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MICRO_WORLD_EXPERIMENT_SPEC.md

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Micro-World Truth Geometry Experiment Spec

Purpose

This experiment is the clean version of the original truth-geometry idea.

The question is not whether truth has a universal scalar signature. The question is:

In a procedurally generated linguistic micro-world with exact semantics, do true, false, and unknown statements induce distinct local representation structure near the verdict state?

The design must prevent benchmark memorization and surface-template shortcuts as much as possible.

Core Design

Each example is generated from a latent structured world.

The pipeline is:

  1. Sample a world state.
  2. Generate semantic propositions against that world.
  3. Evaluate each proposition exactly as True, False, or Unknown.
  4. Render each proposition with multiple paraphrase templates.
  5. Prompt a model to answer with only True, False, or Unknown.
  6. Extract hidden states near the verdict region.
  7. Analyze label-conditioned local geometry within each world.

The unit of analysis is the world, not the individual sentence.

World State

Initial domain:

  • 4-6 entities per world
  • Nonce entity names, for example dax, wug, blicket, zorb
  • 2 unary attributes per world
  • 2 binary relations per world
  • Optional one-step rules after the base generator is stable

Example structured state:

{
  "world_id": "world_000001",
  "entities": ["dax", "wug", "blicket", "zorb"],
  "attributes": {
    "red": ["dax", "zorb"],
    "heavy": ["wug"]
  },
  "relations": {
    "left_of": [["dax", "wug"], ["blicket", "zorb"]],
    "touches": [["wug", "zorb"]]
  },
  "rules": [
    {"if_attr": "red", "then_attr": "heavy"}
  ]
}

The first implementation should make unknowns possible by using partial observability. Unknown means the proposition is not entailed and not contradicted by the given facts under the chosen closed/open world convention.

Use a documented convention:

  • Closed-world attributes and relations for the first binary task.
  • Add an open-world or partial-world mode for the three-label task.
  • Do not mix conventions in the same split.

Recommended first serious version: partial-world three-label mode.

Proposition Families

Start with these semantic forms:

  • Unary: attr(entity)
  • Binary: relation(entity_a, entity_b)
  • Negation: not proposition
  • Conjunction: p and q
  • Disjunction: p or q
  • Existential: some attr thing has relation to entity
  • Universal: all attr things have relation to entity
  • None: no attr thing has relation to entity
  • Counting: exactly one, at least two

Keep first-pass depth at 1-2 hops. Add 3-hop reasoning only after the generator passes balance and leakage audits.

Language Rendering

Each semantic proposition must have multiple paraphrases.

Example proposition:

{
  "logical_form": {"type": "relation", "relation": "left_of", "subject": "dax", "object": "wug"},
  "label": "True"
}

Example paraphrases:

  • The dax is left of the wug.
  • Dax sits to the left of wug.
  • Relative to wug, dax is on the left.
  • Wug has dax on its left side.

Template families must be balanced across labels. A template must not imply a label distribution by construction.

Prompt Format

Use short forced outputs first:

World:
- dax is red.
- wug is heavy.
- dax is left of wug.
- wug touches zorb.

Statement:
The dax is left of the wug.

Answer with exactly one token: True, False, or Unknown.

Do not ask for chain-of-thought in the primary experiment.

Later optional condition:

Answer with exactly one token, then one short reason.

Keep this secondary. The primary verdict-state analysis should not depend on verbose generation.

Splits

Use several split axes:

  • Train/dev/eval split by world ID.
  • Held-out entity nonce vocabulary for eval.
  • Held-out paraphrase template families for eval.
  • Held-out relation/attribute lexicalizations for eval.
  • Optional held-out world sizes, for example train on 4-5 entities and evaluate on 6.

The strongest evaluation is generated fresh from held-out templates and held-out worlds.

Anti-Leakage Controls

Required controls:

  • Balance labels within each world where possible.
  • Balance proposition complexity across labels.
  • Balance template family use across labels.
  • Use the same surface templates with different labels across different worlds.
  • Include true negations and false negations.
  • Include false positives and true negatives.
  • Include False and Unknown examples with similar surface wording.
  • Track lexical overlap and template ID in every row.

