# Fock-PARFLM v2.1 (SQ3 structured V_theta) — Causal Leak Fix vs. Leaky Baseline (`A2`, seed 0)

Comparison of two runs of the same arm, `A2` (SQ3: mixture of `K_mix=8` diagonal
quadratic wells, `tau=1.0`, `K_xi=4`, `lambda_V=0.01`), differing only in
whether the cross-layer Fock register state carries the causal leak identified
in [`Fock-PARFLM_Causal_Leak_Audit_Results.md`](https://github.com/dimitarpg13/semsimula-paper/blob/main/companion_notes/Fock-PARFLM_Causal_Leak_Audit_Results.md):

- **leaky** — legacy register lifecycle (`prefix_causal_registers=False`
  behavior; the field didn't exist yet in this run). Registers are one bank
  per sequence, evolved across the full window, so token *t*'s force in
  later layers can be influenced by tokens after *t*.
- **fixed** (`checkpoint/ckpt_best.pt` in this repo) — `prefix_causal_registers=True`.
  Registers are one bank per *position*; the bank consulted at position *t*
  is built exclusively from tokens 1…t.

Same architecture in both: `d=256, L=8, V_theta=SQ3(K_mix=8, tau=1.0), K_xi=4,
lambda_V=0.01, M=16, d_k=64, top_k=8`, same seed (0), same 16,000 steps,
TinyStories (5M train tokens). This is the structured-V_theta counterpart of
the MLP-V_theta [Fock-PARFLM v2.1 leak fix](https://huggingface.co/dimitarpg13/semsimula-fock-parflm/blob/main/causal_leak_fix_verification.md);
the base architecture, register mechanism, and fix are identical — only the
scalar potential parameterisation differs.

## Headline: the fix costs a modest, honest tax on standard PPL

| | leaky | fixed | Δ |
|---|---|---|---|
| Best val PPL (step 14,400) | **10.36** | **10.90** | +0.54 (+5.2%) |
| Final val PPL (step 16,000) | 10.68 | 11.36 | +0.68 |

The leaky number (10.36) is the one originally published on this model card.
The fixed run is consistently worse across training — the same qualitative
signature as the MLP variant's leak-closure tax (+0.40 PPL there), just
somewhat larger here (+0.54 PPL). Consistent with that pattern, the SQ3
mixture potential appears to lean on the leaked future-token signal slightly
more than the MLP potential does at this scale, though both effects are small
compared to the ~33× (+3.51 nats) inflation measured on the much larger
OpenWebText-scale variant.

## The proof the fix actually worked, at the trained scale

**Future-perturbation test, run on the live trained model** at steps 8,000 and
16,000: perturbing tokens after the position of interest changed past logits
by exactly **0.0** — bit-exact, not "small":

```json
"probe_max_dlogit_past": 0.0,
"probe_mean_dnll_past_nats": 0.0,
"probe_gate_zero_control": 0.0
```

**Honest PPL vs. standard PPL**, same live model:

| step | standard PPL (mid-window) | honest PPL (last-position, leak-free) | paired diff | SE |
|---|---|---|---|---|
| 8,000 | 16.06 | 15.51 | −0.0346 nats | 0.0252 |
| 16,000 | 13.44 | 14.00 | +0.0408 nats | 0.0210 |

Both differences are within ~1.4–2.0 standard errors of zero — not
statistically distinguishable from no leak, the same qualitative result as
the MLP variant (where the two checks landed at <1 SE). The architectural
causal probe (`event: causal_probe`) also reports the deterministic,
no-noise check `eval_max_delta = 0.0` bit-exact at all four checkpoints
(steps 4k/8k/12k/16k) — the `passed: False` flag in the log is a known
overly-strict artifact of the noisy `.train()`-mode branch (Gumbel-softmax
routing jitter, `train_max_delta` ~1e-5–4e-5), not a residual leak; see the
MLP variant's verification note for the full explanation of why this flag
can be ignored in favor of `eval_max_delta`.

## A parameter-count correction found along the way

This model card previously reported **17,407,980 total parameters** (copied
from the MLP-V_theta sibling model's card). Reconstructing the exact SQ3
architecture and loading `ckpt_best.pt` with **zero missing/unexpected keys**
gives the true count:

| | Reported (was wrong) | Actual |
|---|---|---|
| Total parameters | 17,407,980 | **18,194,420** |
| \\(V_\theta\\) parameters | not previously broken out | **4,207,625** |

The SQ3 mixture's per-position hypernetwork (`mu_proj`, `a_proj`, `pi_proj`,
`b_proj`, each mapping the `K_xi·d = 1024`-dim xi-context to `K_mix·d = 2048`-dim
outputs) is larger than the 3-layer MLP it replaces, despite producing a much
flatter landscape (see below) — this model has *more* parameters devoted to
\\(V_\theta\\) than the MLP baseline (4.2M vs 3.4M) even though the resulting
potential is nearly flat.

## V_theta landscape statistics, recomputed on the fixed checkpoint

| Metric | leaky (published) | fixed (this checkpoint) |
|---|---|---|
| Mean | 0.008 | 0.017 |
| Std | 0.26 | 0.42 |
| Min | −5.49 | −1.23 |
| Max | 13.61 | 14.78 |
| Range | 19.10 | 16.01 |

Both checkpoints show the same qualitative picture — a near-flat \\(V_\theta\\)
landscape (mean close to 0, most of the force budget carried by \\(V_\phi\\)
and the Fock registers) — the fixed run is an independently-trained model
with different weights, so exact values shift, but the "flattest landscape
among the three architectures" conclusion is unaffected.

## Data sources

- leaky rerun: `semsimula_fock_multixi_structured_vtheta_buggy2/A2/seed0/`
- fixed (this repo's checkpoint): `semsimula_fock_multixi_structured_vtheta/A2/seed0/`
- Landscape stats recomputed via a fresh forward pass of the reconstructed
  SQ3 architecture over TinyStories validation batches, loading
  `ckpt_best.pt` with `strict=True` semantics (0 missing / 0 unexpected keys).
- Root-cause audit: [`Fock-PARFLM_Causal_Leak_Audit_Results.md`](https://github.com/dimitarpg13/semsimula-paper/blob/main/companion_notes/Fock-PARFLM_Causal_Leak_Audit_Results.md)
- MLP-V_theta sibling verification: [`semsimula-fock-parflm/causal_leak_fix_verification.md`](https://huggingface.co/dimitarpg13/semsimula-fock-parflm/blob/main/causal_leak_fix_verification.md)