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Contrastive Representations for Temporal Reasoning
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Proposes CRTR, a temporal contrastive learning method that samples in-trajectory negatives so representations ignore static context, enabling search-free planning on combinatorial puzzles such as Rubik's Cube and Sokoban.
Problem
Standard temporal contrastive learning yields representations that overfit to static, instance-specific context (e.g., Sokoban wall layouts) rather than temporal structure, limiting its usefulness for planning and search in combinatorial reasoning tasks.
Approach
Repeat trajectories within a batch (repetition factor) so that some negative pairs come from the same trajectory at different times; this forces the encoder to discard context features shared within a trajectory, with a theoretical link to lowering I(X_+;C) in the InfoNCE objective.
Key results
- On Rubik's Cube, CRTR without search solves about 50% of configurations in under 300 moves and can solve all instances within 6000 moves.
- CRTR achieves the highest or near-highest success rates across environments, with largest gains over CRL in Sokoban and Digit Jumper.
- Without search, CRTR's average Rubik's Cube solution length is 448.7 moves versus 1830.3 for the contrastive baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use in-trajectory negatives in contrastive training (CRTR instead of CRL) | CRTR representations with A* planning · Rubik's Cube | success rate: 0.54 vs 0.63; 0.50 vs 0.62; 0.44 vs 0.59; 0.40 vs 0.54; 0.30 vs 0.33 | Helped |
| Use in-trajectory negatives in contrastive training (CRTR instead of CRL) | CRTR representations with A* planning · Rubik's Cube | average solution length: 62.96 vs 56.76; 49.88 vs 46.35; 41.94 vs 38.42; 36.11 vs 32.84; 31.77 vs 29.16 | Helped |
| Use CRTR representations rather than contrastive baseline representations | Greedy planning without search · Rubik's Cube | average solution length: 1830.3 -> 448.7 | Helped |
| Use CRTR representations rather than contrastive baseline representations | Greedy planning without search · 15-Puzzle | average solution length: 119.5 -> 82.4 | Helped |
| Increase the repetition factor above 2 (ablation) | CRTR · Sokoban | success rate | Hurt |
| Increase the repetition factor excessively (ablation) | CRTR · Other tested environments | success rate | Hurt |
| Use repetition factor R=2 rather than the tested alternatives (ablation) | CRTR · All evaluated environments | success rate | Helped |
| Add unanchored in-trajectory hard negatives to the contrastive loss (ablation) | CRTR-style contrastive training · Sokoban | success rate | Hurt |
| Normalize the unanchored in-trajectory negative scores (ablation) | Contrastive training · Rubik's Cube scrambled 10 times | success rate | Helped |
| Use CRTR sampling rather than alternative negative-sampling strategies (ablation) | Contrastive representation learning · Rubik's Cube scrambled 15 and 20 times | success rate | Helped |
| Use symmetric contrastive loss instead of backward loss (ablation) | Contrastive representation learning · Rubik's Cube | success rate | Hurt |
| Combine in-trajectory negatives with symmetric loss (ablation) | CRTR · Rubik's Cube | success rate | Hurt |
Surprising findings
- Using search (BestFS) on Rubik's Cube decreases the fraction of solved configurations compared with greedy no-search planning.
- Standard contrastive learning reaches near-perfect classification accuracy almost immediately on Sokoban and Digit Jumper by exploiting static layout features.
Limitations
- Sokoban success rates remain low, attributed to dead-ends.
- No-search solutions are much longer than search-based ones (e.g., ~400 moves vs optimal 26 for Rubik's Cube).
- Only evaluated on deterministic, known-dynamics combinatorial problems.
Experimental setup
Datasets: Sokoban trajectories from prior work Rubik's Cube random-walk trajectories 15-Puzzle random-walk trajectories Lights Out random-walk trajectories Digit Jumper random paths D4RL Adroit robotic trajectories
Benchmarks: Sokoban Rubik's Cube 15-Puzzle Lights Out Digit Jumper
Metrics: success rate at fixed search budget Spearman rank correlation average solution length
Baselines: contrastive RL (CRL) supervised distance baseline DeepCubeA random-init representations
Builds on: contrastive reinforcement learning InfoNCE DeepCubeA best-first search
Closest papers by meaning
- Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making (ICML 2024 · similarity 0.86)
- Reasoning in Visual Navigation of End-to-end Trained Agents: A Dynamical Systems Approach (CVPR 2025 · similarity 0.84)
- Inference via Interpolation: Contrastive Representations Provably Enable Planning and Inference (NeurIPS 2024 · similarity 0.84)
- State Chrono Representation for Enhancing Generalization in Reinforcement Learning (NeurIPS 2024 · similarity 0.84)
- Unleashing Perception-Time Scaling to Multimodal Reasoning Models (ICLR 2026 · similarity 0.83)
- Towards Principled Representation Learning from Videos for Reinforcement Learning (ICLR 2024 · similarity 0.83)
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