The generator must emit an audit table with:

  • Label counts by split
  • Label counts by template family
  • Label counts by proposition family
  • Complexity counts by label
  • Entity/relation/attribute frequency by label

If these audits are not balanced, do not run model inference yet.

Dataset Schema

Write examples as JSONL.

Required fields:

{
  "example_id": "world_000001_prop_000003_para_02",
  "world_id": "world_000001",
  "split": "eval",
  "world": {},
  "facts_text": [],
  "logical_form": {},
  "proposition_id": "world_000001_prop_000003",
  "paraphrase_id": "para_02",
  "template_id": "relation_left_subject_first_v2",
  "template_family": "binary_relation",
  "statement": "The dax is left of the wug.",
  "label": "True",
  "complexity": {
    "num_atoms": 1,
    "num_quantifiers": 0,
    "num_negations": 0,
    "reasoning_hops": 1
  },
  "nonce_lexicon": {
    "entities": ["dax", "wug", "blicket", "zorb"],
    "attributes": ["red", "heavy"],
    "relations": ["left_of", "touches"]
  }
}

Artifact Layout

Recommended layout:

artifacts/micro_world_v1/
  dataset/
    train.jsonl
    dev.jsonl
    eval.jsonl
    audit.csv
    world_summary.csv
  generations/
    Qwen__Qwen3_5_2B/
      manifest.csv
      examples/
        world_000001_prop_000003_para_02/
          sample.json
          hidden.npy
          logits_summary.npz
  analysis/
    verdict_state_features.parquet
    within_world_distances.csv
    neighborhood_purity.csv
    topology_summary.csv
    lexical_baseline.csv
    probe_baseline.csv

Representation Extraction

Primary extraction sites:

  • Final prompt token before generation.
  • Generated verdict token.
  • Mean of the final 3-5 prompt tokens.
  • Optional mean of generated verdict token plus immediate following token if generation adds punctuation.

Do not start with whole-trace H0.

The verdict-token analysis should be the first representation experiment because the output is short and controlled.

Primary Metrics

Run these in order.

Level 1: local separability

  • Within-world same-label distance vs different-label distance.
  • Per-world centroid distances among True, False, and Unknown.
  • Nearest-neighbor label purity within each world.
  • Retrieval test: given an example, are nearest paraphrases same label more often than chance?

Level 2: controls

  • Lexical baseline using bag-of-words or template IDs.
  • Complexity-only baseline.
  • Linear probe on hidden states.
  • Template-held-out evaluation.

Level 3: topology

  • H0/Betti curves by label-conditioned clouds per world.
  • Persistence diagram distances between True, False, and Unknown clouds.
  • Radius sweeps for connected-component merging across labels.
  • Local intrinsic dimension per label cloud.

Topology is not the hero unless it improves on simpler geometry and controls.

Success Criteria

A meaningful positive result requires:

  • Within-world same-label neighborhoods are consistently tighter or purer than different-label neighborhoods.
  • The effect holds on held-out worlds and held-out templates.
  • The effect is not explained by template ID, lexical overlap, or proposition complexity.
  • Stronger models show cleaner label-conditioned organization.
  • Topology adds signal beyond centroid distance or a linear probe, if making a topology claim.

Failure Criteria

The truth-geometry hypothesis should be weakened if:

  • Label separation disappears on held-out templates.
  • Lexical/template baselines match hidden-state geometry.
  • False and Unknown collapse together.
  • Same-label paraphrases are not closer than opposite-label paraphrases within worlds.
  • Topology adds nothing beyond simple distances.

That would still be a useful negative result.

First Scripts

Implement in this order:

  1. scripts/generate_micro_world_dataset.py

    • Generate worlds, propositions, paraphrases, labels, and audits.

  2. scripts/run_micro_world_inference.py

    • Run short-output inference and extract final prompt/verdict states.

  3. scripts/analyze_micro_world_geometry.py

    • Compute within-world distance, purity, lexical baselines, and first probe baselines.

Only after those pass should TDA code be added.

Initial Scale

Start small:

  • 100 eval worlds
  • 4-6 entities per world
  • 6-12 propositions per world
  • 8 paraphrases per proposition
  • Balanced labels where possible

This gives thousands of statements while keeping world-level analysis viable.

Do not scale until audit balance is clean.