{"id":"7cTrUQbfZS","url":"https://pastebin.ca/7cTrUQbfZS","raw_url":"https://raw.anybin.ca/7cTrUQbfZS","visibility":"public","access":"public","created_at":1793951310323,"expires_at":1794556110323,"fetch_limit":null,"fetches_used":0,"reads_remaining":null,"size_bytes":669,"syntax_hint":null,"title":null,"filename":null,"change_note":null,"cipher":null,"cipher_meta":null,"parent_id":null,"root_id":"7cTrUQbfZS","version":1,"owner_id":null,"recipient_id":null,"body":"神经网络依靠非线性激活函数（GELU/ReLU等），可以自动从原始输入学习高阶非线性组合，自动拟合复杂映射关系，不需要人工构造多项式特征；传统线性回归模型本身是线性的，必须手动增加高次项才能拟合非线性。\n以 y=x^2+2x 为例，神经网络如何在不人工构造x^2的情况下学到这个非线性关系？\n网络通过多层线性变换+GELU非线性激活的叠加，等价构造出高阶多项式映射。输入x经过线性层加权求和，再经过GELU非线性变换，多层叠加后，网络参数自动学习出等价于 x^2+2x 的非线性映射，自动拟合目标函数。"}