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Exploratory experiment: Deep anima beliefs

Source: exp_anima_deep.sx — four exploratory sub-experiments on Bayesian belief agents

What was run

Bayesian belief agents with configurable desire vectors, memory thresholds and working-memory sizes observe a 500-step stationary Bernoulli stream (\(p = 0.7\)) and update by a contractive rule. Four sub-experiments record how prediction loss varies with: pairwise interaction between agents, the memory-consolidation threshold, the sign and size of the desire–evidence coupling, and working-memory capacity under three ordering strategies. These are exploratory runs; the tables are the outcomes and nothing further is claimed for them.

Method

Four sub-experiments, each using Bayesian belief agents with configurable desire vectors, memory thresholds, and working memory sizes. All agents observe the same 500-step stationary Bernoulli stream (\(p = 0.7\)).

Experiment 1: Belief Interaction

Two agents observe the same stream. One pair interacts (projects beliefs pairwise through a learned interaction matrix); the other pair remains isolated. Prediction loss is squared error against the true parameter.

Condition Final Loss Difference
No interaction (isolated) 0.000492 —
Learned interaction 0.000496 -0.8% (within noise)

Result 1

On a stationary stream with identical agents, interaction makes no measurable difference. Both agents carry the same information, so there is nothing to transfer; the interaction term does not add signal that is not there.

Experiment 2: Memory Consolidation

Agents with memory consolidation thresholds ranging from 0 (retain all) to 0.05. The threshold controls which belief updates are consolidated into long-term memory based on their magnitude.

Threshold Final Loss Notes
0.00 (retain all) 4.92 × 10-4 Baseline
0.01 1.2 × 10-4 Lower
0.05 6.6 × 10-5 Lowest of the values tried

Result 2

Of the thresholds tried, \(\tau = 0.05\) gives the lowest final loss, 7.5× below retain-all in this run. Filtering small updates removes noise on a stationary stream; whether the same threshold suits a non-stationary stream is not tested here.

Experiment 3: Desire-Belief Coupling

Three agent configurations: aligned desire (\(\mathbf{d}\) parallel to evidence), misaligned desire (\(\mathbf{d}\) partially opposing evidence), and neutral desire (\(\mathbf{d} = \mathbf{0}\)). Each runs for 500 steps on the same stream.

Desire Configuration Coupling Final Loss
Aligned \(c = +1.0\) 0.000608
Neutral \(c = 0.0\) 0.000625
Misaligned \(c = -0.5\) 0.000430

Result 3

In this run the misaligned agent ends with the lowest loss (0.000430), the aligned agent at 0.000608 and the neutral agent at 0.000625. A desire term partially opposing the evidence acts like a shrinkage term on the update, damping the response to recent observations on this stationary stream; the aligned term amplifies it. One stream and one seed per configuration are run here.

Experiment 4: Working Memory Capacity

Agents with varying working memory sizes (number of belief slots). Three ordering strategies: most informative beliefs first, random, and least informative first.

Strategy Slots at plateau Notes
Most informative first 40 beliefs Lowest plateau error
Random ordering 30 beliefs Plateaus earlier at higher error
Least informative first 15 beliefs Plateaus earliest at the highest error

Result 4

The number of slots at which error stops improving depends on the ordering: 40 with the most informative beliefs first, 30 for random, 15 for reversed, with plateau error increasing in that order.

Observations

  • Interaction between identical agents on the same stream changes nothing, as expected when there is no information to transfer.
  • A non-zero consolidation threshold lowers final loss on this stationary stream; 0.05 is the best of the values tried.
  • A partially opposing desire term lowers final loss relative to neutral and aligned terms in this run; the loss ordering is misaligned < aligned < neutral.
  • Working-memory plateau position and level depend on the ordering strategy.

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_deep.sx -o build/exp_anima_deep.ll

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

# Run
./build/exp_anima_deep

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