用可微分方法实现算术算法的精确学习，训练后能无误差处理超长输入。
Exact Learning of Arithmetic with Differentiable Agents
- 设计可微有限状态转换器，支持常精度、常时间生成与端到端可微训练。
- 在极小数据集上训练后，算术运算可零误差推广至训练长度千倍以上的输入。
- 适合研究可微分算法学习、符号推理或需要精确计算的AI系统设计者。
我们探索了基于梯度的方法实现精确算法学习的可能性，并提出一种可微分框架，可在算术任务中实现强长度泛化。该方法核心是可微有限状态转换器（DFSTs），这是一类图灵完备模型，避免了先前架构的缺陷，具备常精度、常时间生成能力，且支持端到端对数并行可微训练。通过专家代理生成的策略轨迹观察，我们训练DFSTs完成二进制与十进制加法和乘法。令人惊讶的是，模型在极小数据集上训练后，能无错误地推广到比训练样本长数千倍的输入。这些结果表明，在结构化中间监督下训练可微代理，可能为算法技能的精确梯度学习开辟道路。代码已公开于https://github.com/dngfra/differentiable-exact-algorithmic-learner.git。
原文摘要 · Abstract (English)
We explore the possibility of exact algorithmic learning with gradient-based methods and introduce a differentiable framework capable of strong length generalization on arithmetic tasks. Our approach centers on Differentiable Finite-State Transducers (DFSTs), a Turing-complete model family that avoids the pitfalls of prior architectures by enabling constant-precision, constant-time generation, and end-to-end log-parallel differentiable training. Leveraging policy-trajectory observations from expert agents, we train DFSTs to perform binary and decimal addition and multiplication. Remarkably, models trained on tiny datasets generalize without error to inputs thousands of times longer than the training examples. These results show that training differentiable agents on structured intermediate supervision could pave the way towards exact gradient-based learning of algorithmic skills. Code available at \href{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}{https://github.com/dngfra/differentiable-exact-algorithmic-learner.git}.
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。