Blamed clicks vs random clicks

What we did

• Froze the seed-42 keep-the-pad checkpoint. No training here — scoring only.
• Walked all 15,697 MIND-small validation impressions in order, updating the notepad click by click.
• At each impression, split the score into per-click credits and ranked clicks by how much credit they carry.
• Replayed the session twice: once without the top-k blamed clicks, once without k random clicks.
• Measured how far the scores moved in each case. Sessions held about 49 clicks on average.

The maths

Every score the model produces breaks into three parts, exactly:

This works because the notepad is a decaying sum of one rank-1 write per click. Unrolling it gives a closed form:

So each click's credit, in score units, is:

• Exactness is checked, not assumed. Every impression asserts |Σ terms − score| ≤ 1e-5 before it counts. A failure stops the run.
• Ranking clicks. Importance of click t is its mean size across the candidate list: mean_c |credit_t(c)|.
• The test statistic. Gap = mean |Δscore| after deleting the top-k blamed clicks − mean |Δscore| after deleting k random clicks. Bigger gap means the credits point at history that actually matters.

Mean score drop after deletion

Full results · seed 42 · validation

• The gap grows from k=3 to k=5, so blaming more clicks does keep finding real signal.
• The ratio falls from 12× to 8× because credit is concentrated. Random deletions scale roughly with k (0.060 → 0.110), blamed deletions do not (0.716 → 0.892) — clicks four and five add little on top of the first three.

Why this strengthens the explainability claim

• Credits are in score units, not shares. Attention weights are positive and sum to 1, so they can only say which click got more of the model's focus. A credit of −0.4 says this click pushed the score down by 0.4.
• The decomposition is exact. The parts add back up to the score the model actually served, verified to 1e-5 on every impression. Nothing is left in an unexplained remainder.
• The credits are causal, not decorative. That is what this run tests. If credits were a post-hoc story, deleting the blamed clicks would move the score about as much as deleting random ones. It moves it 12 times more.
• It comes free with the architecture. The decomposition falls out of the notepad's decaying-sum update. It is not a separate surrogate model fitted after the fact.
• An attention-only model cannot produce this. It has no signed, additive, score-unit account of each past click to test in the first place.

What this run does not show

• It is not a ranking-quality result. Nothing here says the model recommends better.
• It is not a head-to-head against SASRec attention. That comparison has not been run.
• Deleting k clicks at once changes the sequence the later clicks were written into, so the drop is not a clean sum of k separate one-click effects. The slower single-click deletion pass covers that and is still running.
• The spread is wide (std ≈ 0.72). The average is strongly positive; individual impressions vary a lot.
• One seed, one dataset, validation split only.