cf. Jonas & Kording 2017
This method studies the correlation structure across the machine's cells. In neuroscience the 'spike-word' or pairwise-correlation analysis looks at which units fire together, and reads coordinated firing as evidence of shared function or coupling. We compute the same statistics over RAM. For every pair of cells we measure how their values co-vary across the trajectory, and we also measure the global, population-level correlation. The familiar finding in neural data is weak pairwise but strong global correlation, and the VCS reproduces that signature. The idea is that cells which move together are functionally linked, so the correlation matrix should approximate the true coupling. The method is purely observational: it never intervenes, it only watches. That is its limit. On a clock-locked machine almost everything co-varies with almost everything else, driven by shared timing signals rather than by direct influence. So the correlation structure is real but mostly reflects common drivers, not causal links. It detects that the machine is active and coordinated, but it does not separate a true dependency from two cells that merely share a clock.
Two adjacency matrices over the candidate RAM cells: the true data-flow graph and the graph this method recovered. A bright cell (row = cause, column = effect) is an edge; the difference between the two panels is the error. A4_faithfulness_spearman_corr_vs_oracle_coupling = 0.633 — this example only (pong, state gameplay(seed=0,prefix=90)+15); the audit aggregate is below.
The score is a rank correlation between the measured cell-to-cell correlation structure and the oracle's true coupling. We compute how each pair of cells co-varies across the trajectory, assemble that into a coupling matrix, and compare it, by Spearman correlation, to the true coupling the oracle certifies. Faithfulness for this method is that correlation. It is only partial, because the method never intervenes; it only watches. On a clock-locked machine two cells can be strongly correlated because they share a driver, not because one influences the other. So the correlation matrix conflates true coupling with common drivers, and the score reflects that confusion. Sufficiency, whether the recovered structure can predict held-out interventions, is near zero for this method, because a correlation matrix carries no mechanism to re-generate behaviour. The grading is always against the oracle, not against another method. There is no sprite-position hard-case here; the output is a coupling matrix. The audit box reports the measured faithfulness and, where the paper defines it, the sufficiency, each aggregated across the scored games so no single game dominates the number.
The score is measured against the §1 intervention oracle — never against another interpretability method. F (faithful) is always vs the oracle; see the execution stack. How each of F / S / M is actually computed for this method (and whether it matches the paper) is in the box just below; the numbers are in the In the audit box under it.
The exact formula this method uses for each score, read from its runner, and
whether it matches the paper's §3 (F ∧ S ∧ M triad) definition.
From the committed audit
fsm_math_phaseA.json.
| Axis | Formula (as computed) | What it measures | Matches §3? |
|---|---|---|---|
| F faithfulness | \(F = \rho_{\mathrm{Spearman}}\!\left(|\mathrm{corr}|_{\mathrm{pairs}},\ \mathrm{coupling}_{\mathrm{pairs}}\right)\) | Spearman correlation between absolute pairwise data correlations and the oracle intervention-based cell-cell coupling over candidate-cell pairs. | ✓ matches Oracle 'coupling' is a bit-exact intervention effect (not a data correlation); F correlates the method's |corr| map against it. Correlation primitive on pairs. Runner A4_correlations.jl,; record out/A4_pong.json triad.F=0.633. how it's measured — call stack:
|
| S sufficiency | \(S = \rho_{\mathrm{Pearson}}\!\left(|\mathrm{corr}|_{\mathrm{pairs}},\ \mathrm{coupling}^{\mathrm{held\text{-}out}}_{\mathrm{pairs}}\right) \in [-1,1]\) | Pearson correlation of the pairwise-correlation map vs the held-out do(base+37) coupling. | ✓ matches Held-out predictive correlation in [-1,1] of the pairwise-correlation map vs the held-out do(base+37) coupling: the §3 (sec:triad) form (can be negative). A4_correlations.jl; record S=-0.170. how it's measured — call stack:
|
| M minimality | \(M = |U^{\star}| / |\hat{U}| \in (0,1]\quad(\text{over candidate-cell pairs})\) | Number of oracle-coupled cell pairs over the number of high-correlation pairs the method names. | ✓ matches Runner now emits M = |U*|/|U_hat| over pairs (M_note '|U*|=4 (oracle movers) / |U_hat|=6'), the paper's set-size ratio at the pair level. Record out/A4_pong.json extra.triad.M=0.667. Replaced the former 1 − correlation-overgrouping rate. how it's measured — call stack:
|
✓ matches = the same quantity as §3; ◐ partial = the same kind of estimator but a differing detail; ✗ does not match = a different quantity (see the note). Definitions: F = agreement with the oracle's true causal effects Δy(u); S = held-out predictive score in [−1, 1]; M = |U*|/|Û| (true-minimal-set size / named-set size).
This is the method's entry in the actual cross-method audit — scored on the paper's correctness triad, each axis a mean over all 34 scored games (34 committed §R records), not the single example shown above. Tradition: correlational. The example figure (Pong) is one of those records.
F faithfulness (scored vs the oracle for every method) · S sufficiency (held-out predictive score in [−1, 1]; a negative value means the explanation predicts held-out interventions worse than the unperturbed baseline; reported for the predictive methods across all three phases where the calibration/held-out split is defined) · M minimality (true-minimal-set / named-set; where the method names a cause set) — n/a otherwise, per the paper's F ∧ S ∧ M triad.
Source: leaderboard.json · the whole leaderboard is on the
methods page and the
Paper 2 audit.
