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Exploratory experiment: Correlated anima beliefs

Source: exp_anima_correlated.sx — correlated evidence streams and a desire-coupling sweep

What was run

Two belief agents observe correlated Bernoulli streams ("rain" and "wet ground") or independent streams, with and without a learned interaction matrix, and joint prediction loss is recorded. A second sub-experiment sweeps a single agent's desire–evidence coupling \(c\) from \(-1.0\) to \(+1.0\) on a stationary stream and records final loss. These are exploratory runs; the tables are the outcomes and nothing further is claimed for them.

Method

Two sub-experiments. First: paired belief agents observe correlated Bernoulli streams (\(P(\text{wet}|\text{rain}) = 0.9\), \(P(\text{wet}|\neg\text{rain}) = 0.1\)) versus independent streams, with and without learned interaction. Second: desire coupling sweep from \(c = -1.0\) (fully opposed) to \(c = +1.0\) (fully aligned).

Experiment 1: Correlated vs Independent Streams

Agent A observes "rain" (\(p = 0.6\)). Agent B observes "wet ground" (conditionally dependent on rain). Interaction is learned by meta-gradient on the \(\alpha_{ij}\) matrix.

Condition Joint Loss Change
Independent (no interaction) 0.000203 —
Learned interaction (correlated) 0.0000921 55% lower
Learned interaction (uncorrelated) 0.000201 <1% (interaction weight near zero)

Result 1

With correlated streams, learned interaction lowers joint prediction loss by 55% in this run (0.000203 → 0.0000921). With uncorrelated streams the learned weight \(\alpha_{ij}\) ends near zero and the loss is unchanged. The meta-gradient on \(\alpha_{ij}\) picks up the conditional dependence between the streams when there is one.

Experiment 2: Desire Coupling Sweep

Single agent with desire coupling \(c\) swept from \(-1.0\) to \(+1.0\) in increments of 0.25. Each configuration runs 500 steps on a stationary stream (\(p = 0.7\)).

Coupling \(c\) Final Loss Reading
-1.0 (fully opposed) 0.000510 Strong damping
-0.5 0.000430 Lowest of the values tried
0.0 (neutral) 0.000625 No desire term
+0.5 0.000590 Mild amplification
+1.0 (fully aligned) 0.000602 Amplification

Result 2

Of the values swept, \(c = -0.5\) gives the lowest final loss (0.000430). Full opposition (\(c = -1.0\)) ends higher at 0.000510, neutral at 0.000625, and full alignment at 0.000602. The curve has its minimum at moderate opposition in this run, with one stream and one seed per value.

Observations

The learned interaction weight \(\alpha_{AB}\) ends positive when the two streams are dependent and near zero when they are independent, and the joint loss moves accordingly.

The desire sweep extends the three-point comparison in exp-anima-deep to a nine-point sweep of \(c\). The minimum sits at moderate opposition rather than at either end. A partially opposing desire term damps the update's response to recent observations; a fully opposing one damps it too far on this stream.

Reproducibility

# Clone and build
git clone https://github.com/senuamedia/lab.git
cd simplex && ./build.sh && cd ..

# Clone theorem-proof
git clone https://github.com/senuamedia/theorem-proof.git
cd theorem-proof

# Compile
../simplex/build/sxc exp_anima_correlated.sx -o build/exp_anima_correlated.ll

# Link with runtime
OPENSSL_PREFIX=$(brew --prefix openssl)
clang -O2 build/exp_anima_correlated.ll \
  ../simplex/runtime/standalone_runtime.c \
  -I"$OPENSSL_PREFIX/include" \
  -L"$OPENSSL_PREFIX/lib" \
  -lssl -lcrypto -lm \
  -o build/exp_anima_correlated

# Run
./build/exp_anima_correlated

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