A10 · 真实CTR：线性与FM交叉的预算对照
先修：公用31–34；A09（19–20章）。
证据类型：真实采样曝光的训练与select诊断。本章不声称工业系统复现或线上收益。
学习顺序：先预测 → 只改一个变量 → 运行 → 解释结果。
问题与输入输出契约
FM logit=b+Σw_i+Σ_{i<j}<v_i,v_j>；复用推荐课程fm_interaction的向量恒等式，避免复制算法。相同26个类别字段、train-only top64词表、相同训练批次/8 epochs/Adam；唯一结构变量是是否添加4维交互因子，参数量不同明确报告。取原固定Criteo分片前10k真实曝光，不新增数据；仅select开发诊断，不用audit挑模型，不替换正式latest。
运行前预测：本章只改变的变量会使哪一项结果变化？哪些不变量必须保持？
PYTHON · 01
from pathlib import Path
import sys
root=Path.cwd()
if not (root/'reclab').exists(): root=root.parent
if str(root) not in sys.path: sys.path.insert(0,str(root))
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from reclab import ads_curriculum as ac运行单变量对照
本章读取已保存的一次真实训练；显式重训见源码函数，避免每次开课自动修改模型。
PYTHON · 02
from reclab.paths import ROOT,read_json
summary=read_json(ROOT/'results/2026-10-30-ads-curriculum/fm.json')
print('run',summary['run_id']);display(pd.DataFrame([{'method':r['method'],'parameters':r['parameters'],**{k:r['select'][k] for k in ('n','auc','logloss','brier')}} for r in summary['result']['rows']]))
for row in summary['result']['rows']: plt.plot(row['train_loss'],label=row['method'])
plt.xlabel('epoch');plt.ylabel('train logloss');plt.legend();plt.show()
from reclab.learning.networks import fm_interaction,fm_explicit
import torch
x=torch.randn(3,4,5);assert torch.allclose(fm_interaction(x),fm_explicit(x),atol=1e-5)Notebook 保存的输出 · 本页未执行
run 20261030T143314-b0538124
| method | parameters | n | auc | logloss | brier | |
|---|---|---|---|---|---|---|
| 0 | linear | 1691 | 1534 | 0.607724 | 0.132267 | 0.027532 |
| 1 | fm | 8451 | 1534 | 0.558951 | 0.178256 | 0.031998 |
<Figure size 640x480 with 1 Axes>
解释与局限
训练损失下降只说明拟合训练集，select更好也不是正式audit改善。单种子、较小词表、只用类别字段是刻意控制预算的限制。保存结果来自一次实际训练；重训需显式调用ctr_interaction_workshop，新建registry记录并保留负结果。
本次实际输出：线性select logloss=0.1323、FM=0.1783；FM训练loss降得更低而select更差，显示这个小预算配置发生过拟合。保留负结果，不据此否定一般FM或证明真实线上表现。
查看源码，再做练习
先预测FM为何可能过拟合；在新的workshop版本只改factor维度并记录参数量，不把改过多次的select当独立测试。
PYTHON · 03
import inspect
print(inspect.getsource(ac.ctr_interaction_workshop))Notebook 保存的输出 · 本页未执行
def ctr_interaction_workshop(rows=10000, epochs=8):
"""Real sampled Criteo categorical LR versus FM; shared recommendation FM operator."""
import torch
import time
from torch import nn
from .learning.networks import fm_interaction
from .ads import load_data, split_groups, vocabulary, encode, verify_sources, CAT
from .probability import evaluate
from .experiments import begin, finish
from .paths import ROOT, read_json, atomic_json
if rows!=10000 or epochs!=8: raise ValueError('Frozen teaching budget: 10k rows, 8 epochs')
folder=begin('ads',{'workshop':'categorical_fm','rows':rows,'epochs':epochs,'seed':42,'evaluation':'select only'},read_json(ROOT/'docs/ads_sources.json'))
try:
verify_sources();frame,_=load_data(rows);masks,_=split_groups(frame)
vocab=vocabulary(frame.loc[masks['train']],64)
x=encode(frame,vocab)[:,13:].astype(np.int64)+np.arange(len(CAT))*65
y=frame.label.to_numpy(dtype=np.float32)
xt=torch.tensor(x);yt=torch.tensor(y)
tr=torch.tensor(np.flatnonzero(masks['train'])); se=torch.tensor(np.flatnonzero(masks['select']))
class Response(nn.Module):
def __init__(self, interaction):
super().__init__();self.linear=nn.Embedding(26*65,1);self.bias=nn.Parameter(torch.zeros(()));self.interaction=interaction
nn.init.zeros_(self.linear.weight)
if interaction: self.factors=nn.Embedding(26*65,4);nn.init.normal_(self.factors.weight,std=.01)
def forward(self,x):
logit=self.linear(x).sum((1,2))+self.bias
return logit+fm_interaction(self.factors(x)) if self.interaction else logit
results=[]; old_threads=torch.get_num_threads();torch.set_num_threads(2)
try:
for interaction in (False,True):
started=time.perf_counter()
torch.manual_seed(42);model=Response(interaction);optimizer=torch.optim.Adam(model.parameters(),lr=.02,weight_decay=1e-5)
generator=torch.Generator().manual_seed(42);curve=[]
for _ in range(epochs):
order=tr[torch.randperm(len(tr),generator=generator)]
for batch in order.split(256):
optimizer.zero_grad();loss=nn.functional.binary_cross_entropy_with_logits(model(xt[batch]),yt[batch]);loss.backward();optimizer.step()
with torch.no_grad():curve.append(float(nn.functional.binary_cross_entropy_with_logits(model(xt[tr]),yt[tr])))
with torch.no_grad():p=model(xt[se]).sigmoid().numpy()
name='fm' if interaction else 'linear'
torch.save(model.state_dict(),folder/(name+'.pt'))
np.savez_compressed(folder/(name+'.npz'),select_probability=p,select_row=se.numpy(),label=y[se.numpy()])
results.append(dict(method=name,features=26,fit_seconds=time.perf_counter()-started,parameters=sum(p.numel() for p in model.parameters()),train_loss=curve,select=evaluate(y[se.numpy()],p)))
finally: torch.set_num_threads(old_threads)
atomic_json(folder/'vocabulary.json',vocab)
result=dict(kind='workshop',rows=results,shapes={'raw':[rows,39],'categorical':[rows,26],'train':len(tr),'select':len(se)},
changed_variable='FM pair interactions; extra factor parameters explicitly counted; same rows/order/epochs/optimizer',
scope='Real sampled Criteo categorical-only select diagnostic, not independent audit or population CTR.',
limits='Capped train vocab, small prefix, one seed, numeric features omitted equally; no production selection or revenue claim.')
finish(folder,result);return folder.name,result
except Exception as exc:
receipt=read_json(folder/'receipt.json');receipt.update(state='failed',error=str(exc));atomic_json(folder/'receipt.json',receipt);raise
来源与下一步
A-RTB 39–69页，FM在58页；复用Lab推荐06机制。这是Lab自行设计的小实验，不复制讲义全文。
GitHub中文单章 · 作者RTB讲义。中文PPT不是现代广告工程全套课；不将历史平台机制描述当作当前市场事实。
完成练习后回到广告学习路径，继续下一语义单元。