Kernel • Streaming • Bands
Datum and collapse
Each value carries a bounded confidence lane: x := (m,a) with a in (-1,+1).
Collapse: phi((m,a)) = m.
Clamp-first policya_c := clamp(a, -1+eps_a, +1-eps_a) with default eps_a = 1e-6.
Rapidity map (stable composition)u := atanh(a_c); compose in u-space, then map back with tanh.
Binary combine (M2 policy)
Multiplication/division in the lane use rapidity addition/subtraction:
- Mul:
a' = tanh(atanh(a1) + atanh(a2)) - Div:
a' = tanh(atanh(a1) - atanh(a2))
(Clamp each operand beforeatanh.)
Streaming fuse (order-independent)
Accumulate confidence for streams, batches, or shuffles identically:U += w*atanh(a) ; W += w ; a_out := tanh( U / max(W, eps_w) )
Default weights: w := |m|^gamma with gamma = 1.
Default eps_w = 1e-12. (Uniform option: set w = 1 explicitly.)
Bands (global defaults — normative)A++: a >= +0.90A+ : +0.60 <= a < +0.90A0 : -0.60 < a < +0.60A- : -0.90 < a <= -0.60A--: a <= -0.90
Overrides must be declared explicitly (manifest and CSV header).
Non-negotiable invariants (normative)
(i) Collapse parity: phi((m,a)) = m.
(ii) Order invariance: batch == stream == shuffled (within a fixed epsilon).
(iii) Determinism: same knobs ⇒ same outputs.
(iv) Hardware parity: software vs RTL agree within fixed tolerances.
(v) Lane purity: policies act only on a; m is never mutated by SSMH.
(vi) Division near zero (default): division_policy = "strict"; alternatives (e.g., "meadow", "soft") require explicit declaration.
Navigation
Back: Shunyaya Symbolic Mathematical Hardware – Executive Summary & Introduction (0, 0A)
Next: Shunyaya Symbolic Mathematical Hardware – Architecture & Rationale (0C, 0D)
Directory of Pages
SSMH – Table of Contents
SHUNYAYA 