What SSM-AI Is (Positioning & Promise) — Purpose, Non-Goals, Beam-Pick Micro-Example
What it is (in one line).
Carry a bounded alignment lane beside every classical value you already trust:x := (m, a) with a in (-1,+1) and collapse parity phi((m,a)) = m.
How it composes.
Clamp → map to rapidity → compose → inverse-map → band. Streams fuse order-independently.
a_c := clamp(a, -1+eps_a, +1-eps_a)
u := atanh(a_c)
a' := tanh(u') # after composition in u
U += w*atanh(a); W += w
a_out := tanh( U / max(W, eps_w) ) # order-invariant fuse
One bounded chooser. A declared lens turns evidence into a single RSI; an optional calm gate scales alignment only.
RSI := tanh( (V_out - U_in) / max(W_in, eps_w) )
RSI_env := g_t * RSI
1.1 Purpose & Non-Goals
Purpose. Add a bounded, comparable, order-invariant lane so selection, routing, retries, and audits become clear without touching m. Numbers remain identical via phi((m,a)) = m.
Why now.
• Speed: calculator-fast checks → idea→pilot in hours, pilot→portfolio in weeks
• Quality: fewer over-confident outputs; calmer agent loops; banded risk (A++/A+/A0/A-/A--)
• Comparability: same manifest ⇒ apples-to-apples across prompts, models, vendors
• Time & audit: per-decision stamps enable replay and day/week roll-ups
Scope (where it drops in). Decoding/beam pick • RAG/doc ranking • Search (internet/intranet/local) • Tools/agents • Evaluators/judges • Multi-model ensembles. SSM-Clock/Stamp adds time-sliced replay; SSMH later accelerates the exact same math; domain packs (e.g., SSM-Chem, SSM-Audit) supply lenses and banded KPIs.
Non-Goals (hard constraints).
• No model surgery: training/logits/probabilities remain intact (phi((m,a)) = m)
• No hidden smoothing: all knobs live in a public manifest (bands, clamps, weights, policies)
• No order dependence: batch == stream == shuffled (same U/W fuse)
• No silent actuation: gate scales alignment only (RSI_env := g_t * RSI); control/UX changes need a safety case
• No PII usage: lenses derive from non-sensitive signals or declared metrics
• No “explainability” claims: SSM-AI reports bounded stability/fit; it does not infer intent beyond declared lenses
Traditional vs SSM-AI (micro-example — beam pick)
Goal: choose the best candidate consistently across vendors.
Traditional
Pick argmax(prob) or ad-hoc blends; retries on thresholds; unstable under turbulence.
SSM-AI
Compute lens contrasts (e_in, e_out) → map to alignments → pool in u → choose by bounded clarity. m remains identical.
# contrasts to alignments
a_in := tanh(-c*e_in)
a_out := tanh(+c*e_out)
# pooled chooser (bounded)
RSI := tanh( (SUM w*atanh(a_out) - SUM w*atanh(a_in)) / max(SUM w, eps_w) )
# optional environment gate (alignment only)
RSI_env := g_t * RSI
Pocket pseudocode (drop-in, 8 lines).
def choose(cands, c=1.0, eps_w=1e-12, g_t=1.0):
best = None
for cand in cands: # cand.lens -> [(e_in, e_out, w), ...]
U_in = V_out = W = 0.0
for e_in, e_out, w in cand.lens:
U_in += w*atanh(tanh(-c*e_in))
V_out += w*atanh(tanh(+c*e_out))
W += w
RSI = tanh( (V_out - U_in) / max(W, eps_w) )
best = max([best,(cand, g_t*RSI)], key=lambda x: x[1]) if best else (cand, g_t*RSI)
return best[0]
Acceptance snapshot (must pass).
Collapse parity ✔ phi((m,a)) = m • Order invariance ✔ U/W • Clamp bounds ✔ (eps_a, eps_w) • Gate purity ✔ (m untouched) • Determinism ✔ (same manifest ⇒ same outputs)
Navigation
Previous: SSM-AI – What’s Inside & Elevator Summary (0I, 0J)
Next: 1.2 Observation-Only Ethos & Collapse Parity
Directory of Pages
SSM-AI — Table of Contents
Explore Further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-AI
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