SSM-AI – Appendix P — FAQ & Troubleshooting (P6–P10)

Deployment discipline, priors, bias handling, and numeric stability checks.

P6) Priors & bias control

Purpose. Maintain interpretability and ethical purity in alignment lanes. Priors and gates are bounded and declared explicitly — never implicit or learned.

Rules and best practices:

  1. Keep priors tiny and transparent.
    u' := u + beta*b where b ∈ [-1,+1] and beta ≤ 0.25.
    Priors should only nudge alignment, not dominate it.
  2. Declare priors publicly.
    Every b and beta must appear in the manifest or logged under audit. No hidden bias vectors.
  3. Never bake in sensitive attributes.
    Exclude demographic, textual, or geographic factors. Use only declared domain metrics.
  4. Bounded safety.
    Always clamp the result:
    u'_safe := clamp(u', -atanh(1-eps_a), +atanh(1-eps_a)).
  5. Zero-prior fallback.
    If no explicit priors exist, use beta := 0, b := 0.
    Resulting behavior equals pure SSM-AI baseline.

Quick numeric example:

u = 0.6, b = +0.2, beta = 0.1 → u' = 0.6 + 0.02 = 0.62
a' = tanh(u') = 0.5519  # bounded, gentle influence

P7) Performance & scaling

Vectorization and mixed precision

  • Use SIMD or batched operations.
    All tanh/atanh computations are scalar-safe; vectorize where possible.
  • Mixed-precision tip.
    Use float32 for atanh/tanh, float64 for long accumulators (U,W).
    Clamp aggressively for stability (eps_a = 1e-6, eps_w = 1e-12).

Streaming behavior

  • Maintain per-window accumulators:
    U += w*atanh(a) ; W += w.
    Reset every evaluation horizon (e.g., day/week).

Stability checks

CheckFormulaExpected
Clamp saturationabs(a) < 1-eps_a✓
Rapid decay near edgesd(tanh(u))/du = 1 - tanh(u)^2→ 0 near ±1
Numerical parityatanh(tanh(u)) ≈ uwithin dtype tolerance

P8) Common misconceptions

MisconceptionClarification
“RSI is a probability.”No. RSI is a bounded symbolic chooser in (−1,+1), not a probability.
“Gate changes outputs.”No. Gate only scales RSI or its curvature; m remains identical.
“We can average a directly.”Never. Always combine via (U,W) in u-space.
“Changing bands is harmless.”Bands affect routing logic; any change must yield a new knobs_hash.
“Manifest isn’t needed for audit.”It is the reproducibility contract. No manifest, no verifiable results.

P9) End-to-end worked mini example

Parameters:
c = 1, Unit = 1, eps_a = 1e-6, eps_w = 1e-12, g_t = 0.80.

Steps:

e_in  = 0.2 ; e_out = 0.5
a_in  = tanh(-1*0.2) = -0.197375
a_out = tanh(+1*0.5) = +0.462117
U_in  = atanh(a_in) = -0.200000
V_out = atanh(a_out) = +0.500000
W_in  = 1.000000
RSI   = tanh( (V_out - U_in)/W_in ) = tanh(0.700000) = 0.604368
RSI_env = g_t * RSI = 0.80 * 0.604368 = 0.483494
Band = A0/A+ boundary

Observations:

  • Order/shard invariance verified (U/W deterministic).
  • Clamp boundaries respected (|a| < 1).
  • Gate scales RSI only; phi((m,a)) = m holds true.

P10) One-minute acceptance checklist

  1. Parity: Confirm phi((m,a)) = m for a sample of 10+ random rows.
  2. Bounds: Ensure all a, RSI, and RSI_env ∈ (−1,+1).
  3. Determinism: Re-run same manifest twice → identical RSI/bands.
  4. Order invariance: Shuffle inputs → identical pooled results.
  5. Replay: tanh(sum(U)/max(sum(W),eps_w)) matches original.
  6. Gate purity: Gate affects RSI only.
  7. Hash verification: knobs_hash stable under canonical JSON.

Quick parity snippet:

for row in sample:
    assert abs(row["m"] - row["phi_m"]) < 1e-12
    assert abs(row["RSI_env"]) < 1.0

Stamp example (one line, ASCII)

SSMCLOCK1|iso_utc|k=troubleshoot|U=0.700000|W=1.000000|RSI=0.604368|g=0.80|RSI_env=0.483494|band=A0|manifest=knobs_hash

One-line takeaway.
Every operation in SSM-AI — from priors to pooling — reduces to a deterministic, bounded, and reversible path:
clamp → atanh → sum → tanh → band, with phi((m,a)) = m ensuring classical values never change.

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