# Python俄罗斯方块可操纵卷积分类 | 稀疏辨识算法 | 微分方程神经求解器

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Python | 组卷积 | 循环组 | 可视化 | 卷积核 | 泛化 | 紧群 | 表征 | 调和分析 | 不可约 | 傅里叶 | 深度概率 | 模型 | 高维 | 结构化 | 单变量 | 分类响应 | 离散 | 潜变量 | 伯努利 | 分布 | 流生成 | 微分方程 | 神经网络
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{% embed url="https://viadean.notion.site/Python-7382d54a70b64342a144f22ea15d76b9" %}

{% content-ref url="../zhi-dian-mi-jin-brief" %}
[zhi-dian-mi-jin-brief](../zhi-dian-mi-jin-brief)
{% endcontent-ref %}

### 🎯要点

🎯组卷积网络：实现循环组，可视化组动作，实现提升卷积核，MNIST 训练数据集训练组卷积网络的泛化能力 | 🎯可操控卷积网络：紧群的表征与调和分析，代码验证常规表征结果，不可约表征实现，傅里叶变换对群调和分析，实现可操控卷积网络 | 🎯深度概率模型：给定高维和结构化对单变量响应变量建模，实现分类响应模型，顺序响应模型、序列标记模型 | 🎯深度离散潜变量模型：使用FashionMNIST数据集，实现伯努利分布的乘积，实现均匀分类分布，测试先验分布，实现条件概率分布 | 🎯流生成模型 | 🎯超参数调优和多GPU编程 | 🎯贝叶斯神经网络实现 | 🎯非线性动力系统稀疏辨识算法 | 🎯偏微分方程神经网络求解器 | 🎯常微分方程神经网络求解器

🎯语言模型：[Python发票合同 | 解缠注意力语言模型](python-fa-piao-he-tong-jie-chan-zhu-yi-li-yu-yan-mo-xing)

🎯非线性系统：[Julia和Python蛛网图轨道图庞加莱截面曲面确定性非线性系统](../gong-cheng-engineering/julia-he-python-zhu-wang-tu-gui-dao-tu-pang-jia-lai-jie-mian-qu-mian-que-ding-xing-fei-xian-xing-xi)

### 🍇Python俄罗斯方块可操纵卷积分类

方块，有时也被称为四块、方块，骨牌或四格，是所有已知的俄罗斯方块游戏中使用的方块。它们有七种形状，都可以旋转然后放下。方块的面积都是四个方格。在某些俄罗斯方块游戏中，它们的颜色会有所不同。四格骨牌是由四个方块组成的多格骨牌。七个单面四格骨牌分别是 I、O、T、S、Z、J 和 L。

💦使用门实现模型拟合俄罗斯方块数据集

```python
 import logging
 ​
 import torch
 from torch_cluster import radius_graph
 from torch_geometric.data import Data, DataLoader
 from torch_scatter import scatter
 ​
 def tblock():
     pos = [
         [(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, 1, 0)],  
         [(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, -1, 0)],  
         [(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)],  
         [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3)],  
         [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0)],  
         [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0)],  
         [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 1)], 
         [(0, 0, 0), (1, 0, 0), (1, 1, 0), (2, 1, 0)],  
     ]
     pos = torch.tensor(pos, dtype=torch.get_default_dtype())
 ​
     labels = torch.tensor(
         [
             [+1, 0, 0, 0, 0, 0, 0],  
             [-1, 0, 0, 0, 0, 0, 0],  
             [0, 1, 0, 0, 0, 0, 0],  
             [0, 0, 1, 0, 0, 0, 0],  
             [0, 0, 0, 1, 0, 0, 0], 
             [0, 0, 0, 0, 1, 0, 0],  
             [0, 0, 0, 0, 0, 1, 0],  
             [0, 0, 0, 0, 0, 0, 1],  
         ],
         dtype=torch.get_default_dtype(),
     )
 ​
 ​
 def mean_std(name, x) -> None:
     print(f"{name} \t{x.mean():.1f} ± ({x.var(0).mean().sqrt():.1f}|{x.std():.1f})")
 ​
 ​
 class Convolution(torch.nn.Module):
     def __init__(self, irreps_in, irreps_sh, irreps_out, num_neighbors) -> None:
         super().__init__()
 ​
         self.num_neighbors = num_neighbors
 ​
         tp = FullyConnectedTensorProduct(
             irreps_in1=irreps_in,
             irreps_in2=irreps_sh,
             irreps_out=irreps_out,
             internal_weights=False,
             shared_weights=False,
         )
         self.fc = FullyConnectedNet([3, 256, tp.weight_numel], torch.relu)
         self.tp = tp
         self.irreps_out = self.tp.irreps_out
 ​
     def forward(self, node_features, edge_src, edge_dst, edge_attr, edge_scalars) -> torch.Tensor:
         weight = self.fc(edge_scalars)
         edge_features = self.tp(node_features[edge_src], edge_attr, weight)
         node_features = scatter(edge_features, edge_dst, dim=0).div(self.num_neighbors**0.5)
         return node_features
 ​
 ​
 class Network(torch.nn.Module):
     def __init__(self) -> None:
         super().__init__()
         self.num_neighbors = 3.8 
         self.irreps_sh = o3.Irreps.spherical_harmonics(3)
 ​
         irreps = self.irreps_sh
 ​
         # First layer with gate
         gate = Gate(
             "16x0e + 16x0o",
             [torch.relu, torch.abs], 
             "8x0e + 8x0o + 8x0e + 8x0o",
             [torch.relu, torch.tanh, torch.relu, torch.tanh],  # gates (scalars)
             "16x1o + 16x1e",  
         )
         self.conv = Convolution(irreps, self.irreps_sh, gate.irreps_in, self.num_neighbors)
         self.gate = gate
         irreps = self.gate.irreps_out
 ​
         # Final layer
         self.final = Convolution(irreps, self.irreps_sh, "0o + 6x0e", self.num_neighbors)
         self.irreps_out = self.final.irreps_out
 ​
  
