On-distribution counterfactual

What it does?

An on-distribution counterfactual asks the smallest realistic change that flips the output. Instead of occluding with an artificial value, it edits the input toward a genuine alternative the system could actually produce, and finds the smallest such edit that changes the output. The explanation is the edit itself: 'change these cells to these plausible values and the outcome changes'. The point of the on-distribution constraint is to answer the objection that occlusion and clamping can set an input to a value the running system would never create, making the explanation off-manifold. We apply it to the VCS by substituting candidate cells toward a real alternative state, the RAM of another frame of the same ROM, and re-running the bit-exact program. Because the substituted values are ones the machine genuinely produced, the edit stays on the data manifold by construction, and because we re-render the whole machine it is a valid intervention. We compare the minimal edit to the oracle's minimal cause set. The method works on a sprite's position where gradients fail. Its faithfulness here is limited: on some frames no on-distribution content byte varies between frames, so the search finds nothing and the map is flat, and even when it does edit, the single-edit search only partly recovers the true minimal set.

Top row (image domain, as in Paper 1): the game frame, then the oracle's true causal region and this method's attributed region — each painted onto the frame through the screen footprint of the RAM cells it implicates (brighter = more important). A faithful method's heat matches the oracle's. Bottom: per-cell importance — oracle (green) vs method (blue) — and the deletion/insertion faithfulness curves (perturb the ranked causes and watch the output move). Note: the image-domain overlay footprints are illustrative, computed on the pre-redesign boot frame; the bars, curves and all reported numbers come from the re-run records on the shared gameplay states. pearson_corr_with_oracle = 0.696 — this example only (pong, state f90+15); the audit aggregate is below.

Reading this example's causal region

This example explains the content of RAM $36 (byte 54) — the most causally-active concept byte at this state. Its strongest true-causes are: RAM $36 (the play area — ball / paddles); RAM $31 (17% of its footprint sits in the score band, the rest in the play area). The score digits appear in the region because RAM $31 reaches them: perturbing it over the 30-frame NOOP window changes the game outcome, and hence the score — a downstream effect, not direct rendering.

How it's scored

The score is the Pearson correlation of the minimal counterfactual edit with the oracle's exact causal map, together with the edit's minimality against the oracle's minimal cause set, and the grading is always against the intervention oracle. The method substitutes candidate cells toward a real alternative state, another frame of the same ROM, and re-runs the bit-exact program, so the edit is on-distribution and a valid intervention, and it works on a sprite's position where the gradient family scores zero. That is why there is no position collapse here in principle. Its faithfulness is nonetheless only moderate. On some frames no on-distribution content byte varies between frames, so the search finds no valid edit and the map is flat; we mark those cells invalid rather than score them as important. Even when a valid edit exists, the single-edit search only partly recovers the true minimal set, so the correlation stays modest. Minimality is central here, because the method explicitly seeks the smallest flipping edit. The grading is always against the oracle. The audit box reports the measured all-regime faithfulness across the 42 scored games, so the moderate number reflects both the no-op frames and the partial recovery on the frames where the search does run.

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.

How F, S, M are computed here

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_phaseB.json.

