Kinetic AI

Language Modeling as Equilibrium Computation

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:

Data Flow

Validated findings from research/memory/findings.md are transformed into:

  1. This results.json file (structured data).
  2. Figures in the paper (generated by paper/figures/make_paper_figures.py).
  3. This results page (rendered dynamically).

This ensures the paper, site, and code remain in sync—every number is derived from the same validated source.