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Regime Router Experiment

Purpose

This experiment tests a sharper version of the current solver challenge hypothesis.

The working idea was:

maybe the remaining pose-free anisotropic solver challenge is not “find a universally better alpha estimator,” but “route each trial to the right refinement policy before refinement starts.”

The candidate routing signals tested here are:

  • a raw anisotropy-to-skew ratio from the top marginalized seed
  • a support-aware orbit-alias index from the same top seed plus the actual observation mask

The two refinement policies are:

  • fixed-family alpha-only search
  • geometry-plus-alpha family-switching search

The experiment script is run_regime_router_experiment.py.

Pre-Benchmark Logic Audit

Before the benchmark, the new script was checked explicitly.

Code sanity:

  • script compiled cleanly

Support-aware alias-index invariance:

  • audit cases: 20
  • max joint-shift delta: 1.3323e-15

That matters because the new index is supposed to measure pose-related alias pressure. If jointly rotating the seed signature and the mask changed the index materially, the index itself would be suspect.

Router logic audit:

  • leave-one-out toy accuracy: 1.0
  • leave-one-out toy mean routed alpha error: 0.1

That is a direct audit of the threshold-and-direction selection logic used in the benchmark.

Method

This is a focused pilot on the current hard branch.

Scope:

  • observation regimes:
    • sparse_full_noisy
    • sparse_partial_high_noise
  • anisotropy band:
    • moderate
  • geometry-skew bins:
    • low_skew
    • mid_skew
    • high_skew

Trials:

  • 4 trials per cell
  • 24 trials total

For each trial:

  1. take the top marginalized seed
  2. compute two candidate router signals from that seed
  3. run both refinement policies:
    • alpha-only fixed-family search
    • geometry-plus-alpha family switching
  4. record which policy actually gives lower alpha error
  5. evaluate leave-one-out threshold routers for each signal

The raw ratio is:

  • anisotropy strength |log(alpha_seed)|
  • divided by top-seed skew magnitude |t_seed|

The support-aware orbit-alias index is:

  • how much alpha perturbations around the top seed can be absorbed by optimal shifts under the current mask
  • divided by how visible small skew perturbations remain under the same mask

So the support-aware index tries to encode:

hidden pose pressure relative to visible geometry anchor strength

Main Result

The result is informative, but it does not validate the simplest scalar-router design.

Neither scalar router beats the fixed alpha-only policy overall. The raw anisotropy-to-skew ratio carries some useful signal and tracks the sparse-full branch surprisingly well, but the current support-aware alias index does not improve routing enough to beat the simple baseline. So the routing idea has legs, but not yet in one-scalar form.

The summary file is regime_router_summary.json.

Overall means:

  • alpha-only fixed-family search: 0.1648
  • geometry-plus-alpha family switching: 0.1678
  • raw-ratio router: 0.1692
  • support-aware alias router: 0.2038
  • oracle router over the two methods: 0.1193

Overall leave-one-out routing accuracy:

  • raw-ratio router: 0.4167
  • support-aware router: 0.3750

So the direct practical answer is clear:

in this pilot, neither scalar router is good enough yet to replace the current fixed alpha-only default.

By Condition

Sparse full, moderate

This branch establishes a real part of the routing idea.

  • alpha-only: 0.1565
  • geometry-plus-alpha: 0.1101
  • raw-ratio router: 0.1104
  • support-aware router: 0.1861
  • oracle router over the two methods: 0.0772

This is the strongest positive surprise in the experiment.

The raw ratio almost matches the better geometry-plus-alpha policy here.

So in the sparse-full branch:

the simple ratio already contains a real clue about when geometry freedom helps.

Sparse partial, moderate

This branch behaves the other way.

  • alpha-only: 0.1730
  • geometry-plus-alpha: 0.2254
  • raw-ratio router: 0.2281
  • support-aware router: 0.2214
  • oracle router over the two methods: 0.1614

Here the fixed alpha-only policy is still the best practical choice.

Both routers lose ground relative to the alpha-only baseline.

So in the sparse-partial branch:

neither scalar signal is strong enough yet to suppress harmful geometry motion reliably.

Cell-Level Pattern

The cell summaries show why the scalar routing rule is not complete.

Sparse full

  • low_skew

    • alpha-only: 0.1073
    • family switch: 0.1043
    • raw router: 0.1043
    • support-aware router: 0.1043

  • mid_skew

    • alpha-only: 0.2247
    • family switch: 0.2088
    • raw router: 0.2088
    • support-aware router: 0.3128

  • high_skew

    • alpha-only: 0.1376
    • family switch: 0.0172
    • raw router: 0.0179
    • support-aware router: 0.1411

The raw router is very close to the right answer in every sparse-full cell.

The current support-aware index is not.

Sparse partial

  • low_skew

    • alpha-only: 0.2011
    • family switch: 0.2474
    • raw router: 0.2695
    • support-aware router: 0.2474

  • mid_skew

    • alpha-only: 0.2022
    • family switch: 0.2163
    • raw router: 0.1988
    • support-aware router: 0.2022

  • high_skew

    • alpha-only: 0.1159
    • family switch: 0.2124
    • raw router: 0.2159
    • support-aware router: 0.2147

This is the branch where the scalar-router idea still falls short.

The raw ratio keeps over-choosing geometry freedom, and the current support-aware index does not suppress that strongly enough.

What This Means

This result does not kill the routing idea.

It sharpens it.

What it establishes:

  • the solver challenge is a policy-routing problem rather than a single-estimator problem
  • the raw ratio carries real signal in the sparse-full branch
  • the current support-aware index is not the right compressed variable

What it does not establish:

  • a single scalar based only on the top seed is already enough to route all moderate sparse cells correctly

The strongest reading is:

support regime itself still matters too much to be compressed away by the current scalar router design. The sparse-full and sparse-partial branches remain qualitatively different even after adding the first support-aware alias metric.

That is the central outcome of the experiment.

Strongest Clue

The most useful clue is this:

the raw ratio nearly solves the sparse-full branch, while the sparse-partial branch resists both scalar routers.

That points to a stronger next question:

  • not “find a better single scalar”
  • but “can we build a two-stage router that first identifies support type or visible support geometry, then applies a scalar rule inside that branch?”

In other words:

  • sparse-full is a ratio-routable branch
  • sparse-partial needs an explicit support-aware gate before any scalar alias measure becomes useful

Figures

Key figures:

The scatter is the right first look. It shows how each trial’s gain from geometry freedom relates to:

  • the raw anisotropy-to-skew ratio
  • the support-aware orbit-alias index

The bar figure then makes the practical outcome obvious:

  • the raw router almost tracks the sparse-full winner
  • neither router is good enough to beat alpha-only overall