Similar Class Style Augmentation for Efficient Cross-Domain Few-Shot Learning

1. BatchNorm Adaptation

Given the universal feature extractor, we adapt only the BatchNorm affine parameters \(\{\gamma, \beta\}\) at each layer \(l\), without changing any other part of the model. Batch-normalized activations are:

\begin{align} f^l_\text{BN} = \gamma^l \hat{f}^l + \beta^l; \quad \hat{f}^l = \frac{f^l - \mu^l}{\sqrt{(\sigma^l)^2 + \epsilon}} \end{align}

The BN parameters \(\{\gamma, \beta\}\) are optimized to minimize the Nearest Centroid Classifier (NCC) loss over the support set:

\begin{align} \min_{\gamma, \beta} \; \frac{1}{n_\mathcal{S}} \sum_{(x_i^s, y_i^s) \in \mathcal{S}} \mathcal{L}_\text{NCC}(z_i^s, y_i^s; \eta) \quad \text{where} \quad z_i^s = F(x_i^s) \end{align}

Class centroids are the mean of support features per class:

\begin{align} \mathbf{c}_k = \frac{1}{|\mathcal{S}_k|} \sum_{x_i^s \in \mathcal{S}_k} z_i^s \end{align}

2. Cosine Similarity Scale Factor

The NCC loss uses cosine similarity with a scale hyperparameter \(\eta\):

\begin{align} p(y=k \mid z_i^s; \eta) = \frac{e^{\eta \cos\theta_{i,k}}}{\sum_{j=1}^{C} e^{\eta \cos\theta_{i,j}}} \end{align}

Prior works URL and TSA fixed \(\eta = 10\). In CD-FSL, the test domain can be very different from training, so cosine similarities tend to be low. We find that \(\eta = 25\) is significantly better: it expands the probability range so that correctly classified samples receive high confidence without the collapse seen at \(\eta = 50\) (which causes rapid overfitting on the support set within ~10 iterations).

3. Similar Class Style Augmentation (SSA)

To overcome limited support data, we augment each sample with the style (channel-wise feature statistics) of a semantically similar class sample. Class similarity is measured via cosine similarity of centroids:

\begin{align} \text{sim}(\mathbf{c}_i, \mathbf{c}_j) = \frac{\mathbf{c}_i^T \mathbf{c}_j}{\|\mathbf{c}_i\| \|\mathbf{c}_j\|} \end{align}

The similar class set for class \(k\) is:

\begin{align} \mathcal{S}_k = \{t \mid \text{sim}(\mathbf{c}_t, \mathbf{c}_k) > \tau;\; t = 1,\ldots,C\} \end{align}

For sample \(x_i\) of class \(y_i\), we randomly pick \(x_j\) from a similar class \(y_j \in \mathcal{S}_{y_i}\) and mix their intermediate feature statistics at layer \(l\):

\begin{align} \mu_\text{ssa}(f_i; f_j) &= \lambda\,\mu(f_i) + (1-\lambda)\,\mu(f_j) \\ \sigma_\text{ssa}(f_i; f_j) &= \lambda\,\sigma(f_i) + (1-\lambda)\,\sigma(f_j) \\ f_i^\text{ssa} &= \sigma_\text{ssa} \odot \frac{f_i - \mu(f_i)}{\sigma(f_i)} + \mu_\text{ssa} \end{align}

The content of \(x_i\) is preserved in \(f_i^\text{ssa}\), so the augmented sample retains its class label \(y_i\). The final SSA-BNS objective jointly minimizes NCC loss on real and augmented features:

\begin{align} \min_{\gamma, \beta} \; \frac{1}{2n_\mathcal{S}} \sum_{(x_i^s, y_i^s)} \left[ \mathcal{L}_\text{NCC}(z_i^s, y_i^s; \eta) + \mathcal{L}_\text{NCC}(z_i^\text{ssa}, y_i^s; \eta) \right] \end{align}

SSA is inserted after the first two ResNet blocks with \(\lambda = 0.5\) and similarity threshold \(\tau = 0.7\). No additional parameters are introduced.