Falsification-Coupled Particle Transformer

Status: mechanics implementation; no reasoning claim yet.

Thesis

Shohin's repeated failure is not simply too little recurrent depth. Several runs learn useful local fields but settle into incompatible complete programs; softly averaging those fields destroys strict causality. FCPT therefore treats a complete candidate world/program as the indivisible inference unit.

FCPT maintains K exchangeable particles

P_i^t = (S_i^t, log w_i^t, lineage_i^t)

where S_i is a complete structured state. One shared recurrent proposer creates B complete branch candidates per particle:

S_tilde_(i,b) = T_theta(S_i, source, challenge, branch_b)

Each candidate predicts outcomes for source-owned evidence probes. The contradiction bus admits only R probes with high behavioral disagreement:

q* = TopR_q Var_(i,b)[p_theta(y_q | S_tilde_(i,b))]

Observed source evidence updates candidate credibility with a proper log score. The next population is selected as complete states:

log w_tilde_(i,b) = log w_i + mean_(q in q*) log p(y_q | S_tilde_(i,b))
P^(t+1) = WholeTopK({S_tilde_(i,b), log w_tilde_(i,b), lineage_(i,b)})

No opcode, pointer, register, relation, or latent field can be copied from a different lineage. The late reader consumes one winning complete state. Query and answer targets are absent from proposal, contradiction, and selection APIs.

Honest novelty boundary

Particles, recurrent depth, latent reasoning, global workspaces, differentiable particle filters, counterexample-guided synthesis, and hard selection all have prior art. FCPT's candidate contribution is their specific composition as model-owned falsification-coupled sequential Monte Carlo over structured latent programs, with persistent whole-program identity and no fieldwise aggregation.

This is only a credible contribution if the learned contradiction channel is causal. Merely sampling several states or choosing the best one is a control, not FCPT.

Minimal implementation

train/falsification_coupled_particles.py currently provides:

• exchangeable particle-axis operations with shared branch proposals;
• complete-state gathering and explicit lineage tracking;
• behavioral outcome prediction over source evidence;
• a fixed-bandwidth disagreement-selected contradiction bus;
• evidence log-score updates and whole-state top-K selection;
• independent-particle, soft-aggregation, and selection-without-falsification controls from the same components;
• a late query reader over one state; and
• behavioral-equivalence certification over predicted consequences.

The first mechanics suite requires finite gradients, selection invariance under particle permutation, preserved nonnegative lineage, no query in the deliberation signature, and a soft-control marker proving where identity is intentionally destroyed.

Three-family gate

All families expose evidence in the source; no hidden answer, tool, teacher, or external verifier is available during inference.

1. Ambiguous noncommuting programs. Several operation orders explain early local observations; later input/output evidence distinguishes the complete order. OOD changes depth, operation combinations, symbols, and renderer.
2. Repeated-binding graph programs. Candidate entity bindings agree on local attributes but differ on multi-hop consequences. OOD changes graph size, repeated-name frequency, relation composition, and renderer.
3. Counterexample-guided function induction. Several functions fit an initial example prefix. Additional source examples falsify alternatives; the late query asks for a new value. OOD changes function families, coefficient ranges, and number of distractor hypotheses.

Training uses depths 2--4 and cardinalities 3--6. Development uses depths 5--7 and cardinalities 7--9. Confirmation uses a separately frozen generator, renderer, depth range, and seed set that training jobs cannot load.

Matched controls

• ordinary Transformer;
• one tied recurrent stream;
• K independent recurrent particles;
• particles with soft latent aggregation;
• whole-particle selection with fixed probes and no disagreement bus;
• full FCPT;
• FCPT with shuffled contradiction messages;
• FCPT with lineage swapped before the late reader.

The single-stream recurrent control receives the same total proposal calls as all FCPT particles and branches combined. Results report both trainable parameters and measured forward/backward FLOPs; parameter and total-FLOP mismatches must each remain within 1% for the primary comparison.

