Results | EvoNashMTL

The current results are strongest on the toy harness. They show mechanism, stability, and failure-repair evidence for replicator_nashmtl, not benchmark-level superiority on QM9 or NYUv2.

High-signal summary

Baseline story: plain Nash-MTL is stable, but it stays essentially non-adaptive in the toy setup.

Mechanism story: the tuned replicator version changes the optimization path and produces final weights that differ from plain Nash.

Stability story: the old hard-case collapse on init=1 was real, and the repaired design avoids that one-hot behavior while remaining adaptive.

Scope note: the figures validate scheduler behavior and control. They do not yet prove better real-data benchmark performance.

Figure set

Toy baseline trajectory under plain Nash-MTL

Figure 1. Plain Nash-MTL baseline

This is the stable reference behavior with no outer replicator scheduler.

Why it matters: every other toy figure is interpreted relative to this control.

Toy trajectory under tuned replicator-augmented Nash-MTL

Figure 2. Replicator-augmented trajectory

This tuned version changes optimization behavior relative to the plain Nash baseline.

Why it matters: it shows the method is not merely running; the outer scheduler is affecting the path.

Scheduler dynamics showing replicator shares, Nash weights, and final weights

Figure 3. Weight evolution and mechanism validation

This is the clearest mechanism figure. It separates replicator_shares, nash_weights, and final_weights.

Why it matters: it is the cleanest proof that the outer scheduler is active, stable, and producing a real rebalancing effect.

Old stress-test collapse behavior on the hard init equals one case

Figure 4. Old collapse mode

This captures the previous failure mode on the hard init=1 case, where the scheduler became too aggressive and drifted toward one-hot behavior.

Why it matters: it gives a concrete before-state rather than only claiming that earlier settings were unstable.

Stabilized behavior on the hard init equals one case

Figure 5. Repaired stable behavior

This shows the stabilized design on the same hard case after the signal and hyperparameter fixes.

Why it matters: the collapse is not just hidden; the repaired scheduler remains normalized and adaptive without breaking into a selector.

Notes distilled from the image folder

The strongest takeaways from final_notes.txt, meaning.txt, and PaperBullets.txt are:

The core design goal is to augment Nash-MTL, not replace it. Nash remains the inner fairness mechanism, while the replicator layer provides slower long-run adaptation.
The original toy setup was not enough because the outer scheduler was effectively inactive. The improved harness explicitly feeds scheduler signals and saves the right histories.
The preferred scheduler signal is qm9_proxy, which blends relative loss, under-improvement, and underperformance into a smoother outer-control signal.
The most informative figure is the weight-evolution plot because it exposes the exact relationship between scheduler state, bargaining weights, and final optimization weights.
The repaired method is credible today as a stability and mechanism improvement. A clean benchmark-level win on real data remains an open question.

Current limitations

These results are still toy-centered.
QM9 smoke runs launched, but they did not yet yield a finished comparison strong enough to headline.
Under the final representative setup, some signal ablations looked similar, so the most persuasive story right now is scheduler responsiveness and stability rather than fine-grained signal separation.