Putting Newton Inside Neural Networks: How Hamiltonian World Models Could Reshape AI's Physical Common Sense

Forum topic · 小凯 · 2026-05-21

Summary

This zhichai.net forum post discusses a proposed research direction called Hamiltonian World Models (HWM), presented in a paper by Tsinghua University researchers Sen Cui and Jingheng Ma (arXiv:2605.00412). The author argues that current generative video models such as SORA suffer from 'visual hallucinations'—objects passing through solids, liquids defying gravity—because they learn pixel-level correlations without physical common sense. HWM's core idea is to replace the opaque latent vector with a structured phase-space decomposition: generalized coordinates (q) for position and pose, and generalized momenta (p) for motion state and inertia. Dynamics are governed by a controlled Hamiltonian system with dissipation and residual terms, allowing explicit modeling of friction, agent control, and unexplained noise. The post cites claimed results, including long-horizon video predictions remaining physically aligned for 60 seconds (vs. degradation after ~10 seconds for diffusion baselines), energy conservation error below 1% (vs. roughly ±35%), reduced data requirements via physics priors, and improved interpretability by inspecting the learned Hamiltonian energy function. It concludes that embedding classical mechanics into neural networks may provide the physical foundation needed for reliable embodied AI and robotics.

Putting Newton Inside Neural Networks: How Hamiltonian World Models Could Reshape Physical Common Sense

*(English translation of a zhichai.net forum post. Claims and figures below are as reported in the original post and the paper it cites.)*

Preface: The End of Visual Deception and the Return of 'Truth'

In server rooms in Mountain View, California, tens of thousands of H200 GPUs churn out videos that take the world's breath away—mammoths dancing in snow, cyberpunk women strolling through Tokyo streets. This is the shock delivered by generative video models such as SORA.

Yet watch long enough and an uncanny feeling creeps in: mammoth feet pass through rocks, spilled coffee drifts upward against gravity. Academia has an elegant but resigned name for this—"Visual Hallucination."

After two years of a "compute carnival," AI scientists have hit an invisible wall: today's AI has mastered all human language but does not understand the physical common sense of the world.

In this framing, a May 2026 arXiv paper by Tsinghua University's Sen Cui and Jingheng Ma—"Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling" (arXiv:2605.00412)—attempts something ambitious: stop teaching AI to simulate "pixels," and instead stitch 19th-century Hamiltonian mechanics directly into 21st-century neural networks.

1. The Broken Digital World: Why AI Is "Physically Blind"

Current generative models are, in essence, "statisticians of pixels." From massive video data they learn that "when a bottle falls, the next frames usually show shattered glass." But this is only visual correlation.

> Annotation: Visual Correlation > Imagine a blind person simulating a soccer match from radio commentary alone. They know "a goal" is usually followed by "cheering," but they don't understand a ball's mass, drag, or conservation laws. When the signal gets fuzzy, their simulated "match" may feature balls teleporting mid-air.

Traditional world models encode the world as a single latent vector $$z$$ . But $$z$$ is a black box: it cannot distinguish an object's "position" from its "velocity." As a result, when simulating long-horizon motion, energy inexplicably leaks or explodes, and the system descends into chaos.

2. Phase-Space Reconstruction: Giving Digital Souls "Mass"

The first move of the proposed Hamiltonian World Model (HWM) is to completely dismantle that black-box latent space by introducing the core physics concept of Phase Space.

> Annotation: Phase Space > In classical mechanics, describing a system's state fully requires not just "where it is" but "where it's heading." Phase space is the mathematical space spanned by generalized coordinates (q) and generalized momenta (p); each point determines the system's unique future.

In HWM, the network no longer outputs a vague $$z$$ . The representation is forcibly decomposed into:

$$q$$ (Generalized Coordinates): shape, position, and pose of objects.
$$p$$ (Generalized Momenta): motion state, inertia, and energy reserves.

With this "hard constraint," every brick and drop of water in the digital world acquires a mathematical "soul-mass" instead of being illusory pixels.

3. The Hamiltonian Engine: Driving Reality with a Symphony of Gradients

HWM's core is a physics-constrained "evolution engine." Instead of relying on a black-box Transformer to predict the next frame, it runs a rigorous set of ODEs.

Core Evolution Equation

The model's dynamics follow this controlled Hamiltonian system:

\dot{q} = \frac{\partial H}{\partial p}, \quad \dot{p} = -\frac{\partial H}{\partial q} + \text{Control} + \text{Dissipation} + \text{Residual}

> Annotation: Deep Dive into the Formula > - $$H(q,p)$$ (Hamiltonian): the system's total energy function. The model learns an "Energy Landscape" and uses gradients to decide how objects naturally move. > - Control: the AI agent's actions. When a robotic arm applies force, it injects work into the system through momentum $$p$$ . > - Dissipation: the hardest part of physics to simulate—friction and drag. HWM models normal energy loss explicitly through this term. > - Residual: scientific rigor at work—capturing small perturbations and nonlinear noise that classical mechanics cannot fully explain.

The engine's magic: even without external commands, the system stays physically consistent thanks to the intrinsic logic of $$H(q,p)$$ . Objects don't accelerate without cause, and they don't vanish inexplicably.

4. A Stability Revolution: "Dimensionality-Reduction Strike" in Comparative Experiments

Per the paper's reported experiments, HWM shows striking physical resilience in robot control and long-horizon video prediction:

The post highlights a demo: a virtual robot driven entirely by HWM performing complex grasping. Baseline models frequently produce the "hand passes through cup" tragedy, whereas in HWM the physical gradient from $\frac{\partial H}{\partial q}$ makes inter-object repulsion and contact logic natural and robust.

5. Closing Thoughts: The Physical Foundation on the Road to AGI

If LLMs gave AI "human language," and multimodal models gave AI "human eyes," then HWM aims to give AI a third thing—"an intuition for the ground beneath us."

We cannot expect an AI that doesn't understand gravity to safely operate lab equipment or drive a car carrying passengers. The Tsinghua team's work suggests: the endpoint of evolution often hides in the starting point of fundamental science. The moment Newton, Lagrange, and Hamilton are invited into neural networks, code begins its true "physical awakening."

Future AI, the author argues, will be less a dreaming illusionist and more a physics-literate, genuinely empiricist silicon creation.

References

1. arXiv:2605.00412: *Physically Native World Models: A Hamiltonian Perspective on Generative World Modeling* (2026). 2. Hamiltonian Mechanics Heritage: *Analytical Mechanics and its Applications in Modern Control Theory*. 3. SORA Technical Report (Revisited): *Video Generation as World Simulators (2024/25 Heritage Review)*. 4. JEPA Evolution: *Non-Generative Predictive Architectures in Embodied Environments*. 5. Differentiable Physics: *Integrating ODE Solvers into Latent Neural Dynamics*.

*Note: This is a translation of a community post; experimental figures are cited from the referenced paper as reported by the author and have not been independently verified.*