Heterogeneous Channels

Previous experiments encoded text as char mod q in every channel -- 7 projections of the SAME signal. This experiment makes each channel encode a DIFFERENT feature: structural type, phonemic class, character identity, and bigram transition class.

If channels specialize, the partition into feature carriers {mod 8, 25, 49} vs parity checksums {mod 9, 11, 13, 17} becomes functional structure, not just algebra.

Het Encoding Design

Each channel encodes a different LEVEL of text structure. Key lesson: both input AND target must be het (het input + homo target fails).

mod 8
Structural type
space=0, lower vowel=1, lower cons=2, upper vowel=3, upper cons=4, digit=5, punct=6, other=7
mod 9
Phonemic class
space=0, plosive=1, fricative=2, nasal=3, liquid=4, glide=5, affricate=6, vowel=7, other=8
mod 25
Character identity
Top 25 chars by English frequency (case-insensitive). space=0, e=1, t=2, ..., j=23, other=24
mod 49
Bigram transition
coarse(prev)*7 + coarse(cur). 7 coarse types crossed. Encodes the TRANSITION, not the character.
mod 11/13/17
Parity channels
Weighted sums of the 4 feature channels: (a+b+c+d)%11, (2a+3b+5c+7d)%13, (a+2b+4c+8d)%17

Results

Per-channel bigram tallies on the same 471-character corpus. Given prev char's encoding, predict next char's encoding. Reconstruct via majority vote over 128 candidates.

Het ch_score
1205/3290 (36.6%)
Per-channel prediction. +170 over homo (+16.4%). Channels SPECIALIZE.
Homo ch_score
1035/3290 (31.5%)
Homogeneous char%q. All channels see same signal.
Het accuracy
124/470 (26.4%)
Reconstruction from het features. -6 vs homo.
Homo accuracy
130/470 (27.7%)
CRT algebraic uniqueness beats feature voting.

Feature vs Parity Channels

Feature channels {mod 8, mod 25, mod 49} carry direct data. Parity channels {mod 9, mod 11, mod 13, mod 17} are computed from features. Het encoding makes the split dramatic:

Het feature
684 ch_score
Feature channels +48% over homo (463). mod-8 (+134) and mod-49 (+83) drive the gain.
Het parity
405 ch_score
Parity channels -4% vs homo (424). Independently predicted checksums = harder.
mod 8 (structural)
+134 het advantage
58.5% raw accuracy. Structural type is the most predictable feature.
mod 49 (bigram)
+83 het advantage
53.4% raw accuracy. Transition patterns carry strong signal.
mod 11/13/17 (parity)
-20/-23/-32
Parity channels LOSE in het. They depend on feature channels, not vice versa.

What This Means

Het channels DO specialize -- mod-8 and mod-49 carry structural/transition info far better than char%q. The feature/parity split is meaningful: feature channels gain +48%, parity channels lose -4%. But reconstruction from qualitatively different features is harder than CRT algebraic reconstruction.

The reconstruction gap (-6 accuracy) reveals the key insight: channel specialization helps PERCEPTION but hurts RECONSTRUCTION. CRT's power is algebraic uniqueness (one number mod coprime moduli has exactly one solution). Het features lack this guarantee.

Next experiment (Ring Substrate): instead of encoding text INTO the ring, make the ring the computation substrate. Text goes in, text comes out. Between them: ring arithmetic IS the machinery. Modular multiplication for feed-forward, channel matching for attention, projectors for regularization.

Source code · Public domain (CC0)

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