. Without WebGPU the two-dimensional graph takes its place, with the same panels.

For the same settings both models give the native Nagare command line’s losses, AUROC and cells bit for bit: Nagare computes every elementary function with one implementation on every target. Drawing changes no training number. One run at one seed is a demonstration, not a measurement.