Reversal Blessing: Thinking Backward May Outpace Thinking Forward in Multi-choice Questions
This model card accompanies the research paper, Reversal Blessing: Thinking Backward May Outpace Thinking Forward in Multi-choice Questions.
Here we release 4 models' checkpoints trained with simulation data described in out paper Section 4. Please follow our github README to download and evaluate these models.
Results of the Controlled Simulation Study of 4-Digits Multiplication
| Forward X | Reverse X | |||||
|---|---|---|---|---|---|---|
| L2R | R2L(m,n) | R2L(m) | R2L | L2R(m,n) | L2R(n) | |
| Test Accuracy (%) | 99.81±0.15 | 59.71±1.99 | 60.93±0.88 | 100±0 | 97.82±0.35 | 99.85±0.10 |
| Train Accuracy (%) | 99.76±0.15 | 59.03±1.66 | 61.22±1.12 | 100±0 | 97.90±0.42 | 99.98±0.04 |
| Test Cond. Ent. (nats) | 0.06 | 1.18 | 0.08 | 0 | 0.84 | 0.01 |
| Train Cond. Ent. (nats) | 0.06 | 1.17 | 0.08 | 0 | 0.83 | 0.01 |
| Theo. Cond. Ent. (nats) | 0 | 1.49 | 0 | 0 | 1.49 | 0 |
| Training loss | 0.86 | 0.94 | 0.94 | 0.86 | 0.94 | 0.94 |
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