用自监督方法让模型学会逆向简化复杂公式，效果远超旧方法。
Learning to Unscramble: Simplifying Symbolic Expressions via Self-Supervised Oracle Trajectories
- 通过打乱公式并记录还原路径，生成带目标与步骤的训练数据。
- 在高能物理问题上达到接近100%的简化成功率，可处理超200项的表达式。
- 适合需要精确符号运算的科研人员，尤其在粒子物理领域实用。
我们提出一种新的自监督机器学习方法，用于简化复杂的数学表达式。通过打乱简单表达式并记录其逆操作，生成包含目标状态和明确路径的“最优轨迹”作为训练数据。基于排列等变性的Transformer策略网络，在此数据上逐步训练，以预测给定输入表达式应采取的最优操作。我们在高能物理两个问题上验证该方法：双对数函数约简和旋量-螺旋度散射振幅简化。在两种情况下，训练后的策略网络在广泛难度范围内均达到接近完美的求解率，显著优于以往基于强化学习和端到端回归的方法。结合对比分组与束搜索后，模型在杨-米尔斯理论中五点胶子树图振幅的代表性样本上实现100%完全简化率，包括初始项超过200项的表达式。
原文摘要 · Abstract (English)
We present a new self-supervised machine learning approach for symbolic simplification of complex mathematical expressions. Training data is generated by scrambling simple expressions and recording the inverse operations, creating oracle trajectories that provide both goal states and explicit paths to reach them. A permutation-equivariant, transformer-based policy network is then trained on this data step-wise to predict the oracle action given the input expression. We demonstrate this approach on two problems in high-energy physics: dilogarithm reduction and spinor-helicity scattering amplitude simplification. In both cases, our trained policy network achieves near perfect solve rates across a wide range of difficulty levels, substantially outperforming prior approaches based on reinforcement learning and end-to-end regression. When combined with contrastive grouping and beam search, our model achieves a 100\% full simplification rate on a representative selection of 5-point gluon tree-level amplitudes in Yang-Mills theory, including expressions with over 200 initial terms.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。