Phase 1A: modality-balanced encoder init + decoder variance-target scaling

Two new init toggles on RegularizedMultimodalVI, both off by default so
in-flight runs are byte-identical:

- use_modality_balanced_encoder_init (F1): rebalance per-modality
  mean_encoder/var_encoder weights so per-element variance equals
  1/(3·total_n_hidden) — equivalent to a single virtual Linear of
  fan_in = sum_m n_hidden_m. Counters per-modality posterior collapse
  driven by Kaiming's fan-in-only normalisation in multimodal encoders.

- decoder_init_variance_target_fraction (F2, plus burst_size_head
  variant): rescale per-feature decoder weight rows so the pre-softplus
  output variance lands at fraction × clip_per_feature_variance_to_theta_bounds(
  excess_biological_g, mean_g, theta_min, theta_max). Symmetric to
  z_loc_init_scale on the encoder side; lifts decoder output variance
  off the Kaiming default 1/3 toward the per-gene biological excess.

Supporting changes:
- _compute_theta exposes excess_biological in diagnostics with
  np.maximum(..., eps**2) floor (single source of truth).
- compute_bursting_init reads excess_biological from diagnostics and
  uses the new clip_per_feature_variance_to_theta_bounds helper for
  the stochastic_v_scale clip — byte-identical to the prior inline form.
- ValueError if decoder fraction is set with dispersion_init not in
  {data, variance_burst_size}; LayerNorm warning if decoder LayerNorm
  is disabled (Var(h_dim) ≈ 1 assumption broken).

Tests: 11 new (5 F1 + 6 F2); full suite 406/406.

Phase 1B sweep TSV (8 conditions × 3 datasets = 24 rows) with F1 always
on, F2 main fraction in {0.2, 0.02} and burst_size r = main / 10 for
bursting variants.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: Vitalii Kleshchevnikov

docs/notebooks/immune_integration/bm_pbmc_rna_training_v3_slurm.ipynb

@@ -116,6 +116,11 @@
     "use_softplus_var_activation = True\n",
     "use_ard_z_sigma_scale = False\n",
     "z_loc_init_scale = 1.0\n",
+    "# Phase 1A: modality-balanced encoder init (F1) and decoder weight init scaled\n",
+    "# by per-feature biological variance (F2). Defaults preserve in-flight runs.\n",
+    "use_modality_balanced_encoder_init = False\n",
+    "decoder_init_variance_target_fraction = None\n",
+    "decoder_burst_size_init_variance_target_fraction = None\n",
     "decoder_weight_l2 = 0\n",
     "batch_size = 1024\n",
     "# --- Attribution ---\n",
@@ -427,6 +432,12 @@
     "    use_softplus_var_activation=(use_softplus_var_activation, bool),\n",
     "    use_ard_z_sigma_scale=(use_ard_z_sigma_scale, bool),\n",
     "    z_loc_init_scale=(z_loc_init_scale, float),\n",
+    "    use_modality_balanced_encoder_init=(use_modality_balanced_encoder_init, bool),\n",
+    "    decoder_init_variance_target_fraction=(decoder_init_variance_target_fraction, \"float_or_none\"),\n",
+    "    decoder_burst_size_init_variance_target_fraction=(\n",
+    "        decoder_burst_size_init_variance_target_fraction,\n",
+    "        \"float_or_none\",\n",
+    "    ),\n",
     "    batch_size=(batch_size, int),\n",
     "    attribution_batch_size=(attribution_batch_size, int),\n",
     "    attribution_method=(attribution_method, str),\n",
@@ -484,6 +495,9 @@
     "use_softplus_var_activation = params[\"use_softplus_var_activation\"]\n",
     "use_ard_z_sigma_scale = params[\"use_ard_z_sigma_scale\"]\n",
     "z_loc_init_scale = params[\"z_loc_init_scale\"]\n",
+    "use_modality_balanced_encoder_init = params[\"use_modality_balanced_encoder_init\"]\n",
+    "decoder_init_variance_target_fraction = params[\"decoder_init_variance_target_fraction\"]\n",
+    "decoder_burst_size_init_variance_target_fraction = params[\"decoder_burst_size_init_variance_target_fraction\"]\n",
     "batch_size = params[\"batch_size\"]\n",
     "attribution_batch_size = params[\"attribution_batch_size\"]\n",
     "attribution_method = params[\"attribution_method\"]\n",
@@ -612,6 +626,9 @@
     "    use_softplus_var_activation=use_softplus_var_activation,\n",
     "    use_ard_z_sigma_scale=use_ard_z_sigma_scale,\n",
     "    z_loc_init_scale=z_loc_init_scale,\n",
+    "    use_modality_balanced_encoder_init=use_modality_balanced_encoder_init,\n",
+    "    decoder_init_variance_target_fraction=decoder_init_variance_target_fraction,\n",
+    "    decoder_burst_size_init_variance_target_fraction=decoder_burst_size_init_variance_target_fraction,\n",
     ")"
    ]
   },

docs/notebooks/model_comparisons/balanced_encoder_decoder_slurm_jobs.tsv

@@ -0,0 +1,25 @@
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