SWAT Set A: Zt amplitude too low → deep-sleep (level 2) almost never fires

[ajaytalati]

Observation

Inspecting the simulated SWAT Set A 14-day artifact (produced by psim v0.1.2 from `PARAM_SET_A` + `INIT_STATE_A`), the latent Zt trace stays mostly in [0, 3] over the full trajectory. The deep-sleep threshold is c2 = c_tilde + delta_c = 3.0 + 1.5 = 4.5. So sleep_level=2 almost never fires.

In the ordinal sleep generator (`gen_sleep` in `version_1/models/swat/simulation.py`):

```
P(level=2 = deep) = sigmoid(Zt - c2)
```

With Zt peaking at ~3 (and rarely at ~3.5), P(deep) ≈ sigmoid(-1.5) ≈ 0.18 at peaks, P(deep) ≈ sigmoid(-3) ≈ 0.05 typically. The simulated label sequence shows < 5% deep-sleep coverage, vs the ~20-25% deep sleep typical for healthy adults.

See attached: psim diagnostic plot (`outputs/swat/set_A_healthy_14d/swat_channels.png` produced by `psim/examples/swat/14d_set_A_healthy.py`).

Why Zt amplitude is low

The flip-flop dynamics:
```
dZt = (A_SCALE * sigmoid(u_Z) - Zt) / tau_Z # A_SCALE = 6.0
u_Z = -gamma_3 * W - V_n + beta_Z * a
```

For overnight sleep (W=0) with Set A defaults (Vn=0.3, beta_Z=2.5, tau_a=3h):

• Adenosine `a` rises during wake (W=1), with timescale tau_a=3h. After ~16h wake, a≈1.
• At sleep onset: u_Z = -0.3 + 2.5·1 = 2.2 → Zt → 6 · sigmoid(2.2) ≈ 5.4 (deep)
• But `a` clears with same timescale 3h during sleep, so Zt's peak drops over the night.

In practice, the Zt peak in the artifact is only ~3, suggesting either:

• `a` doesn't reach high values during wake (peak in plot looks like 0.7-0.8, not 1.0)
• OR `tau_Z=2h` slow-tracks a fast-changing target
• OR coupling `beta_Z=2.5` is on the low side relative to what's needed

Suggested re-tuning (any one or combination)

For the healthy basin (Set A) to produce realistic deep-sleep proportions (~20-25%):

1. Lower c_tilde (e.g. 2.5 → c2 = 4.0 makes deep-sleep threshold reachable for typical Zt~3-4)
2. Boost beta_Z (e.g. 2.5 → 4.0) to amplify a→Zt coupling, pushing Zt closer to 5-6 in deep sleep
3. Lower tau_Z (2h → 1h) so Zt tracks a more aggressively
4. Keep tau_a=3h but lower its decay during sleep — would require a model change

Empirically, (1)+(2) combined would make the deep-sleep threshold reachable without changing the timescales.

Why this matters

For SMC² inference, the sleep ordinal channel is essentially providing only binary information (wake vs any sleep) when level=2 almost never fires. This impairs identification of:

• `c_tilde` (the level-1 threshold)
• `delta_c` (the level-2 threshold offset; effectively unconstrained because no level-2 data)
• `beta_Z`, `tau_a` (which together set Zt's overnight amplitude)

All three currently come back with narrow CIs locked off-truth in the SMC² rolling-window estimation (separate finding from the SMC² bug currently being investigated as part of the SWAT port to smc2-blackjax-rolling).

Out of scope here

• Fix for the SMC² inference bug (in `smc2-blackjax-rolling/smc2bj/log_density/gk_dpf_v3_lite.py`). That's tracked separately in the SMC² repo (private).
• Sets B/C/D may need similar audit but Set A is the immediate concern.

Reference

• Plot: `~/Repos/Python-Model-Scenario-Simulation/outputs/swat/set_A_healthy_14d/swat_channels.png`
• Generator: `version_1/models/swat/simulation.py:gen_sleep`
• Healthy-adult deep-sleep reference: 13-23% of total sleep, declining with age (Ohayon et al. 2004).

[ajaytalati]

Update: quantitative analysis on the actual artifact

Computed from the simulated truth (psim v0.1.2 `set_A_healthy_14d`,
4032 5-min bins over 14 days):

```
level=0 (wake): 3178/4032 = 78.8%
level=1 (light+REM): 566/4032 = 14.0%
level=2 (deep): 288/4032 = 7.1%

Of total sleep (854 bins): deep = 33.7% (healthy ~20-25%)

Zt range: [0.00, 4.30], mean=1.34
Zt > c2=4.5 (deep threshold): 0.0% of bins
Zt > c1=3.0 (sleep threshold): 5.7% of bins
```

So actually:

1. Deep sleep IS being generated — at 33.7% of total sleep, modestly above the healthy 20-25% range. This is because the ordinal sleep is generated stochastically: `P(level=2) = sigmoid(Zt - c2)`, which gives non-zero deep probability even when Zt < c2. With Zt peaks at 4.3 and c2=4.5, the noise floor sigmoid(-0.2) ≈ 0.45 fires deep ~45% of the time at peak Zt.

2. The real concern is Zt amplitude: Zt never exceeds c2=4.5 over the entire 14-day record. The deep-sleep label happens via the stochastic noise floor of the sigmoid, NOT via the deterministic dynamics crossing the threshold. This is a model-design fragility — small parameter perturbations (e.g. boost beta_Z) would either send Zt cleanly past c2 (clean deep-sleep dynamics) or push it further down (collapse).

