Validated Findings
Results are published as each experimental phase closes, sourced directly from research/memory/findings.md. Every number reported here is backed by a peer-reviewed finding with confidence intervals and statistical testing.
Findings Summary
MMD converges linearly to its magnetic fixed point where GDA cycles
ID: F1 | Status: VALIDATED
Uniform-anchor MMD fixed points differ from logit-QRE for asymmetric games
ID: F2 | Status: VALIDATED
Regularized Nash Dynamics reach Nash universally
ID: F3 | Status: VALIDATED
DEQ peak activation memory is O(1) in effective depth
ID: F4 | Status: VALIDATED
Anderson acceleration beats Picard on stiff fixed points
ID: F5 | Status: VALIDATED
Second-price auction is exactly truthful; weighted aggregation is manipulable
ID: F6 | Status: VALIDATED
Warm-started homotopy accelerates QRE path tracing
ID: F7 | Status: VALIDATED
Undamped logit-QRE requires damping for high rationality
ID: F8 | Status: VALIDATED
Tier B EqLM pipeline validated end-to-end (SMOKE)
ID: F9 | Status: VALIDATED (method finding)
EqLM matches explicit transformer at smoke scale after init fix
ID: F10 | Status: VALIDATED (smoke scale) · sign-off pending
exp05 token-budget description was wrong (data cap)
ID: F10-correction | Status: VALIDATED
MagneticAdamW coupled-weight-decay bug
ID: F11 | Status: VALIDATED · fixed in kinetic_ai/optim/magnetic_adamw.py
Magnetic pull (τ≤1e-2) is loss-neutral at pretraining scale; solver budget beyond 12 iters buys nothing
ID: F12 | Status: VALIDATED · sign-off pending
H1 iteration 1: MISSED at scale; diagnosis points to non-contractive fixed-point map
ID: F13 | Status: VALIDATED (honest miss + diagnosis) · sign-off pending
EqLM's map has no bona fide fixed point: weight-tied iterated transformer, not equilibrium model
ID: F14 | Status: VALIDATED · sign-off pending · discovery via exp07
EqLM-v3 (post-LN map): fixed points now exist but contraction is weak at LM width (H1 frontier identified)
ID: F15 | Status: VALIDATED · sign-off pending · H1 iteration 2 remains open — this is the identified scientific frontier
Solver-aware auxiliary loss teaches contraction almost for free (BREAKTHROUGH; resolves F15 frontier)
ID: F16 | Status: VALIDATED (smoke scale) · pending full-run confirmation
H1 iteration 2: post-LN EqLM reaches 94.4% of baseline BLiMP (near-miss, within noise); aux loss trades capacity for contraction at scale
ID: F17 | Status: VALIDATED · seeds pending for H1 verdict
H1 verdict (3 seeds): EqLM reaches 93.0% of the explicit baseline's BLiMP — formally below the 95% threshold (HONEST MISS with a tight CI)
ID: F18 | Status: VALIDATED (formal H1 miss) · closes RQ-3 iteration 3
Warm-started equilibrium decoding cuts solver cost 79% at 97.6% token agreement (H1'a: reduction PASS, agreement narrow miss; smoke scale)
ID: F19 | Status: VALIDATED (smoke scale)
At 121M parameters the truncation penalty widens with width: quality ratio 0.787, memory −23%
ID: F20 | Status: VALIDATED (sign-off pending)
H3 PARTIAL: the magnet under-doses at pre-registered tau — but DPO damages unseen phenomena, and EqLM is 1655x more drift-resistant
ID: F21 | Status: VALIDATED (Tarka-resolved, sign-off pending)
H4 MET (3/3 seeds): truthful token-auction selection beats the best single specialist by 23% on mixed-domain perplexity
ID: F22 | Status: VALIDATED (Tarka-resolved, sign-off pending)
H5 MISSED (3/3): the auction's teacher-forced advantage inverts in closed-loop generation - and the judge metric itself is style-dominated
ID: F23 | Status: VALIDATED (Tarka-resolved with rescoping, sign-off pending)
H6 PARTIAL - with parity: anytime-unrolled training closes the ENTIRE width gap (ratio 0.991 vs explicit at 121M); certification achieved separately; naive combination refuted
ID: F24 | Status: VALIDATED (Tarka-resolved, sign-off pending)
The baseline ladder, and the thinness of subject-level headroom
ID: F28 | Status: VALIDATED
The influence game does not beat averaging at answer level, and confidence is the reason
ID: F29 | Status: VALIDATED
Eleven aggregation rules, none better than the mean, and the reason
ID: F30 | Status: VALIDATED
Correction: the twenty-point oracle gap is mostly not extractable
ID: F32 | Status: VALIDATED
The arena was homogeneous, and that is why nothing beat averaging
ID: F33 | Status: VALIDATED
The bar is a domain router, not the best single player
ID: F34 | Status: VALIDATED
Cross-examination ties the domain router and beats nothing
ID: F36 | Status: VALIDATED
The solve is cheap; the council is not
ID: F37 | Status: VALIDATED
The anchored answer vote beats the router held-out (confirmation pre-registered)
ID: F39 | Status: SUPERSEDED BY F40
The anchored vote's margin is redundancy, not anchoring
ID: F40 | Status: VALIDATED
Pre-registered confirmation: anchoring refuted, the system beats the baseline
ID: F41 | Status: VALIDATED
What the win is made of, and the condition under which it exists
ID: F42 | Status: VALIDATED
The council advantage does not generalise; it is conditional on non-domination
ID: F43 | Status: VALIDATED
The parity claim was never compute-matched
ID: F44 | Status: VALIDATED
At equal compute: 96% quality, 2.70x fewer parameters
ID: F45 | Status: VALIDATED
Depth conditioning makes tying worse
ID: F47 | Status: VALIDATED
The memory saving is in weights, not activations
ID: F48 | Status: VALIDATED
GGUF cannot represent the architecture honestly
ID: F49 | Status: VALIDATED
The exchange rate holds at 31 BLiMP phenomena
ID: F50 | Status: VALIDATED
The conversion leap gate fails as pre-registered
ID: F51 | Status: VALIDATED
ONNX carries the weight saving that GGUF destroys
ID: F52 | Status: VALIDATED
The KD pilot fails its gate; the empirical record closes
ID: F53 | Status: VALIDATED
The council survives matched compute and loses matched capacity
ID: F54 | Status: VALIDATED
The exchange rate does not transfer unchanged to a billion parameters; the programme halts at that boundary
ID: F55 | Status: RECORDED AS A BOUNDARY
Experimental Phases
Phase 1: Matrix Games. Synthetic convergence tests on 2×2 games; validation of QRE recovery.
Phase 2: Implicit Depth. Memory and computational tradeoffs between explicit layers and fixed-point iteration.
Phase 3: BabyLM Pretraining. Token-matched comparison vs GPT-2, BERT on standard benchmarks.
Phase 4: Preference Learning. Auction-based decoding (MPO vs DPO) for alignment.
Benchmarks
We evaluate on:
- BLiMP (Linguistic Minimal Pairs): Compositional generalization.
- Synthetic Games: Convergence rate and QRE exactness.
- Alignment Metrics: Preference learning efficiency under auction-based mechanisms.
Data Flow
Validated findings from research/memory/findings.md are transformed into:
- This
results.jsonfile (structured data). - Figures in the paper (generated by
paper/figures/make_paper_figures.py). - This results page (rendered dynamically).
This ensures the paper, site, and code remain in sync—every number is derived from the same validated source.