canonical correlation analysis for networks

**Canonical correlation analysis for networks** is the **statistical method that finds maximally correlated linear combinations between two neural representation spaces** - it helps compare internal codes across layers or different models. **What Is Canonical correlation analysis for networks?** - **Definition**: CCA identifies paired directions that maximize cross-space correlation. - **Use Cases**: Applied to study representational alignment during training and transfer. - **Subspace View**: Provides interpretable dimensional correspondence rather than unit matching. - **Output**: Correlation spectra summarize degree and depth of shared representation structure. **Why Canonical correlation analysis for networks Matters** - **Comparative Insight**: Reveals where two networks encode similar information. - **Training Diagnostics**: Tracks how internal representations evolve and converge. - **Architecture Evaluation**: Supports analysis across models with differing widths and parameterizations. - **Theory Support**: Useful for studying redundancy and invariance in deep representations. - **Limit**: Linear correlation misses some nonlinear correspondence patterns. **How It Is Used in Practice** - **Preprocessing**: Center and normalize activations consistently before CCA computation. - **Layer Mapping**: Evaluate full layer-to-layer correlation matrices for correspondence structure. - **Method Ensemble**: Use CCA with CKA and task metrics for stronger conclusions. Canonical correlation analysis for networks is **a foundational statistical lens for inter-network representation comparison** - canonical correlation analysis for networks is most reliable when interpreted alongside nonlinear and causal evidence.