SSM-AI – Appendix H — Comparisons & Synergies (H4–H6)

Bound one lane; plug any confidence cue; decide by RSI (values unchanged).

H4) Pros/cons by method (engineering quick view)

  • Entropy / margins — Pros: simple, cheap, ubiquitous. Cons: scale varies by model/vendor. Use: normalize to a dimensionless e; band on RSI, not raw probs.
  • MC-dropout — Pros: captures epistemic cheaply (no retrain). Cons: extra passes; depends on dropout config. Use: map variance/entropy as e_in penalty.
  • Deep ensembles — Pros: strong uncertainty in practice. Cons: costly to serve. Use: pool each model’s a in u-space; same manifest across vendors.
  • Conformal — Pros: finite-sample coverage (exchangeability). Cons: set size coarse; calibration drift. Use: penalize large |S| or high nonconformity via e_in.
  • Evidential — Pros: single pass; separates aleatoric/epistemic proxies. Cons: loss-sensitive. Use: map evidence strength to e_out, penalties to e_in.
  • Calibrated prob (Platt/Isotonic) — Pros: better-behaved than raw softmax. Cons: can drift. Use: treat calibrated top-1 as support lens.
    Invariant: Classical numbers remain untouched: phi((m,a)) = m.

H5) Worked minis (calculator-fast)

H5.1 Entropy lens (K = 5)

H = 0.900000
H_max = log(5) ≈ 1.609438
conf_H = 1 - H/H_max ≈ 0.440383
tau = 0.300000, Unit = 1.000000, c = 1.000000
e = 0.140383
a = tanh( c * e ) ≈ 0.139474      # → band A0

H5.2 MC-dropout variance penalty

var_mc = 0.250000, target s = 0.100000, Unit = 0.200000, c = 1.000000
e = (s - var_mc)/Unit = -0.750000
a = tanh(-0.750000) ≈ -0.635148   # penalty pushes negative

H5.3 Ensemble margin (3 models)

margins = [0.600000, 0.400000, 0.200000]
e_k = margin - 0.300000
a_k = tanh(e_k) = [0.291313, 0.099668, -0.099668]
U = 0.300000 + 0.100000 - 0.100000 = 0.300000
W = 3
a_pool = tanh(U/W) = tanh(0.100000) = 0.099668   # → band A0

H5.4 Conformal set-size penalty

|S| = 3, Unit = 2
e_in = (|S| - 1)/Unit = 1.000000
a_in = tanh(-1.000000) = -0.761594
a_out = tanh(0.800000) = 0.664037
U_in = 1.000000; V_out = 0.800000; W_in = 1
RSI = tanh( (V_out - U_in)/W_in ) = tanh(-0.200000) = -0.197375  # → band A-

H6) How to combine multiple methods cleanly (no double counting)

  • Bundle by surface (e.g., bundle_decode = {entropy, margin, calibrated_prob}).
  • De-correlate highly related cues: either downweight (w_small) or pre-combine e := w1*z1 + w2*z2 - w3*z3 before mapping to a.
  • Declare weights once for comparability: w := 1 (uniform) or w := |m|^gamma.
  • Fuse only in u-space and choose by a bounded index (RSI or RSI_env).
  • Acceptance: increasing a penalty must not raise alignment; shuffling inputs or shards must leave RSI unchanged.
# Clean fusion template (copy-paste)
U = 0.0; W = 0.0
for cue in cues:               # each cue -> contrast e_cue (dimensionless)
    a = tanh(c * e_cue)        # or two-channel mapping
    x = max(-1+eps_a, min(1-eps_a, a))
    U += w_cue * atanh(x)
    W += w_cue
a_pool := tanh( U / max(W, eps_w) )
RSI     := a_pool
RSI_env := g * RSI                         # or tanh(g * atanh(RSI))

One-line takeaway. Treat entropy, margins, MC-dropout, ensembles, conformal, and evidential signals as simple lenses feeding a single bounded lane; fuse fairly in u-space, decide by RSI/RSI_env, and keep all classical values pristine via phi((m,a)) = m.

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