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hellojais/
lewm-billiards

Name: lewm-billiards
Availability: InStock

auxiliary-supervision

2603.19312

mit

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LeWM Billiards — Trained World Model

Author: Santosh Jaiswal (@hellojais)
Base architecture: LeWM by Lucas Maes et al. (2025)
Training data: hellojais/billiards-worldmodel
Code: hellojais/le-wm

Model variants

File	embed_dim	Input	λ_aux	Best epoch	val/pred_loss	Notes
`lewm_epoch_8_object.ckpt`	192	3-ch	—	8	0.00946	Original full-size transformer
`lewm_small_epoch_8_object.ckpt`	32	3-ch	—	8	0.00280	Transformer baseline
`lewm_mamba_best_object.ckpt`	32	3-ch	—	best	0.00340	Mamba predictor
`lewm_framestacked_best_object.ckpt`	32	9-ch	—	7	0.00594	Frame-stacking; JEPA eviction occurs
`lewm_auxloss_full_best_object.ckpt`	32	9-ch	0.1	7	0.00105	Aux state supervision; eviction fixed; best model

What this model learned

Trained on 4,000 episodes (971,321 frames) of 2D billiards gameplay. The model learned to predict future frame embeddings from current embeddings and actions — encoding billiards physics purely from pixels.

Probe results (linear probe on encoder representations; 192-dim = pre-projector CLS token, 32-dim = post-projector):

Model	Rep dim	pos R²	vel R²
`lewm_small`	32	0.983	0.296
`lewm_mamba`	32	0.983	0.297
`lewm_framestacked`	192	0.446 ⚠️	0.138
`lewm_framestacked`	32	0.599	0.417
`lewm_auxloss_full`	192	0.999 ✅	0.947 ✅
`lewm_auxloss_full`	32	0.982	0.554

Key finding: Frame-stacking causes JEPA representational eviction — the ViT encoder stops encoding ball position (pos R²=0.446 at 192-dim) under optical-flow pressure. Adding a lightweight auxiliary state supervision head (λ=0.1) fully recovers position encoding (pos R²=0.999) and achieves the best prediction loss across all variants.

Planning results

Approach	Same-episode	Novel cross-episode
Pure JEPA embedding CEM	❌ FAIL	❌ FAIL
State-based hybrid CEM	✅ SUCCESS (9 steps)	✅ SUCCESS (13 steps)

Pure JEPA planning failed due to uniform embedding geometry in this visually simple domain. See FINDINGS.md for complete analysis.

Usage

python

# Load checkpoint
import stable_worldmodel as swm
import torch

device = torch.device("mps")  # or "cuda" or "cpu"

# Load the small model (recommended)
checkpoint = torch.load(
    "lewm_small_epoch_8_object.ckpt", 
    map_location=device
)

Training setup

Hardware: Apple M5 Max (64GB unified memory)
Backend: PyTorch MPS
Training time: ~10–11 hours per run (10 epochs); 4 model variants trained
Framework: PyTorch Lightning + stable-worldmodel

Credits

Original LeWM architecture by: Lucas Maes, Quentin Leroux, Gauthier Gidel, Glen Berseth
Mila / McGill University (2025)
arXiv:2603.19312

hellojais/lewm-billiards