This public write-up and the attached PDF refer to exactly one successfully
graded Phase 1 entry: submission 326680. I am submitting it for the Phase 1
Algorithmic Contribution Prize and, by publishing it here, for Community
Contribution consideration as well.
On WhestBench 0.14.0 / FlopScope 0.10.0, submission 326680 completed 100/100
MLPs with zero failures. Its official final-layer raw MSE is
2.4258079704964076e-7, adjusted score is 1.43914441754321e-7, mean
effective compute is 161367794290.68, and score multiplier is
0.5932639495980835.
What the estimator does
The estimator is deterministic and target-free at prediction time:
- It uses the complete dimension-256 real Kerdock mutually unbiased basis
construction: 129 bases and both signs of every vector, for 66,048 angular
directions. The construction has a checked algebraic rank/multiplicity
certificate. - ReLU positive homogeneity removes Gaussian radius sampling exactly. A
signed fast Walsh-Hadamard transform evaluates the first layer of the
Kerdock carrier. - A diagonal-Gaussian recurrence proposes inactive coordinates, while the
first 1,652 carrier rows are reused as a billed pilot. A coordinate is
omitted only when the analytic and pilot tests agree. - Omitted inputs are not silently replaced by zero. Their recurrence mean is
added analytically to the next preactivation, while the remaining columns
follow deterministic compacted routes. - The final three layers use a dead/on/kink structural fold. Only kink paths
need row-level ReLU evaluation; always-on paths are composed linearly. - Four exact source-level rewrites preserve every prediction bit while
removing billed work: pilot-zero input compaction, pilot-mask reuse,
single assembly of Winograd quadrant blocks, and deletion of advanced
identity gathers after local compaction.
Every predict-time numerical operation uses a FlopScope primitive. The exact
submitted archive was package-validated and replayed after extraction.
Contribution boundary
The published SOX estimator already describes analytic dead/kink/on
classification, pilot reclassification, structural sampling, and sparse
continuation. I do not claim those ideas as new.
The narrower contribution here is the combined, metered route from a complete
Kerdock angular construction to a legal depth-32 estimator: the algebraic
carrier certificate, exact radial conditioning, signed-FWHT evaluation,
conservative intersection of analytic and reused-carrier pilot tests,
analytic omitted-input fill, deterministic compacted continuation, and exact
prediction-preserving compiler reductions.
The result is also deliberately bounded. Relative to the published SOX
result, submission 326680 has a better adjusted score and lower compute, but
its raw MSE is about 11.3% worse. Its measured advantage is compute-driven; it
should not be described as a more accurate raw estimator than SOX.
What failed
The attached paper records representative negative results rather than only
the final survivor:
- teacher-forced scalar-energy and conditional-product closures had depth-32
bias more than 2,200 times above the predeclared raw-error ceiling; - a pair/gate family failed even with an impossible truth-informed oracle;
- two local nonlinear residual heads regressed untouched validation by more
than 3.5 times; - a train-only alpha-tail ridge had validation adjusted-product ratio 1.923;
- a terminal Gaussian gate-count control failed its stability floor before
truth generation; - a six-bin alpha calibration regressed validation and remained
non-promotable; - deeper Winograd recursion preserved predictions but increased effective
compute in every paired repeat; and - carrier-self-piloted dead-tail fusion saved counted work but changed one
dead/live decision and failed bitwise parity on 1/16 frozen cases.
These kills suggest that one scalar energy, a low-capacity alpha calibration,
or another compiler micro-variant is not the missing sufficient statistic.
They do not prove that all learned residual or joint-distribution methods must
fail.
Limitations
The Kerdock rule is a deterministic finite angular cubature and is generally
biased for a deep ReLU integrand. A coordinate-sign symmetry is not a Haar
randomization or an unbiasedness theorem. The diagonal recurrence ignores
cross-neuron dependence, and a finite pilot cannot prove global inactivity.
The public score is one noisy aggregate on known Phase 1 networks; it does not
establish fresh-private generalization.
LLM disclosure
I used ChatGPT/Codex and Claude extensively for literature search,
derivations, implementation discussion, experiment design, drafting, and test
review. Multiple model-proposed mechanisms were rejected by the frozen gates
reported in the paper. Numerical claims come from frozen receipts or the
terminal AIcrowd readback. I chose the experiments, own the submission, and am
responsible for every claim and limitation.
Attachment: I would especially welcome technical discussion of (1) deterministic angular
designs versus randomized QMC for deep ReLU means, (2) principled corrections
for omitted low-activity coordinates, and (3) which joint-distribution
statistic could survive propagation without relying on public-target fitting.
e211_dead_compacted_kerdock.pdf (88.5 KB)