Axis	Formula (as computed)	What it measures	Matches §3?
F faithfulness	\(F = \rho_{\mathrm{Pearson}}\!\left(\mathrm{attr},\ |\Delta y(u)|\right)\)	Raw Pearson correlation between the method's per-cause attribution magnitudes and the oracle's true absolute causal effects |Delta_y(u)|, scored separately for the content and position output regimes.	✓ matches counterfactual.jl: cf_attr = single-cell on-distribution counterfactual per cause, pr = pearson(cf_attr, odelta); triad_extra_dict(f.pearson, f.cf_attr_per_cause, f.oracle_abs_delta). Record: out/counterfactual_air_raid_content.json (metric_name=pearson_corr_with_oracle, value=0.79). Scorer pilot_ig_vs_oracle.jl pearson() (raw Statistics.cor, zero-variance->0); F = pearson(attr, oracle_abs_delta) where oracle_abs_delta = abs.(cmap.delta) (true |Delta_y| per cause). Also reports spearman, precision@k, deletion/insertion AUC (paper's auxiliary F metrics). Per-regime split: separate *_content.json and *_position.json records, each carrying its own extra.triad.{F,S,M}. how it's measured — call stack: per-cause on-distribution counterfactual attribution — counterfactual.jl:305 raw Pearson of attribution vs oracle |Δy(u)| — pilot_ig_vs_oracle.jl:173 assemble the F∧S∧M triad record — counterfactual.jl:713 true causal effect Δy(u) by bit-exact re-run — oracle_intervene.jl:242
S sufficiency	\(S = \dfrac{\#\{\,u_{\mathrm{held}}:\ |\hat{y}-y|\le\varepsilon\,\}}{|\mathrm{held\text{-}out}|}\in[0,1]\)	Fit Delta_y = a*attr + b on a calibration half of the do(u) causes, predict the disjoint held-out half, and report the fraction of held-out causes whose predicted output lands within an epsilon band of the oracle's bit-exact re-run.	✓ matches common/triad_sm.jl sufficiency_score() (interleaved calib/held split by seed, least-squares 1-D fit Delta_y~a*attr+b on calib, epsilon = max(0.5, 0.10*heldout_spread)); assembled in triad_extra_dict(). The new §3 (sec:triad) admits the fraction-within-tolerance [0,1] special case of the held-out predictive test, which this held-out do(u) fit-then-predict estimator satisfies, so it matches. (Detail: epsilon is a self-scaled band 0.10*spread; the [-1,1] correlation form is available but this method reports the [0,1] hit fraction.) how it's measured — call stack: sufficiency_score: fit Δy=a·attr+b on a calib half, predict held-out within ε — triad_sm.jl:111 assemble the F∧S∧M triad record (calls sufficiency_score) — triad_sm.jl:173 true causal effect Δy(u) by bit-exact re-run — oracle_intervene.jl:242
M minimality	\(M = |U^{\star}| / |\hat{U}| \in (0,1]\quad U^{\star}=\{u:\Delta y(u)>0\},\ \hat{U}=\{u:|\mathrm{attr}(u)|>\tau\}\)	Ratio of the number of oracle causal movers (causes with nonzero true Delta_y) to the number of cells the method names above 1e-6 of its own max attribution; null when the oracle finds no mover or the method names nothing.	✓ matches common/triad_sm.jl minimality_score() with name_frac=1e-6, mover_floor=0.0; the above-threshold named set is used (topk kept but not passed), see triad_extra_dict(). This is the paper's M = |U*|/|U_hat| in (0,1] (standardized everywhere), so it matches the new §3. (Detail: |U*| is taken as all oracle movers with Delta_y>0, an upper bound on the strictly-smallest reproducing subset, so M can be optimistic.) how it's measured — call stack: minimality_score: |U*| oracle movers / |U_hat| named cells — triad_sm.jl:57 assemble the triad record (calls minimality_score) — triad_sm.jl:178 true causal effect Δy(u) by bit-exact re-run — oracle_intervene.jl:242

✓ 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).

In the audit

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 42 scored games (84 committed §R records), not the single example shown above. Tradition: intervention. 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.

Results per game

This method's faithfulness on each of the 42 scored games (all-regime F, and the content vs position split). Click a header to sort. Every number is read from site_data.json (methods.counterfactual.per_game).

M is n/a on 8 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 34 games where the method did name a cause set.

