Four questions about merging neural networks, as simulators

Interactive companions to Lakhanpal (2026), “A Missing Sign Symmetry Accounts for the Linear-Mode-Connectivity Barrier in Minimal-Width Sigmoid Networks” (preprint v2). Simulators 1 and 2 are labelled toy models; 3 and 4 use only the paper’s tables.

Series 2 · Weights ≠ Function (Three.js, rotatable)

Why is merging models so hard?Weight-space view: every straight line between mirror twins passes through the erasure point; the spare-unit detour does not. What does the loss landscape really look like?Schematic loss surface: isolated wells that join into one ring when a spare dimension is added. Do two networks trained from different seeds learn the same thing?Live lab: trains real networks in your browser, shows mirror-flipped neurons and the barrier before and after alignment; includes a capacity scan. Can your measurement hide what is really happening?The pre-registered prediction that failed, the exploratory re-test, and why the error barrier saturates.

Series 1 · Four questions about the preprint

1. If two networks compute the same function, why can’t you average them?Prediction game, flip simulator, heat map. 2. If two solutions are secretly the same, why is there a hill between them?Rotatable toy loss landscape. 3. When does “a missing symmetry explains it” stop being enough?Heat map of five tasks by three thresholds. 4. Does making the network wider make the problem go away?Barrier versus width graph. All-in-one explainerThe full paper walkthrough on one page.

Code and results: github.com/MrigeshLakhanpal/sign-flips-lmc · doi:10.5281/zenodo.23314245