Solving the Rubik's Cube Under Strict 3-Face Partial Observability via Recurrent Attention Feedback

• 🧊 Live Interactive 3D & 2D Simulator (Hugging Face Space): https://huggingface.co/spaces/sumitk/rubik-cube-3face-sim
• 🤗 Trained Checkpoints & Model Repository (Hugging Face Hub): https://huggingface.co/sumitk/rubik-cube-3face-recurrent-ai
• 📄 Full Technical White Paper: WHITEPAPER.md

An attention-based neural network trained from scratch to solve a $3\times 3\times 3$ Rubik's cube in closed loop under strict 3-face partial observability:

• 3-Face Partial View (U, F, R = 27 stickers): At every step $t$, the agent only sees the 27 stickers of the Top (U), Front (F), and Right (R) faces. The Back (B), Left (L), and Down (D) faces are completely occluded.
• View Replacement (POMDP): Each step's 27-sticker view replaces the previous view. Whole-cube rotations (x, y, z) bring occluded faces into view while pushing previously visible faces out of view.
• Recurrent Continuous Attention Feedback (RecurrentCubeLM, 5.35M params): Maintains 16 gated continuous memory vectors across time, paired with a cross-attention next-view world-model head (predict_next_view).
• Zero Search & Zero Kociemba at Inference: The neural network outputs raw face turns (U, R, F, D, L, B), whole-cube rotations (x, y, z), and <done> in a greedy closed loop with zero external search or state scaffolding.

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Key Benchmark Results (256 Episodes / Task, 3-Face View Only)

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Architecture (RecurrentCubeLM)

flowchart TB
  subgraph inputs [76 Input Tokens at Step t - Bidirectional Full Self-Attention]
    direction LR
    M_in["[0..15] Memory Input<br/>RMSNorm(M_{t-1}) + mem_pos_emb<br/>(16 x 256)"]
    V_in["[16..42] Visible 3-Face View<br/>tok_emb(o_t) + view_slot_emb<br/>(27 x 256)"]
    A_in["[43..58] Recent Action Window<br/>tok_emb(a_{t-16:t-1}) + act_pos_emb<br/>(16 x 256)"]
    Q_act["[59] Action Query<br/>act_query<br/>(1 x 256)"]
    Q_wr["[60..75] Memory Write Queries<br/>write_queries<br/>(16 x 256)"]
  end

  inputs --> Trunk["6x Bidirectional Transformer Blocks<br/>(d_model = 256, n_heads = 4, d_ff = 688, SwiGLU, RMSNorm)"]

  Trunk --> H_act["h_act = h[59]"]
  Trunk --> H_wr["h_write = h[60..75]"]

  H_act --> HeadAct["Action Head: Linear(256 -> 64)<br/>Logits over 18 Moves, 9 Rotations, <done>"]
  H_wr --> MemUpdate["Gated Residual Memory Update<br/>M_t = g * M_{t-1} + (1 - g) * cand<br/>(16 x 256 Continuous State)"]
  MemUpdate --> NextViewHead["Cross-Attention Next-View Head<br/>Predicts Next 27 Visible Stickers o_{t+1} (27 x 6)"]

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Quick Start

1. Install Dependencies & Run Verification Suite

python -m venv .venv
.\.venv\Scripts\pip install -r requirements.txt
.\.venv\Scripts\python.exe -m pytest -q

2. Launch the Interactive 3D & 2D Web Simulator

Visualizes the 3-face partial view (U/F/R) alongside the 6-face ground truth, with smooth 3D whole-cube rotation (x, y, z) and face-twist animations, live 16-slot memory heatmap, mental next-view prediction, and memory-wiping ablation toggle:

.\.venv\Scripts\python.exe web_sim.py --port 8765
# Open http://127.0.0.1:8765 in your browser

3. Evaluate Checkpoints in Closed Loop

# Standard closed-loop evaluation
.\.venv\Scripts\python.exe eval.py --ckpt runs/rnn_v3/final.pt --n 256

# Causal memory-wiping ablation (--reset_mem)
.\.venv\Scripts\python.exe eval.py --ckpt runs/rnn_v3/final.pt --n 256 --reset_mem

4. Generate Trajectories & Train from Scratch

# 1. Generate active-slot CFOP trajectories (builds PDB caches automatically on first run)
.\.venv\Scripts\python.exe -m rubik.data.gen --out data_rnn3 --stage all --n 60000 --workers 8 --p_scratch 0.0 --p_rot 0.0 --inspect x_z2 --stage_glance --f2l_rotate --canonical_start

# 2. Pretrain 3-face next-view world model on random move+rotation walks
.\.venv\Scripts\python.exe pretrain_wm.py --out runs/wm_pretrain --iters 1500 --batch 256 --seq_len 24 --lr 5e-4

# 3. Train Recurrent v3 solver with W=64 full BPTT + next-view loss + online DAgger
.\.venv\Scripts\python.exe train_rnn_v2.py --data data_rnn3 --out runs/rnn_v3 --init runs/wm_pretrain/wm_final.pt --bptt 64 --batch 192 --lr 4e-4 --vp_weight 0.25 --short_iters 400 --all_iters 1600 --dagger_every 4 --dagger_batch 64 --f2l_rotate --canonical_start

See WHITEPAPER.md for the complete mathematical formulation, all six experimental iterations, root-cause analyses of negative results, and full command-line reference.