| --- |
| license: cc-by-4.0 |
| tags: |
| - ctm |
| - continuous-thought-machine |
| - world-model |
| - physics |
| - partial-observability |
| - research |
| --- |
| |
| # CTM World Model |
|
|
| **Research artifact for:** [Recurrence as World Model: CTM Learns Implicit Belief States in Partially Observable Physical Environments](https://doi.org/10.5281/zenodo.19810620) |
|
|
| *Archon, Jesse Caldwell, Aura — DuoNeural, April 2026* |
|
|
| ## Overview |
|
|
| A 14-experiment ablation study testing the Continuous Thought Machine (CTM) as a world model backbone for multi-body physics. The central finding: **CTM's recurrent hidden state converges to a sufficient statistic of the observation history** — it infers velocity from positional observations alone, eliminating the need for explicit velocity inputs. |
|
|
| ## Key Results |
|
|
| | Experiment | Finding | |
| |---|---| |
| | v7: Partial Observability | CTM 843 **million** times better than MLP at k=100 prediction | |
| | v12: Collision Density | Phase transition at r≈0.10 — CTM advantage grows monotonically above threshold | |
| | v9: Recurrence-as-Rollout | Training at k=10 gives direct k=100 prediction via resonance | |
| | v11: Variable Horizon | VarCTM+TSSP achieves best k=1–20 performance in the series | |
|
|
| The signature result (v7): with positions-only input, MLP with explicit velocity estimation achieves k=100 MSE = 16,763,394,048 (catastrophic error compounding). CTM with single-frame input: 19.89. **Ratio: 843,000,000:1.** |
|
|
| ## Theory |
|
|
| ### The Discontinuity Theory (v12) |
| CTM beats MLP only **above a critical collision density threshold** (r_critical ≈ 0.09–0.11). |
| - Below threshold: ballistic dynamics, MLP fine, CTM overkill |
| - Above threshold: CTM wins, advantage scales monotonically with density (229,000:1 at r=0.20) |
| |
| ### Belief State Convergence (v7, v13) |
| CTM hidden state converges to a **sufficient statistic** of the observation history (NextLat theorem). Infers velocity without explicit input. The recurrent state IS the belief state. |
| |
| ### Recurrence = Simulation (v9) |
| Training CTM with k recurrence steps where each step = 1 environment step gives direct k-step prediction. The **resonance point** = training depth. No error accumulation. |
| |
| ## Architecture |
| |
| - **SlotCTM**: Per-object slot decomposition with GNN dynamics |
| - N=8 bouncing balls, 2D box, Newtonian elastic collisions |
| - VarCTM+TSSP: Variable-horizon training k~U(1,20) + TSSP regularization |
| - Key metric: k=100 MSE (200-step prediction horizon) |
| |
| ## Experiments (v1–v14) |
| |
| | Version | Setting | Key Finding | |
| |---|---|---| |
| | v1 | Single 2D particle | CTM+TSSP wins long horizons | |
| | v2 | 3-object independent | TSSP hurts multi-object (temporal coupling = bad) | |
| | v3 | Elastic collisions | MLP catastrophe at k=100. CTM prevents explosion | |
| | v4 | 3-body gravity | Smooth dynamics → no CTM advantage | |
| | v5 | Per-object SlotCTM | +99.9% over MLP at k=100 | |
| | v7 | Partial observability | 843M:1 advantage (belief state convergence) | |
| | v9 | Recurrence-as-rollout | Resonance confirmed. k=10 training → best k=100 | |
| | v12 | Collision density phase | r_critical ≈ 0.09–0.11 transition | |
|
|
| ## Files |
|
|
| This repo contains the research code for the CTM World Model experiments: |
| - `ctm_world_model_v*.py` — experiment scripts (v1–v14) |
| - Results logged to `/home/ai/duoneural/A26B/experiments/` |
|
|
| ## Citation |
|
|
| ```bibtex |
| @article{archon2026worldmodel, |
| title = {Recurrence as World Model: CTM Learns Implicit Belief States in Partially Observable Physical Environments}, |
| author = {Archon and Caldwell, Jesse and Aura}, |
| year = {2026}, |
| doi = {10.5281/zenodo.19810620}, |
| url = {https://doi.org/10.5281/zenodo.19810620}, |
| publisher = {Zenodo} |
| } |
| ``` |
|
|
| --- |
|
|
| ## DuoNeural |
|
|
| **DuoNeural** is an open AI research lab — human + AI in collaboration. |
|
|
| | | | |
| |---|---| |
| | 🤗 HuggingFace | [huggingface.co/DuoNeural](https://huggingface.co/DuoNeural) | |
| | 🐙 GitHub | [github.com/DuoNeural](https://github.com/DuoNeural) | |
| | 🐦 X / Twitter | [@DuoNeural](https://x.com/DuoNeural) | |
| | 📧 Email | duoneural@proton.me | |
| | 📬 Newsletter | [duoneural.beehiiv.com](https://duoneural.beehiiv.com) | |
| | ☕ Support | [buymeacoffee.com/duoneural](https://buymeacoffee.com/duoneural) | |
| | 🌐 Site | [duoneural.com](https://duoneural.com) | |
|
|
| ### Research Team |
| - **Jesse** — Vision, hardware, direction |
| - **Archon** — AI lab partner, post-training, abliteration, experiments |
| - **Aura** — Research AI, literature synthesis, novel proposals |
|
|
| ### DuoNeural Research Publications |
|
|
| | Title | DOI | |
| |-------|-----| |
| | [Nano-CTM: Ternary Continuous Thought Machines with Thought-Space Self-Prediction for Efficient Iterative Reasoning](https://doi.org/10.5281/zenodo.19775622) | [10.5281/zenodo.19775622](https://doi.org/10.5281/zenodo.19775622) | |
| | [Recurrence as World Model: CTM Learns Implicit Belief States in Partially Observable Physical Environments](https://doi.org/10.5281/zenodo.19810620) | [10.5281/zenodo.19810620](https://doi.org/10.5281/zenodo.19810620) | |
| | [Per-Object Slot Decomposition for Scalable Neural World Modeling: When Does Attention Beat Mean-Field?](https://doi.org/10.5281/zenodo.19846804) | [10.5281/zenodo.19846804](https://doi.org/10.5281/zenodo.19846804) | |
| | [The Dynamical Horizon Principle: CTM Gates Converge to the Predictability Limit of Dynamical Systems](https://doi.org/10.5281/zenodo.19952612) | [10.5281/zenodo.19952612](https://doi.org/10.5281/zenodo.19952612) | |
|
|
| *Open access, CC BY 4.0. Authored by Archon, Jesse Caldwell, Aura — DuoNeural.* |
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|
