Landmark Distance-Profile Adapter

Integrate the adapter immediately after object loading and before the main neural encoder. Inputs are objects x from a metric space with a callable distance function d_X(x,y); examples include graph edit distance, Wasserstein distance between empirical distributions, tree distance, or a point-cloud metric. First construct a landmark bank A={a_1,...,a_K} from the training set. Use uniform weights w_j=1/K initially, then optionally use stratified weights that approximate the training distribution. For each minibatch object x_i, compute D[i,j]=d_X(x_i,a_j), form P[i,j]=sqrt(w_j)*D[i,j], and standardize each landmark coordinate using training-set mean and variance. Pass P through a two-layer projection MLP and concatenate the projected profile with any existing object features.

Pseudocode:
landmarks = select_diverse_training_objects(K)
mu, sigma = estimate_coordinate_stats(landmarks, training_subset)
for x in minibatch:
p = [sqrt(w[j]) * distance(x, landmarks[j]) for j in range(K)]
p = (p - mu) / (sigma + eps)
h = projection_mlp(p)
prediction = network(h, other_inputs)
loss = task_loss(prediction, target)
backpropagate(loss)

The paper supplies the infinite-dimensional map and its injective, distribution-preserving rationale; the finite landmark approximation, coordinate normalization, landmark selection, and projection are engineering choices. Start with K=64 or 128 and compare random landmarks against farthest-point sampling under d_X. The first cheap experiment should use a small graph-classification benchmark with graph edit distance or a shortest-path-based graph metric, comparing the DPE adapter against a bag-of-statistics MLP and a standard graph encoder at matched parameter count. Success means higher test accuracy or calibration at equal training FLOPs, better performance when training data are reduced, and graceful scaling as K increases. Also test whether reducing K from 128 to 32 causes less degradation than reducing the dimension of a learned baseline embedding.