Feature and Image Axes

Scalar comparisons return one value per pair. Residual and image-map sources retain multiple values for each pair, motivating feature/spatial tiling.

Residuals use X−Y, with identity, abs or square transforms. Image sources expose aligned Y−X, absolute error, squared error, SSIM or dissimilarity maps according to their selected comparison. They do not align, resize or register images.

Event-Only Reductions Stay Lazy

# X:[N,D], Y:[M,D]
G = tp.residual_operator(X, Y, transform="abs",
                         chunk_size=64, feature_chunk_size=32)  # [N,M,D]
A = G.mean(dim=-1)                          # lazy [N,M]
values, indices = A.topk(3, largest=False)  # [N,3]
joint = G.mean(dim=(-2, -1))                # Tensor [N], joint over M,D

// X:[N,D], Y:[M,D]
tp::ResidualOperator G(X, Y, "abs", 64, 32);    // [N,M,D]
auto A = G.mean(-1);                            // lazy [N,M]
auto [values, indices] = A.topk(3, -1, false);  // [N,3]
auto joint = G.mean(at::IntArrayRef{-2, -1});   // Tensor [N]

The basic reducers sum/mean/var/std/min/max/prod/all/any apply to current logical axes. Selecting only events keeps the source lazy; once N or M is selected, the result is an ordinary Tensor and later operations do not fuse back into it.

An image chain can reduce Hout/Wout first, leaving channels, then reduce C, then select over M. maps.mean(dim=(-2,-1)).mean(dim=-1).amax(dim=-1) therefore means average spatial values, average channels, then the largest reference score. It is not interchangeable with a joint maximum over all axes.

Residual feature top-k and image-event top-k return terminal selected values and indices along one integer axis. Their outputs are Tensors, not new lazy sources. Scalar median/quantile require all event axes to be contracted first.

Regional Execution

Large image reductions can evaluate only the spatial regions needed for their output and replay regions during backward. feature_chunk_size similarly slices residual D. This bounds generated pair-event workspaces; source images, collection features, output tensors and gradients still exist. Some event chains retain whole earlier-stage maps; chunk controls do not guarantee a fixed total peak. See event shape rules and image-map contracts.