```

💦多项式拟合俄罗斯方块数据集

```python
 import logging
 ​
 import torch
 from torch_cluster import radius_graph
 from torch_geometric.data import Data, DataLoader
 from torch_scatter import scatter
 ​
 ​
 ​
 def tblock():
     pos = [
         [(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, 1, 0)],  
         [(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, -1, 0)],  
         [(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)],  
         [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3)],  
         [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0)],  
         [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0)],  
         [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 1)],  
         [(0, 0, 0), (1, 0, 0), (1, 1, 0), (2, 1, 0)],  
     ]
     pos = torch.tensor(pos, dtype=torch.get_default_dtype())
 ​
     labels = torch.tensor(
         [
             [+1, 0, 0, 0, 0, 0, 0],  
             [-1, 0, 0, 0, 0, 0, 0],  
             [0, 1, 0, 0, 0, 0, 0],  
             [0, 0, 1, 0, 0, 0, 0],  
             [0, 0, 0, 1, 0, 0, 0], 
             [0, 0, 0, 0, 1, 0, 0],  
             [0, 0, 0, 0, 0, 1, 0],  
             [0, 0, 0, 0, 0, 0, 1],  
         ],
         dtype=torch.get_default_dtype(),
     )
 ​
     pos = torch.einsum("zij,zaj->zai", o3.rand_matrix(len(pos)), pos)
 ​
     dataset = [Data(pos=pos) for pos in pos]
     data = next(iter(DataLoader(dataset, batch_size=len(dataset))))
 ​
     return data, labels
 ​
 ​
 class InvariantPolynomial(torch.nn.Module):
     def __init__(self) -> None:
         super().__init__()
         self.irreps_sh: o3.Irreps = o3.Irreps.spherical_harmonics(3)
         irreps_mid = o3.Irreps("64x0e + 24x1e + 24x1o + 16x2e + 16x2o")
         irreps_out = o3.Irreps("0o + 6x0e")
 ​
         self.tp1 = FullyConnectedTensorProduct(
             irreps_in1=self.irreps_sh,
             irreps_in2=self.irreps_sh,
             irreps_out=irreps_mid,
         )
         self.tp2 = FullyConnectedTensorProduct(
             irreps_in1=irreps_mid,
             irreps_in2=self.irreps_sh,
             irreps_out=irreps_out,
         )
         self.irreps_out = self.tp2.irreps_out
 ​
     def forward(self, data) -> torch.Tensor:
         num_neighbors = 2  
         num_nodes = 4  # typical number of nodes
 ​
         edge_src, edge_dst = radius_graph(x=data.pos, r=1.1, batch=data.batch)  
         edge_vec = data.pos[edge_src] - data.pos[edge_dst]
         edge_sh = o3.spherical_harmonics(
             l=self.irreps_sh,
             x=edge_vec,
             normalize=False,  
             normalization="component",
         )
 ​
         node_features = scatter(edge_sh, edge_dst, dim=0).div(num_neighbors**0.5)
 ​
         edge_features = self.tp1(node_features[edge_src], edge_sh)
         node_features = scatter(edge_features, edge_dst, dim=0).div(num_neighbors**0.5)
 ​
         edge_features = self.tp2(node_features[edge_src], edge_sh)
         node_features = scatter(edge_features, edge_dst, dim=0).div(num_neighbors**0.5)
 ​
         return scatter(node_features, data.batch, dim=0).div(num_nodes**0.5)
 ​
 ​
 def main() -> None:
     data, labels = tetris()
     f = InvariantPolynomial()
 ​
     optim = torch.optim.Adam(f.parameters(), lr=1e-2)
 ​
     # == Train ==
     for step in range(200):
         pred = f(data)
         loss = (pred - labels).pow(2).sum()
 ​
         optim.zero_grad()
         loss.backward()
         optim.step()
 ​
         if step % 10 == 0:
             accuracy = pred.round().eq(labels).all(dim=1).double().mean(dim=0).item()
             print(f"epoch {step:5d} | loss {loss:<10.1f} | {100 * accuracy:5.1f}% accuracy")
 ​
 def test() -> None:
     data, labels = tetris()
     f = InvariantPolynomial()
 ​
     pred = f(data)
     loss = (pred - labels).pow(2).sum()
     loss.backward()
 ​
     rotated_data, _ = tetris()
     error = f(rotated_data) - f(data)
     assert error.abs().max() < 1e-5
```