Pass and kill rule

FCPT advances only if:

1. exact OOD joint accuracy is at least 10 absolute points above the best matched control across all three families;
2. every family improves and at least four of five fixed seeds improve;
3. removing the learned falsifier costs at least five points;
4. soft aggregation is materially worse than whole-particle selection;
5. shuffled challenges and lineage swaps cause the predicted degradation;
6. randomized counterfactual labels remove the gain;
7. useful particle count and behavioral diversity stay above one; and
8. the unopened confirmation passes without threshold changes.

Kill the lane if a compute-matched deep recurrent stream ties it, particles collapse behaviorally, the scorer learns labels rather than evidence, or the effect does not transfer across all three generated families.

Resource envelope

The mechanics implementation is CPU-testable. The first GPU pilot uses two single H100 jobs: FCPT and the strongest recurrent control, one seed, 1,000 updates, and development cohorts only. Budget: at most two H100-hours.

Only a >=5-point pilot trend with noncollapsed particles authorizes the full development matrix. Six principal arms by five seeds require 30 independent single-H100 jobs. The initial ceiling is 30 H100-hours; jobs stop early for chance-flat or collapsed behavior. Ablations and confirmation are launched only for a development winner. No scratch language pretraining begins from this gate alone.

Pilot v1 result and objective correction

Seed-17 jobs 739194 (FCPT) and 739195 (fixed-probe whole selection) used identical 88,727-parameter models, 1,000 updates, 256 examples per update, and the six frozen depth-5/7 development cohorts. FCPT reaches 12.174% macro exact versus 11.475%, only +0.699 points. It loses slightly on depth-5 binding and ties depth-7 induction. This misses the fixed +5 pilot trend and does not authorize the full matrix.

The failure exposes an objective contradiction rather than a duration issue. V1 applies gold behavior cross-entropy independently to every candidate. That loss explicitly trains every particle to make the same predictions, while a small diversity term tries to separate them. Final hard behavior uniqueness is only 1.2--1.5 among eight branch candidates and mutual-information diversity is about 0.0005--0.0007. The falsifier cannot allocate useful contradiction bandwidth when its candidate set has already collapsed.

V1 is frozen. One corrected pilot replaces all-candidate behavior CE with a multiple-hypothesis coverage objective: for each episode and round, only the lowest complete-candidate evidence NLL is charged. A stronger behavioral mutual-information term keeps the uncharged alternatives distinct. Data, architecture, updates, seed, evaluation, and FCPT-versus-selection comparison remain fixed. This is the only authorized successor. It must still clear +5 points and noncollapse; otherwise FCPT closes before the full matrix.

V1 report SHA-256 values:

• FCPT: 09fc81a4aa0c36153b949e735ff7458d28901e9ac88b3da9ab4296bb1d7226d0
• selection: 3c03af58878f75a57d1907c94cc8e5d4b2dfd82bf34b88d5ce40f72bcad85e63

Pilot v2 result: FCPT closed

The coverage objective succeeds at its intended intermediate effect. FCPT candidate uniqueness rises to 3.06--4.28 of eight on development, and the selection control reaches 2.91--4.39. Behavioral mutual information rises by roughly three orders of magnitude to 0.8--1.2 during training. Posterior collapse is no longer the primary failure.

Capability still does not clear the gate. FCPT macro exact is 12.093% versus 11.800% for fixed-probe whole selection, only +0.293 points. FCPT loses on depth-5 binding and depth-7 induction and remains close to chance on induction. The learned disagreement bus therefore does not produce a material advantage even when distinct hypotheses exist.

No additional FCPT widths, durations, seeds, losses, or full controls are authorized. The lane closes before confirmation. The next architecture target is a single coherent but globally revisable state whose own prediction errors select sparse counterexample-conditioned updates, avoiding both particle collapse and premature whole-hypothesis selection.

V2 report SHA-256 values:

• FCPT: 18cc9e5175979b954ff1c4311404638fd840216846bf4cf7ac545cab80afa536
• selection: 2368c2055e365c239af6308040cb7d18dc55becd2d2f6d22958c73b2c3df84ac