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🦤 LeWorldModel: Learning Physics from Pixels — Stable World Models with Just Two Losses World models: 1️⃣ DINO-WM: pretrained ViT encoder (from ImageNet) → features → predictor. But encoder is frozen, so no end-to-end learning. Its “visual genetics” are tuned for coarse classification (cats vs dogs), not physics: hard to resolve mm-level changes (e.g., 2 mm block motion). A powerful predictor on top of a “myopic” encoder = blind physical reasoning. 2️⃣ PLDM: end-to-end, but unstable and collapse-prone. Rely on reward as prediction target, so it only works in environments with explicit rewards (e.g., games). 3️⃣ JEPA (Joint Embedding Predictive Architecture): predict next latent instead of pixels. Two hard problems: collapse (encoder → constant vector, e.g., all zeros) achieving pixel-level + end-to-end + stable jointly 💡 LeWM solves: 👉 JEPA that trains stably end-to-end from raw pixels 👉 Single hyperparameter λ: next-embedding prediction SIGReg (Gaussian regularization) 🧠 #1: true end-to-end No frozen encoder. Perception + dynamics co-evolve → representation aligned with fine-grained physics, not ImageNet bias. 🧠 #2: “only” one hyperparameter PLDM needs ~6. LeWM needs 1 (λ) → weight of SIGReg. Plug-and-play, stable. ⚠️ Collapse problem Encoder could map all inputs → same vector → trivial prediction → zero loss → useless model. 🧩 SIGReg (Gaussian Integral Signature Regularization) Core: prevent collapse via distribution constraints. Sample 1024 random directions Project embeddings → 1024 1D “shadows” Each must pass Epps–Pulley test (≈ standard normal) Loss pushes test statistic → 0 Any failed projection ⇒ penalty Why it works: Cramér–Wold theorem → a high-dim distribution is determined by its 1D projections. 👉 Enforcing Gaussianity across 1D projections precludes degenerate collapse under projection constraints 🧪 Physical probing Train in PushT (push block to target), then: Linear probe recovers: block position, angle, end-effector 👉 physics is linearly decodable 🚨 Teleport block (physically impossible): embedding anomaly spikes sharply 👉 model internalizes constraint: objects cannot teleport 👉 not inferred from pixel surface features, but encoded as latent constraints 📈 Temporal straightness No smoothness loss, yet trajectories in latent space are ~straight lines 👉 no prior, purely from “predict next embedding” 👉 implies physically consistent motion, not blurry interpolation ⚡ Performance Planning: 0.98s vs 47s (DINO-WM) Success: 96% vs 78% (PLDM) Why faster? DINO-WM: frozen encoder → info loss → extra online passes LeWM: end-to-end → representation already task-aligned 👉 0.98s = fast to handle dynamic obstacles & real-time control ⚠️ Limitations ~15M params (“ant-scale”) → fails on OGBench-Cube (complex physics) not yet tested on real robots 🔥LeWM shows: 👉 JEPA + SIGReg = stable world models 👉 raw pixels → physics-aware latent space 👉 minimal design (2 losses, 1 hyperparameter) Next step: scale + real-world deployment 🤖