3. Total sleep fraction: 21.2% of bins (854/4032). For 14-day record, 21% is on the LOW side (humans sleep ~30-35% of clock time). Zt > c1=3.0 only 5.7% of bins — i.e. the dynamics-driven sleep is brief; the rest of "sleep" comes from the sigmoid noise floor at Zt ∈ [c1−1, c1].

Implications for SMC² inference

This makes c_tilde, delta_c, beta_Z, tau_a all partially identifiable from the observed sleep labels:

• The fraction of level-2 vs level-1 vs level-0 events is informative
• But the Zt-driven structure (Zt rising above c1, then crossing c2) doesn't manifest cleanly
• SMC² estimator therefore has multiple sleep-channel-equivalent (delta_c, beta_Z, tau_a) triples that fit the data

This is independent of the SMC² C-phase bug analog also being investigated. Separate, additive concerns.

Suggested re-tuning (refined)

To get clean deterministic deep-sleep dynamics (Zt peak ~5.5, well above c2=4.5):

1. Boost beta_Z from 2.5 → 4.0 (primary): u_Z = ... + beta_Z·a; with a→1 overnight, this puts u_Z at ~3.7 → sigmoid(3.7)·6 = 5.8 (clean deep)
2. Shorten tau_a from 3h → 2h (alternative): a builds up faster during wake, reaches higher values before sleep onset
3. Lower c2 by lowering delta_c from 1.5 → 1.0: c2 = 4.0, easier to reach
4. Boost tau_W so wake periods are longer, allowing more adenosine accumulation

(2) and (4) interact (longer wake + faster adenosine = same effect). (1) is the most direct.

For Set A to remain "healthy" but with cleaner deep-sleep dynamics, I'd recommend (1) alone. The other params can stay.

Cross-reference

The SMC² inference cascade collapse (private repo) was found to be a C-phase bug analog in `smc2bj/log_density/gk_dpf_v3_lite.py` (within-window vs global time for analytical C_eff computation). Fix landed; full re-run confirming pending. The Zt-amplitude concern raised here is separate and would tighten identifiability further once both fixes are in.

[ajaytalati]

Workflow-gate observation: this should have been caught upstream

User-flagged: the diagnostic plot showing low Zt amplitude was produced from the simulated ground truth (psim's `outputs/swat/set_A_healthy_14d/trajectory.npz`), not from any SMC²-inferred posterior. The data lineage is:

```
swat_channels.png (in SMC² output dir, but plots ARTIFACT data)
↑ trajectory key from
psim's load_scenario(artifact_dir)
↑ which reads
psim's outputs/swat/set_A_healthy_14d/trajectory.npz
↑ packaged by
psim's package_scenario(sim_run, ...)
↑ where sim_run.trajectory came from
psim's synthesise_scenario(SWAT_MODEL, truth_params=PARAM_SET_A, ...)
↑ which Euler-Maruyama simulates
this repo's models/swat/simulation.py with PARAM_SET_A truth params.
```

So the Zt amplitude limit is a property of this repo's PARAM_SET_A. It was visible at the moment the artifact was generated by psim — it just wasn't surfaced as a problem because:

1. `models/swat/simulation.py:verify_physics` only checks state RANGES and FINITENESS:
   ```python
   return {
   'W_in_0_1': bool((W >= 0).all() and (W <= 1).all()),
   'Zt_in_0_A': bool((Zt >= 0).all() and (Zt <= A_SCALE).all()),
   'a_nonneg': bool((a >= 0).all()),
   ...
   'all_finite': bool(np.all(np.isfinite(trajectory))),
   }
   ```
   It does NOT check biological realism: "is the simulated W trajectory showing realistic sleep-wake patterns?" "is deep-sleep fraction in healthy range?" "does Zt cross the deep-sleep threshold deterministically?"

2. SWAT's `TESTING.md` §4.1 (Set A — healthy basin) only documents expected `T ≈ 0.55` — no expectation on Zt amplitude or sleep architecture (sleep fraction, deep sleep fraction, mean wake-after-sleep-onset, etc.).

3. psim's §1.4 consistency discipline tests sim/est CONSISTENCY (drift parity, obs-prediction parity, round-trip), not REALISM. A scenario can pass §1.4 cleanly while producing biologically implausible data.

4. psim's `package_scenario` doesn't currently emit a per-model channel diagnostic plot — only the SMC² repo's per-model driver did, which is why the issue surfaced at the SMC² stage rather than at psim's packaging stage.

Conclusion

The model-tuning issue (low Zt amplitude → rare deterministic deep sleep) was a property of this repo's `PARAM_SET_A` from day 1. It exists in the simulated truth, not the SMC² inference. It should have been caught here, not 1 stage downstream.

Three follow-up issues opened to close the gate

To prevent recurrence on SWAT and any future model:

1. This repo (#TBD): extend `models//simulation.py:verify_physics` to include biological-realism checks per model. SWAT's would compute `sleep_fraction`, `deep_sleep_fraction`, `Zt_max`, `Zt_reaches_deep_threshold`, etc.
2. psim (#TBD): `package_scenario` should emit a per-model channel diagnostic plot (calling `model.plot_fn`) so a human reviewer sees the simulated truth visualised at packaging time.
3. psim (#TBD): `validate_simrun` should separate gating booleans from informational warnings, and surface realism warnings clearly in the console + report.

The first repo's responsibility is the model definition + its quality. The second is the validation-discipline backstop. The third (SMC²) shouldn't have to surface model-design issues.

The proposed re-tuning (boost `beta_Z: 2.5 → 4.0`) remains the immediate fix to ship a usable Set A artifact. The follow-ups above are the structural changes to prevent the next instance.