Game	F (all)	content-F	position-F	S	M	Note
Fishing Derby	0.957	0.948	0.967	0.850	1.000	recovers the true causes
Road Runner	0.826	0.760	0.892	0.895	1.000	holds up on position
Bank Heist	0.825	0.974	0.676	0.833	1.000
Boxing	0.809	0.817	0.801	0.750	1.000
Freeway	0.807	0.747	0.867	0.600	1.000	holds up on position
Name This Game	0.790	0.788	0.792	0.583	1.000	holds up on position
Air Raid	0.787	0.791	0.784	0.571	1.000
Alien	0.781	0.860	0.702	0.429	1.000
Atlantis	0.712	0.773	0.651	0.400	1.000
Krull	0.680	0.753	0.608	0.519	1.000
Bowling	0.661	0.896	0.425	0.881	1.000
Riverraid	0.652	0.690	0.613	0.565	1.000
Ice Hockey	0.644	0.767	0.521	0.591	1.000
Pong	0.641	0.696	0.586	0.389	0.875
Private Eye	0.637	0.764	0.510	0.960	1.000
Demon Attack	0.608	0.955	0.261	0.875	1.000
Jamesbond	0.578	0.747	0.408	0.893	1.000
Frostbite	0.511	0.826	0.196	0.550	1.000
Chopper Command	0.499	0.998	0.000	0.952	1.000	position gradient vanishes
Phoenix	0.455	0.909	0.000	0.538	1.000	position gradient vanishes
Pitfall	0.433	0.545	0.322	0.941	1.000
Centipede	0.425	0.851	0.000	0.450	1.000	position gradient vanishes
Tennis	0.397	0.795	0.000	0.500	1.000	position gradient vanishes
Yars' Revenge	0.388	0.776	0.000	0.464	1.000	position gradient vanishes
Seaquest	0.387	0.775	0.000	0.958	1.000	position gradient vanishes
Video Pinball	0.385	0.770	0.000	0.500	1.000	position gradient vanishes
Carnival	0.383	0.766	0.000	0.474	1.000	position gradient vanishes
Montezuma's Revenge	0.362	0.724	0.000	0.188	1.000	position gradient vanishes
Hero	0.353	0.705	0.000	0.889	1.000	position gradient vanishes
Venture	0.349	0.698	0.000	0.474	0.750	position gradient vanishes
Breakout	0.272	0.544	0.000	0.450	1.000	position gradient vanishes
Assault	0.108	0.216	0.000	0.905	1.000	position gradient vanishes
Berzerk	0.049	0.098	0.000	0.574	1.000	position gradient vanishes
Double Dunk	0.030	0.000	0.061	0.808	1.000	no true-cause signal
Beam Rider	0.000	0.000	0.000	0.417	n/a	position gradient vanishes
Gopher	0.000	0.000	0.000	0.929	n/a	position gradient vanishes
Kangaroo	0.000	0.000	0.000	0.469	n/a	position gradient vanishes
Kung-Fu Master	0.000	0.000	0.000	0.800	n/a	position gradient vanishes
Ms. Pac-Man	0.000	0.000	0.000	0.475	n/a	position gradient vanishes
Pacman	0.000	0.000	0.000	0.556	n/a	position gradient vanishes
Q*bert	0.000	0.000	0.000	0.476	n/a	position gradient vanishes
Space Invaders	0.000	0.000	0.000	0.528	n/a	position gradient vanishes

Call stack — how it runs on jutari / jaxtari

The path from this method's runner (main) into the bit-exact VCS substrate, and the computation it involves. Every step links to the exact source on main. From callstack_phaseB.json.

Applied on the substrate

1. env reset + per-frame step of the bit-exact VCS (counterfactual re-runs step the horizon) — env_reset! / env_step! jutari
2. shared gameplay-state testbed — build_shared_testbed jutari

The computation (intervention path)

1. counterfactual re-run: substitute the chosen RAM cells to the alternative RAM values, step the horizon, read y — cf_read_y -> intervene_ram! jutari intervene_ram! call at counterfactual.jl:118 -> jutari_oracle.jl:174
2. single-cell counterfactual effect per candidate cell (|y_cf - y_x|) — single_cell_cf runner
3. greedy search for the minimal counterfactual cell set that flips the output past tau — greedy_minimal_cf runner
4. snapshot RAM+screen after each counterfactual re-run — snapshot jutari

Scored against the exact intervention oracle Δy(u): run_intervention.

Implementation

tools/xai_study/phaseB_attribution/counterfactual.jl

Reference

cf. Olson 2021; Atrey 2020

Record

counterfactual_pong_content.json

All records

phaseB_attribution/out

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.