Research Audit Trail: From Failure to Phase Transition

The complete story of how CT predicted its own architecture's flaws and prescribed the fixes. Every experiment, every dollar, every wrong turn.

PHASE B · Apr 7-11 · ~$8

Initial Architecture

Built TD6 tile, Hodge projectors, three budget channels, k=2 momentum, Moreau activation. C-Former matched standard transformer on accuracy but provided interpretable budget profiles. HAR: 5/6 physiologically meaningful. Frozen transfer: 96.6% retention.

Finding: “Dynamics > geometry” in ablation. Interpretability is the value proposition.

PHASE C · Apr 11-12 · ~$12

Catastrophic Failure on LRA

ListOps: 17.4% (near random for 10 classes). QM9: B_cx channel collapsed to 0.0% energy on all molecules. The single-tile architecture compressed 2000-token sequences into 13 nodes.

Anti-binder: “C-Former is an interpretability tool, not a benchmark competitor.”

DEEP THEORY ANALYSIS · Apr 13

Two Provable Flaws Identified

Flaw 1: Edge currents as D_T^T @ phi lie in im(D_T^T). P_cyc annihilates them. B_cx = 0 is a mathematical identity. The architecture was d=2.

Flaw 2: All three channels received the same input. B4 (independence) violated.

CT predicted: fix both flaws and the architecture transitions from d=2 to d=3.

v1.5 WRONG FIX · Apr 13 · ~$0.50

Cross-Products Are Not Cycle Flow

Used phi_u * phi_v (symmetric) to inject cycle flow. But cycle flow is antisymmetric (oriented). The “fix” added noise. Ablation: removing Hodge now HELPED by +0.6%.

Lesson: genuine cycle flow must satisfy D_T @ f = 0 (zero divergence). Only ker(D_T) vectors qualify.

v3 ALL FIXES · Apr 13 · ~$1

Phase Transition Confirmed

Fix 1: 12 cycle basis vectors from ker(D_T) via SVD. Verified: zero divergence, orthonormal, full rank.

Fix 2: Independent projections per channel. B4 satisfied.

Fix 3: Multi-tile chain. O(L) cost. Inter-tile cycles: beta_1 = 13N - 1.

81.3%

ListOps (was 17.4%)

99.97%

Pathfinder

Anti-Binder Evolution

How the organism's doubts evolved

STAGE	ANTI-BINDER	STATUS
Phase B	“Just a standard transformer with extra structure that doesn't help”	Partially confirmed
Phase C	“Cannot handle long sequences”	Confirmed for v1, FIXED in v3
v1.5	“Cross-product cycle injection fixes B_cx”	FALSIFIED (symmetric != cycle)
Deep analysis	“Interpretability is the real value, not benchmarks”	True but incomplete
v3 pre-launch	“TD6 cycles are arbitrary relative to data structure”	FALSIFIED at epoch 1 (59.5%)
v3 results	“Multi-tile is slower, unfair comparison”	Addressed: wins despite 8x smaller batch

Complete Cost Accounting

Total GPU cost

6 days

Total duration

4 phases

Including 1 wrong fix

v3 cost (the decisive run)

RELATED RESEARCH

C-Former Paper

The full results: ListOps 81.3%, Pathfinder 99.97%, 40% fewer params.

The d=2 to d=3 Theory

Why the phase transition was predicted and what it means.