用单一硬件友好算子构建可验证的神经符号网络,提升边缘设备部署效率。
Hardware-Efficient Neuro-Symbolic Networks with the Exp-Minus-Log Operator
- 引入EML算子构造统一的符号化网络结构,替代传统异构激活函数。
- 在FPGA/模拟电路上推理延迟可降低一个数量级,同时保持模型可解释性。
- 适合需形式化验证与低功耗部署的自动驾驶、工业控制等场景。
深度神经网络在回归与分类任务中表现卓越,但在安全关键、资源受限场景下仍存在两大缺陷:(i) 学习函数不透明,难以进行形式化验证;(ii) 依赖异构、库绑定的激活函数,导致边缘硬件延迟高、面积大。近期提出的Exp-Minus-Log(EML)Sheffer算子,由Odrzywolek(2026)证明,仅需常数1即可通过二叉树表达所有标准初等函数。本文将EML原语嵌入常规DNN架构,构建混合式DNN-EML模型:主干学习分布式表示,头部为深度受限、权值稀疏的EML树,其权重经截断后可生成闭式符号子表达式。推导前向计算公式,证明计算成本界,分析与多层感知机(MLPs)及物理信息神经网络(PINNs)相比的推理与训练加速性能,并量化其在FPGA/模拟部署中的权衡。研究表明,DNN-EML组合填补了文献空白:先前的神经符号与方程学习方法(EQL、KAN、AI-Feynman)使用异构基元集,未利用单一可硬件实现的Sheffer元素。综合评估表明,EML在训练阶段无明显加速优势,于通用CPU/GPU也难提速;但在定制化EML单元(如FPGA逻辑块或模拟电路)上,渐近延迟优势可达一个数量级,且同步提升可解释性与形式化验证可行性。
原文摘要 · Abstract (English)
Deep neural networks (DNNs) deliver state-of-the-art accuracy on regression and classification tasks, yet two structural deficits persistently obstruct their deployment in safety-critical, resource-constrained settings: (i) opacity of the learned function, which precludes formal verification, and (ii) reliance on heterogeneous, library-bound activation functions that inflate latency and silicon area on edge hardware. The recently introduced Exp-Minus-Log (EML) Sheffer operator, eml(x, y) = exp(x) - ln(y), was shown by Odrzywolek (2026) to be sufficient - together with the constant 1 - to express every standard elementary function as a binary tree of identical nodes. We propose to embed EML primitives inside conventional DNN architectures, yielding a hybrid DNN-EML model in which the trunk learns distributed representations and the head is a depth-bounded, weight-sparse EML tree whose snapped weights collapse to closed-form symbolic sub-expressions. We derive the forward equations, prove computational-cost bounds, analyse inference and training acceleration relative to multilayer perceptrons (MLPs) and physics-informed neural networks (PINNs), and quantify the trade-offs for FPGA/analog deployment. We argue that the DNN-EML pairing closes a literature gap: prior neuro-symbolic and equation-learner approaches (EQL, KAN, AI-Feynman) work with heterogeneous primitive sets and do not exploit a single hardware-realisable Sheffer element. A balanced assessment shows that EML is unlikely to accelerate training, and on commodity CPU/GPU it is also unlikely to accelerate inference; however, on a custom EML cell (FPGA logic block or analog circuit) the asymptotic latency advantage can reach an order of magnitude with simultaneous gain in interpretability and formal-verification tractability.
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