SSM-AI – Appendix H — Comparisons & Synergies (H7–H9)

Small, decisive experiments → bounded fusion → strict acceptance (values unchanged).

H7) Micro experiments you can run in a day (observation-only)

  1. Decode bake-off (bounded chooser vs raw entropy).
    • 1k prompts × 2 vendors, cues {entropy, margin}, c=1, Unit=1, w := 1.
    • Rank by RSI_env := g_t * RSI (start g_t = 1).
    • Compare top-1 accuracy vs ranking by -entropy.
    • Ship: RSI_pool, band histograms, and accuracy lift.
  2. RAG drift guard (MC-dropout + retrieval entropy).
    • Penalty lens: e_in := var_mc/Unit + lambda * H_q/Unit.
    • Support lens: e_out := citation_hit + semantic_gain.
    • Expect fewer low-band selections when drift spikes; stamp all runs.
  3. Conformal set size as penalty.
    • e_in := (|S| - 1)/Unit, optional nonconformity term.
    • Track A-/A– fractions before/after; phi((m,a)) = m must hold.
# H7 – experiment skeleton (copy-paste)
# 1) Map cues -> e -> a (or two-channel), then fuse in u-space
a = tanh(c * e)                                # or a_in := tanh(-c*e_in), a_out := tanh(+c*e_out)
U += w * atanh( clamp(a, -1+eps_a, 1-eps_a) )  # order/shard invariant
W += w
a_pool := tanh( U / max(W, eps_w) )

# 2) Chooser + optional gate
RSI := a_pool
RSI_env := g_t * RSI                           # "mul" (or tanh(g_t * atanh(RSI)))
band := band_of(RSI_env)

# 3) Stamp
stamp := "SSMCLOCK1|iso_utc|svc=expH7|U={:.6f}|W={:.6f}|RSI={:.6f}|g={:.2f}|RSI_env={:.6f}|band={}|manifest=knobs_hash"

H8) When to prefer which cue (rule-of-thumb table)

scenario                    primary cue                  secondary cue
shortlist classification    margin or calibrated p       entropy (low), conformal size
long-tail classification    conformal score/size         MC-dropout entropy
RAG answerability           retrieval set entropy (H_q)  doc citation_hit, MC var
tool success routing        calibrated success prob      MC var of schema match
regression (numeric)        MC var (low)                 ensemble var (low), EDL strength (high)
# Always map cues via a := tanh(c*e) and decide by RSI or RSI_env (bounded).

H9) Acceptance checklist (must pass)

  • Parity: classical values m never change (phi((m,a)) = m).
  • Lens sanity: increasing a penalty lowers a (or raises |a_in|), increasing support raises a.
  • Order/shard invariance: permutations or shard merges yield the same RSI.
  • Boundedness: all a, RSI, RSI_env lie strictly in (-1,+1); bands follow manifest.
  • Determinism: same manifest + inputs ⇒ same outputs and stamps.
# Quick verifier (copy-paste)
def verify_acceptance(rows, manifest):
    eps_a = manifest.get("eps_a", 1e-6); eps_w = manifest.get("eps_w", 1e-12)
    def clamp1(x): return max(-1+eps_a, min(1-eps_a, x))
    from math import atanh, tanh
    # 1) boundedness
    assert all(-1 < r["a"] < 1 for r in rows)
    # 2) order/shard invariance
    def fuse(rows_): 
        U=W=0.0
        for r in rows_:
            U += r["w"] * atanh(clamp1(r["a"]))
            W += r["w"]
        return 0.0 if W<=0 else tanh(U / max(W, eps_w))
    assert abs(fuse(rows) - fuse(list(reversed(rows)))) < 1e-12
    # 3) determinism (same manifest hash + inputs => same RSI)
    return True

One-line takeaway. Run tiny day-one experiments, fuse fairly in u-space, and enforce a strict acceptance checklist—so heterogeneous confidence methods collapse to one bounded, reproducible lane while phi((m,a)) = m keeps classical numbers pristine.

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