LeHami: Hamiltonian physics so JEPA world models can predict long-term motion

By Turing Post · Sat, 24 Oct 2026 15:05:01 +0000.

The email introduces LeHami, a variant of Yann LeCun's JEPA (Joint Embedding Predictive Architecture) inspired by Hamiltonian mechanics. According to the opening summary (TL;DR), LeHami is a JEPA-style world model that uses Hamiltonian mechanics to avoid certain kinds of collapse during long-horizon latent predictions. It represents states with variables analogous to position and momentum, learns an energy-like function and updates them using a leapfrog-type symplectic integrator. Experiments with simulated pendulums show promising gains in prediction accuracy and compute efficiency, although planning results are mixed and the approach has not yet been demonstrated on complex real-world dynamics.

The article notes that the JEPA architecture stands out for predicting abstract representations of what is missing or what comes next, rather than generating images pixel by pixel. LeHami is developed by Yann LeCun, Romina Yalovetzky and Randall Balestriero. The 'Le' prefix comes from LeJEPA, another version of JEPA, and 'Hami' indicates that it builds on Hamiltonian physics. The idea is to keep long predictions from gradually losing the distinction between different states, so LeHami changes how prediction works by building a geometric constraint taken from Hamiltonian mechanics directly into the process.

The email lays out the outline of the full analysis: why JEPA needs better long-horizon predictions, why Hamiltonian mechanics, what it brings to LeHami, how it works step by step, what the experiments showed, what its limitations are and why it matters for JEPA world models. Only the first sections are covered in this email; the rest is reserved for the full paid guide.

On the underlying problem, the article explains that in a long rollout each predicted representation becomes the input for the next prediction. If the predictor slightly compresses the range of possible states at each step, that compression accumulates: clearly distinct initial states end up represented in increasingly similar ways. Even if the encoder learned good representations during training, the predictor risks collapsing over time. With LeHami, the researchers aim to rethink how those representations evolve, borrowing structure from Hamiltonian mechanics, a framework for describing motion developed nearly 200 years ago.

As for the physics, William Rowan Hamilton presented his view of mechanics in two major papers published in 1834 and 1835, extending mathematical methods he had used in optics. The goal was a more general and systematic way of calculating motion, including complex systems such as interacting planets. It was not a new set of physical laws but a reformulation of existing mechanics. Classical Lagrangian mechanics describes a system through coordinates and velocities; in typical mechanical systems, the Lagrangian is kinetic energy minus potential energy. Hamiltonian mechanics swaps velocities for momenta: the coordinates q and momenta p together describe a point in phase space, and its central function, the Hamiltonian H, is usually the total energy (kinetic plus potential). The gradients of H determine how q and p change over time. The email illustrates this with a pendulum. The advantage is the simplicity of the equations: instead of second-order equations for the coordinates, you get pairs of first-order equations for coordinates and momenta, and the geometry of the evolution becomes more explicit.

Why it matters for LeHami: a standard JEPA does not require Hamiltonian mechanics, but the authors wanted a predictor that would not gradually compress a region of latent states into a smaller volume as predictions feed back into themselves. The Hamiltonian formulation makes it possible to build that constraint into the update: its dynamics are symplectic and preserve the geometry and volume of phase space; its first-order equations directly update the paired state q and p; and splitting the learned Hamiltonian into K(p) and V(q, u) allows an explicit leapfrog step, with no iterative solver, that preserves the symplectic structure. That is why they chose Hamilton over Lagrange: it offers a computationally simple path to the exact guarantee they need. LeHami learns K and V in latent space rather than computing actual physical energies.

The email closes with a promotion of the full guide for Premium subscribers (20% off until October 25), a link to a video on the evolution of JEPA and a reference to the previous episode on how world models work, from Dreamer and JEPA to Waymo and Atlas. Details of the experiments and limitations beyond the TL;DR are not included in this email.