Table 1 Accuracy of introducing backdoor under draft attack.
Symbols | Connotation |
|---|---|
n | The total number of calculation nodes |
m | The number of Byzantine |
d | The number of dimensions (parameters) of the model |
\(p_i\) | Calculate parameters for ith worker training |
\((p_i)_j\) | jth dimension in \(p_i\) parameter vector |
p | All calculate parameters |
\(\epsilon\) | Constant variable |
\(\theta\) | N-dimensional variable(\(p_i\)) |
\(<\nabla f_t(\theta _1),\theta _2-\theta _1>\) | Gradient from \(\theta _1\) to \(\theta _2\) |
T | Training batch |
t | tth batch |
\(\theta ^(t)\) | Model parameters for batch t |
\(f_t(\theta )\) | Optimization function for batch t |
K | Sample size for one round of training (including batch T and batch size \(K_t\)) |
\(K_t\) | Batch size |
\(x_k\) | Characteristics of the sample |
\(y_k\) | Label of the sample |
\(g(x_k;\theta )\) | The model |
\(L(g(x_k;\theta )\) | The loss |
\(min\sum _{k=1}^{K}L(g(x_k;\theta ),y_k)\) | Optimization problem of deep learning models |
\(\sum _{t=1}^{T}f_t(\theta ^{(t)})\) | The optimal loss of T batch model |
\(min\sum _{t=1}^{T}f_t(\theta )\) | Minimizing losses in training models |
\(\sum _{t=1}^{T}f_t(\theta ^*)\) | Minimizing losses in training models with optimal parameters |
\(a_t\) | Learning rate of batch t |
\(\delta g_t\) | Training gradient for batch t |
D | The upper bound of any variable |
G | The upper bound of any gradient |
