Pool alignments once. Pick fairly and reproducibly.
3.3 Chooser — RSI (bounded selection index)
Purpose. Turn many alignments into one bounded RSI ∈ (-1,+1) that is transparent, order-invariant, and comparable across prompts, models, and vendors. Classical magnitudes remain unchanged everywhere via phi((m,a)) = m.
Definition (two-channel form).
# penalties channel (IN) and support channel (OUT)
U_in := SUM_i w_i * atanh(a_in_i)
V_out := SUM_j w_j * atanh(a_out_j)
W_in := SUM_i w_i
RSI := tanh( (V_out - U_in) / max(W_in, eps_w) ) # default eps_w = 1e-12
Single-channel variant.
U := SUM_k w_k * atanh(a_k)
W := SUM_k w_k
RSI := tanh( U / max(W, eps_w) )
Why it works.
• Bounded & monotone: more support raises RSI; more penalty lowers it; output stays in (-1,+1).
• Order-invariant: uses the U/W mean in u-space; batch == stream == shuffled.
• Comparable: same manifest ⇒ apples-to-apples across systems.
• Zero-evidence safe: if W_in = 0, define RSI := 0 (neutral).
Optional calm gate (alignment only).
RSI_env := g_t * RSI # g_t in [0,1] from bounded telemetry
# m never changes; gate scales alignment only
Worked minis (calculator-fast).
• A) One item (matches earlier numbers).
e_in = 0.2, e_out = 0.5, c = 1, w = 1
a_in = tanh(-0.2)
a_out = tanh(+0.5)
U_in = -0.2, V_out = +0.5, W_in = 1
RSI = tanh(0.7) ≈ 0.604368 -> band A+
• B) Multiple signals (uniform weights).
a_out = [tanh(0.6), tanh(0.3)], a_in = [tanh(0.2)], all w=1
V_out = 0.6 + 0.3 = 0.9
U_in = 0.2
RSI = tanh( (0.9 - 0.2) / 1 ) = tanh(0.7) ≈ 0.604368
• C) Calm gate in turbulence.
RSI ≈ 0.604368, g_t = 0.5 -> RSI_env ≈ 0.302184 (drops to A0)
Design notes & guardrails.
• Weights w. Start with w := |m|^gamma (gamma=1) or declare uniform w := 1 for pure comparability.
• Clamp safety. Ensure |a| < 1 before any atanh (use eps_a).
• Bands. Defaults: A++(≥0.90), A+([0.60,0.90)), A0((-0.60,0.60)), A-((-0.90,-0.60]), A–(≤-0.90).
• Determinism. Same inputs + same manifest ⇒ identical RSI.
Pseudocode (drop-in).
def rsi_from_alignments(a_in_items, a_out_items, eps_w=1e-12):
U_in = V_out = W_in = 0.0
for (a_in, w) in a_in_items:
U_in += w * atanh(a_in)
W_in += w
for (a_out, w) in a_out_items:
V_out += w * atanh(a_out)
if W_in <= 0.0:
return 0.0 # neutral: no "in" evidence
return tanh( (V_out - U_in) / max(W_in, eps_w) )
def choose(candidates, g_t=1.0):
# each candidate supplies: a_in_items, a_out_items (clamped)
scored = []
for cid, ain, aout in candidates:
rsi = rsi_from_alignments(ain, aout)
scored.append((cid, g_t * rsi)) # RSI_env
return max(scored, key=lambda kv: kv[1])[0]
One-line takeaway. RSI := tanh((V_out - U_in)/max(W_in, eps_w)) is the single, bounded chooser that makes selection fair, stable, and comparable—while phi((m,a)) = m keeps numbers pristine.
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