圆形分类
The hidden layer can approximate a curved boundary.
浏览器真实训练本地教学实验，不调用外部 API。合成示例不能替代生产环境测量。
学习指南与本课目录
LEARNING CONTRACT理解 → 实现 → 研究
目标：解释本课机制、复现一个例子、测试一个失败案例。读完不自动代表掌握。
- 理解层：写明假设、形状/单位和一个反例。
- 实现层：复算数值例子并检查边界。
- 研究层：在匹配预算下比较一个替代方法。
02 · 预测与配置
技术场景说明、参数名称与参考答案目前为英文。
03 · 检查证据
方法与参考资料
Actual full-batch gradient descent in JavaScript. 2 inputs → tanh hidden layer → sigmoid. Binary cross-entropy; 100 synthetic training and 100 held-out samples from the same generator. Held-out accuracy is not real-world generalization.
Text / 原始公式
h=tanh(Wx+b); p=σ(vᵀh+c); L=−mean[y log p+(1−y)log(1−p)]
Training convergence on tiny synthetic data does not imply an LLM can train in the browser.
Dive into Deep Learning · multilayer perceptrons ↗练习题
neural-4 / 01What does “Circle classification” test?
The hidden layer can approximate a curved boundary.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 02Which computation produces the result in “Circle classification”?
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 03What is the baseline configuration for “Circle classification”?
{"rate":0.3,"hidden":16,"epochs":1000,"task":1,"seed":42}
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 04What numerical result should you check for “Circle classification”?
Run the seeded training lab and inspect the actual loss and accuracy; convergence is not assumed.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 05How would you run a controlled comparison for “Circle classification”?
Keep the supplied fixture and other settings fixed; change rate. Watch train loss, held-out accuracy and decision boundary over epochs.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 06What failure could invalidate a conclusion from “Circle classification”?
Training convergence on tiny synthetic data does not imply an LLM can train in the browser.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 07Is “Circle classification” a benchmark of a deployed language model?
No. Actual full-batch gradient descent in JavaScript. 2 inputs → tanh hidden layer → sigmoid. Binary cross-entropy; 100 synthetic training and 100 held-out samples from the same generator. Held-out accuracy is not real-world generalization.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 08Which evidence should you report for “Circle classification”?
Watch train loss, held-out accuracy and decision boundary over epochs. Export inputs, engine, result and method; distinguish synthetic fixtures from observed production data.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 09How can another researcher reproduce “Circle classification”?
Open neural-4, reset the preset, retain the exact inputs and run. Retain the seed, training epochs and all weights.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →neural-4 / 10What is the next validation step after “Circle classification”?
Training convergence on tiny synthetic data does not imply an LLM can train in the browser. Test the hypothesis on a representative held-out workload and document a baseline, success metric and stopping rule before claiming deployment readiness.
Original teaching answer / local derivation. Method reference: Dive into Deep Learning · multilayer perceptrons ↗
打开实验 →假设、参考实现与验收
XOR 标签恰在符号不同时为 1。稳定 logits BCE 为 max(z,0)−zy+log1p(exp(−|z|))，logit 梯度为 sigmoid(z)−y。训练及留出集是独立生成的合成样本，不是现实验证。
已复核引擎公式、场景预设及数值保护。固定种子的合成输入不是生产基准。
运行前：预测一个边界情况
The hidden layer can approximate a curved boundary.
提示：隔离假设
固定基线输入，只改变一个参数或边界；同时比较数值与声明单位。单例通过仅验证该样例。
最小可运行算例
将算例及所链接模块保存在同一目录。使用 Node.js 22 或更高版本，然后运行 node neural-4.mjs. 无需第三方运行依赖。
import {calculate,network} from './academy-core.mjs';
const params={
"rate": 0.3,
"hidden": 16,
"epochs": 1000,
"task": 1,
"seed": 42
};
const result=network(params).step(params.epochs);
console.log(result.metrics);测试与迁移
The hidden layer can approximate a curved boundary.
在下方笔记记录输入、代码版本、期望值和实测值；再构造违反上述假设的反例，解释原结论为何不再成立。
下载完整代码包（.tar.gz） · 完整参考代码与回归检查预测、检验与证据记录
展开答案前先预测一个结果；练习后记录差异和迁移测试。记录仅存本地，在不同语言版本间共用。
打开记录／导出／清除 →数学复核范围逐篇记录，不代表完成论文实证复现；可在笔记中记录疑似错误。 复核范围