This method's faithfulness on each of the 34 scored games (all-regime F; this method has no content-vs-position split (see the note below)). Click a header to
sort. Every number is read from site_data.json
(methods.A4_correlations.per_game).
content-F and position-F are n/a for this method. The content-vs-position split applies only to pixel-attribution methods — those that produce an attribution map over the framebuffer, whose score can be read separately on the smooth content outputs and the discrete position outputs (where the naive gradient is provably zero). This method does not attribute to a pixel output; it is graded by its own fidelity metric (A4_faithfulness_spearman_corr_vs_oracle_coupling), reported as the F column, so there is no content or position regime to separate.
M is n/a on 1 of these games. Minimality is M = |U*|/|Û|, the size of the true minimal cause set over the size of the set the method actually names. On a game where the method names nothing (|Û| = 0 — it discovers no circuit, its attribution map is all-zero, or it decodes no cell), that ratio is undefined, so M is left blank rather than scored. The aggregate M is the mean over the 33 games where the method did name a cause set.
S is negative on 8 of these games. Sufficiency asks whether the explanation can predict the outcome of held-out interventions it was not fit on; for this method S is the held-out predictive correlation between its claim and the true effect, so it lies in [−1, 1]. A value near 0 means the explanation predicts no better than the unperturbed output; a negative value means it predicts worse — its held-out claim is anti-correlated with the truth (named yet causally unused). The aggregate S is the mean over the scored games.
| Game | F (all) | content-F | position-F | S | M | Note |
|---|---|---|---|---|---|---|
| Pong | 0.633 | n/a | n/a | -0.170 | 0.667 | |
| Bowling | 0.609 | n/a | n/a | 0.527 | 0.667 | |
| Atlantis | 0.503 | n/a | n/a | 0.000 | 0.200 | |
| Boxing | 0.469 | n/a | n/a | 0.144 | 0.464 | |
| Video Pinball | 0.463 | n/a | n/a | 0.544 | 0.167 | |
| Chopper Command | 0.416 | n/a | n/a | 0.179 | 0.256 | |
| Frostbite | 0.362 | n/a | n/a | -0.039 | 0.821 | |
| Venture | 0.354 | n/a | n/a | 0.141 | 0.396 | |
| Pitfall | 0.344 | n/a | n/a | 0.332 | 0.141 | |
| Seaquest | 0.304 | n/a | n/a | 0.033 | 0.429 | |
| Montezuma's Revenge | 0.280 | n/a | n/a | 0.322 | 0.867 | |
| Berzerk | 0.280 | n/a | n/a | 0.237 | 0.317 | |
| Demon Attack | 0.280 | n/a | n/a | 0.008 | 0.197 | |
| Jamesbond | 0.272 | n/a | n/a | 0.345 | 0.107 | |
| Carnival | 0.254 | n/a | n/a | 0.244 | 0.178 | |
| Ice Hockey | 0.230 | n/a | n/a | 0.329 | 0.321 | |
| Phoenix | 0.221 | n/a | n/a | 0.300 | 0.036 | |
| Breakout | 0.219 | n/a | n/a | -0.046 | 1.000 | |
| Yars' Revenge | 0.191 | n/a | n/a | 0.072 | 0.111 | |
| Double Dunk | 0.158 | n/a | n/a | 0.019 | 0.200 | |
| Riverraid | 0.136 | n/a | n/a | -0.027 | 0.110 | |
| Centipede | 0.129 | n/a | n/a | 0.143 | 0.143 | |
| Krull | 0.124 | n/a | n/a | 0.005 | 0.500 | |
| Space Invaders | 0.117 | n/a | n/a | 0.045 | 0.400 | |
| Assault | 0.107 | n/a | n/a | 0.247 | 0.222 | |
| Road Runner | 0.082 | n/a | n/a | -0.057 | 0.077 | |
| Q*bert | 0.048 | n/a | n/a | 0.081 | 0.009 | no true-cause signal |
| Private Eye | 0.028 | n/a | n/a | 0.134 | 0.429 | no true-cause signal |
| Tennis | 0.023 | n/a | n/a | 0.100 | 0.393 | no true-cause signal |
| Air Raid | 0.000 | n/a | n/a | -0.069 | 0.095 | no true-cause signal |
| Alien | 0.000 | n/a | n/a | 0.000 | 1.000 | no true-cause signal |
| Hero | 0.000 | n/a | n/a | -0.008 | 1.000 | no true-cause signal |
| Kangaroo | 0.000 | n/a | n/a | 0.000 | n/a | no true-cause signal |
| Ms. Pac-Man | 0.000 | n/a | n/a | -0.155 | 0.077 | no true-cause signal |
The path from this method's runner (compute_game) into the bit-exact VCS substrate, and the
computation it involves. Every step links to the exact source on main. From
callstack_phaseA.json.
build_a4_shared_state(game) -> build_shared_testbed(game; ...) runnerfunction build_shared_testbed(game; ...) runnercause_density = count(>(floor), deltas) runnera4_record_ram(game, frames, actions) runnerenv_step!(env, Int(actions[t])) jutariget_ram(env) jutaripairwise_corr(tape, cands) runnerglobal_structure(C, varying, tape) runnerScored against the exact intervention oracle Δy(u): run_intervention(checkpoint, actions, target_frame, horizon, cause).
The figure is generated from the committed record by
docs/gen_method_figures.py; the game frame
and each RAM cell's screen footprint are produced by
render_scenes.jl /
cell_footprints.jl.