Study005: bounded attention and board geometry¶

Baseline: 13167 exact saved-target stage vectors, 5643 logits, 627 canonical boards; complete legal sets/moves/ties reproduced over4520 raw boards. Frozen model5195 bytes. Host composed proof only; no new emulator execution.

Outcomes¶

Actual attention is heterogeneous and often concentrated: mean row entropy 1.555435 bits (max log2(9)); effective keys 3.4230; zero fraction 0.0940792; mean row maximum 0.599631. Position-mean P MSE (Q15 units squared): 42880578.228090. Within ply/query/key/own-opponent occupancy MSE: 5203803.589037. Local QKV within ply/square/occupancy MSE: 0.000000. Local QKV is token-local, not itself a whole-board detector; attention normalization and weighted values vary with the board. Training-only line selection: {'line_id': 0, 'line': [0, 1, 2], 'train_matched_n': 103, 'mean_candidate_line_mass_contrast': -0.16560823014638956}. Eight fixed geometric groups ranked by natural training pair probability contrast, not lesion outcomes; one selected group confirmed alongside horizontal/diagonal and matched controls.

Finite interventions (19, all retained)¶

All probability overrides have exact nonnegative Q15 row sums32768. Target/control masks have identical per-row cardinality, disjoint edges, and exactly equal moved mass min(target mass,control mass) × dose/2 floored. This caps removal, so full dose does NOT necessarily remove every target edge. Original masked mass is proportionally removed; transferred mass is apportioned to complement keys. Floors then largest remainders, low-key ties. Zero-weight redistribution uses uniform eligible keys; inactive rows are identity. Group controls avoid the selected group but can lie on other winning lines; they are not guaranteed semantically neutral. All19 are upstream: route-changing and route-unchanged outcomes reported separately in machine evidence; no post-routing attribution.

Matched geometry and probe confirmation¶

Same-ply single mark relocation across legal nonterminal raw boards; fixed candidate stays empty; same per-mark corner/edge/center counts; same fold; label-positive receiver versus label-negative donor. Canonical donor is independently canonicalized and both attention axes plus value/projection rows realigned to receiver raw frame. No route matching is imposed; changed routes/gates explicitly retained. One lexicographic donor per positive candidate; donors may be reused. |Task|Fold (0 train,1 val,2 test)|Positive candidates|Matched| |---|---:|---:|---:| |win|0|213|90| |win|1|80|18| |win|2|88|15| |threat|0|349|145| |threat|1|110|17| |threat|2|129|28| |fork|0|247|167| |fork|1|105|28| |fork|2|101|36|

Fixed ridge10 and threshold0.5; controls include ply and candidate identity one-hots plus own/opponent corner/edge/center counts. No tuning or added feature search. These are independent candidate labels, not output softmax choices. AUC/probe increments are descriptive correlates, not causal strategy circuits; no multiplicity significance claimed.

Interpretation and limits¶

Attention, values and projected vectors respond to legal board relocations beyond aggregate occupancy counts. This is not evidence of a dedicated line/threat detector: local embedding/QKV are deterministic occupancy+position+side functions; probabilities vary in concentration; probability changes and actual P*V contributions must not be conflated. Actual Q/K/V and weighted-numerator differences are in matched-relocations005.json, while modified probabilities and downstream projections/logits are in intervention-vectors005.json. Query row never means chosen output square: all nine rows flow through residual, flatten/readout, GELU/norm, learned route/gate and output head. Probability and value/projection changes must be compared separately; the largest PV/P-ratio example does NOT have small absolute P change. There is no uniformly weak-variation finding. Position-mean attention preserving behavior would only show finite-domain robustness at that override; catastrophic identity/group lesions are OOD damage, not selective tactical mediation. Unfavorable matched controls and explicit counterexample remain in examples005.json. Zero positives/zero matched cases are absence of evidence, not zero-error proof. Selection split372/121/134 seed1729 is symmetry-grouped for probes/selection only. All627 were already model-trained/audited; no OOD/model-heldout claim; sparse fork support. Independent geometric fork candidates here include boards excluded by earlier has_fork tactical gating and are NOT the earlier six-positive-board test label. Donor availability restricts conclusions, not repaired through relaxed matching. No training, weight/game change, GPU, install, main checkout execution, merge, upload, services or publication.

Artifacts and reproduction¶

Frozen experiment-manifest005.json precedes all new evaluation. Baseline-only command precedes root manifest. Reproduce with the recorded single-thread environment and dependency interpreter: python study005_execute.py --output <fresh005-directory> (full exact command in FINAL-STUDY-005.md). PNG/SVG rendered from measured JSON only; actual attention panels are unperturbed. Source hashes and preserved69+23+28 artifacts recorded in provenance005.json. Final verification binds independent tests and fresh deterministic bytes.

Measured positive and negative interpretation¶

Training-only selected line [0, 1, 2] had positive-minus-negative line mass contrast -0.165608; a negative contrast is not a bright-line support detector. Test candidate AUC controls -> controls+attention: win 0.81198 -> 0.80721; threat 0.81339 -> 0.81357; fork 0.79496 -> 0.77938; unfavorable controls retained. Position-mean attention causes238/627 canonical selected-move failures (334 route-order changes). Selected-line full-dose lesion: 15 failures vs equal-size/equal-mass control 12; not selective strategic-circuit evidence.

Execution repairs (no design change)¶

The first attempt stopped before interventions on NumPy JSON scalar serialization. A wrapper converts only NumPy scalars/arrays to JSON. All19 interventions then executed; the environment lacked matplotlib. No packages were installed: a Pillow/Canvas evidence-only renderer replaces the unavailable renderer. Frozen experiment source and manifest remain byte-identical; amendment-study005.json binds the execution/renderer repair. Original partial attempts retained separately. Concentration wording is generated to match actual entropy, not the unused generic broad-attention hypothesis.