DIVERGE-VMT1: Verified Multi-Trajectory Matching

Status: closed negative after the one frozen fit.

Capability hypothesis

LTM1 proved that smooth recurrent trajectory credit is learnable, but all exchangeable lineages collapsed because every prompt supplied the same single teacher trace. VMT1 changes the learning substrate. Every prompt supplies two different complete autonomous trajectories generated from candidate sample positions 0 and 1, with exactly one independently verifier-correct outcome. The correct sample position is balanced, so neither latent branch can become an always-correct lane.

VMT1 forms two complete sticky internal trajectories. It computes an exact two-permutation assignment between internal trajectories and observed full trajectory traces. The assignment is whole-lineage: no hidden field, trace step, or response token can be matched independently. A model-owned terminal validity head learns which matched internal trajectory corresponds to the verified-correct outcome. At inference, the head selects one complete latent prefix before ordinary decoding; no candidate text, verifier, gold answer, teacher, host solver, or external model is present.

This is not ordinary DPO. DPO compares output likelihoods but contains no persistent alternative states and no model-owned trajectory selection at inference. It is not an LTM1 diversity repair: branch separation is supervised by two semantically distinct observed trajectories under a bijective matching constraint, not by a generic distance penalty.

Frozen fit board

• Source: corrected fresh 8,192-prompt K=4 candidate bank, SHA-256 20a496867c1afc46d094a1ee2762cc553bd0460bd2915cc7e60d9c53025aa816.
• Candidate positions: exactly 0 and 1.
• Every row has one correct and one wrong non-empty, non-exhausted completion.
• Four cells: math/correct-0, math/correct-1, science/correct-0, science/correct-1.
• Four deterministic rows per cell, 16 rows total.
• Both complete responses and the rendered prompt must fit exactly in 1,024 tokens after reserving eight latent slots. Truncation is forbidden.
• Board seed: 2026080602.

Frozen architecture and objective

• Backbone: pinned Qwen/Qwen3.5-0.8B revision 2fc06364715b967f1860aea9cf38778875588b17.
• Trainable backbone path: rank-8/alpha-16 LoRA in the final four text layers.
• Source pass is differentiable through LoRA; non-LoRA tensors remain frozen.
• Two sticky latent trajectories, width 384, eight slots, eight tied recurrent steps, eight attention heads, feed-forward multiplier two.
• Exact two-way permutation marginal over complete ordered trace assignments.
• Only the lineage assigned to the correct observed trajectory receives response-language NLL. The wrong response is a semantic trace target, not a language-model imitation target.
• A model-owned terminal validity head receives each complete final trajectory probe. It is trained with correctness BCE plus a pairwise margin.
• Loss weights: correct response NLL 1.0, trace assignment 1.0, validity 0.25, monotone halting 0.01. Assignment temperature 0.1; validity margin 1.0.
• Optimizer: fused AdamW, LR 2e-4, betas (0.9, 0.95), weight decay 0.01, cosine decay, gradient clipping 1.0.
• One seed 2026080602, 100 updates, batch one, accumulation 16.

Frozen pass/kill gate

After one mechanical smoke, VMT1 receives exactly one 16-row fit. It advances only if all conditions hold:

1. all 16 source-selected correct-response NLL values improve;
2. model-owned validity selection is at least 15/16 overall and at least 7/8 in both correct-position orientations;
3. mean matched trace cosine is at least 0.85;
4. matched trace cosine exceeds crossed trace cosine by at least 0.10;
5. final internal trajectory cosine is at most 0.95;
6. every tensor and gradient remains finite;
7. every non-LoRA backbone tensor remains hash-identical;
8. swapping validity scores across the two coherent prefixes reduces fit selection by at least 25 points.

Failure closes VMT1 without another seed, branch count, width, depth, trace representation, loss weight, margin, duration, layer count, or schedule. Passing only authorizes a separate matched broad contract; it is not itself a reasoning or benchmark result.

Result

CPU board job 743309 completed in 26 seconds. From 32,768 corrected candidate rows it found 369 structurally admissible opposite-outcome pairs and 208 exact tokenizer-admissible pairs. The selected board has four rows per group/orientation cell, maximum total length 1,010 of 1,024, and zero truncation. Board/report SHA-256 values are 4e5677e00bcf3c1fd72cff11d36a994ec949c9ce658edaedd43676ee8754f685 / aac1fd11b2ea2207b6a015eac511bc31b3cc732780d4f58a1ae8f4a7296d5ae7.

Mechanical H100 smoke 743310 completed cleanly on evc32: all ten on-node tests passed, all 473 pinned Qwen tensors loaded, two finite updates ran, and the frozen hash was unchanged. It used 4,610,052 trainable parameters and 17,659,465,216 peak allocated CUDA bytes. Smoke report/checkpoint SHA-256 values are cb4c715c7d1a753e768143e4c68594bd94ced99197afdda2c277cf7947d9c8db / 20aac48be82fced5457bb2f27b5067ac8e96b99163104937d1c44a7fbc38dad8.

The sole fit 743311 completed all 100 updates and both exact audits in 1,606.677 seconds. It consumed 658,200 logical correct-response tokens, 1,316,400 candidate tokens, and 1,138,900 trace-target tokens at 409.665 logical tokens/s, peaking at 19,281,572,352 allocated CUDA bytes. All tensors remain finite and every non-LoRA parameter is hash-identical.

Language and average trace fit succeed, but coherent alternatives do not:

• token-weighted selected NLL improves 1.084766 -> 0.183080, with 16/16 rows improved;
• matched trace cosine reaches 0.867081, above the 0.85 threshold;
• crossed trace cosine also reaches 0.866763, leaving only 0.000318 advantage versus the required 0.10;
• internal trajectory cosine rises 0.807822 -> 0.998769, failing the 0.95 ceiling;
• model-owned selection reaches 11/16, split 7/8 versus 4/8 across the two balanced observed-correct orientations, below the 15/16 and per-orientation gates;
• swapped selection reaches 5/16, so the swap drop passes, but it acts on a weak asymmetric selector rather than two separated semantic lineages.

The failure has an exact local explanation. When both internal trajectories coincide, the identity and swapped assignments have equal cost and posterior 0.5. The expected validity gradient is exactly zero, every element of the 2-by-2 trace-cost matrix receives the same 0.25 gradient, and both language NLLs receive the same 0.5 gradient. The collapsed barycenter is therefore a symmetric stationary point of the frozen objective. The distinct response texts are not the problem: all 16 selected pairs have different final predictions, median character-prefix overlap is 0.65%, and median word-set Jaccard overlap is 22.05%.

VMT1 is closed. There is no hard-matching, temperature, width, depth, seed, loss, duration, or trace-target repair. A next mechanism must remove exchangeable semantic roles rather than merely repel branches. The ordered candidate data support a materially different hypothesis: a model-owned first draft followed by a prompt-conditioned verified correction trajectory, with correct-draft no-op cases and wrong-draft-to-correct targets. That successor must be compared with an ordinary two-pass correction baseline and must close the teacher-draft/autonomous-draft gap before any broad claim.

Fit report/checkpoint SHA-256 values are 058ac42381dbd9d023a5e6bc716476b60716b871add6ed55dd36de7eb888ab9b / a6ca16175804b8346ad0c8906f1cca3b0a587fb248386963cedbda4d02b50741.