Distributed E-Value Prediction Sets

1. Integration point: use an ensemble of M neural classifiers, federated clients, or graph-neural-network nodes. Each model outputs logits, probabilities, and a scalar uncertainty u_i(x), such as entropy or calibrated energy. Reserve a calibration split and convert each model's nonconformity score into a locally valid e-value. A simple MVP is e_i(x,y)=exp(-lambda s_i(x,y))/Z_i, with the normalizer Z_i selected on calibration data so the held-out mean e-value for each label is at most one. 2. Pseudocode: for each input x, collect outputs from active neighbors; compute w_i=softmax(-kappa u_i); for every label y compute e_F(y)=sum_i w_i e_i(y); return C={y:e_F(y)<1/alpha}; abstain if C contains multiple labels or is empty. 3. Computed directly from the mechanism are nonnegative e-values, convex fusion, and the 1/alpha threshold. Estimated empirically are calibration normalizers, uncertainty scores, and graph effects. Avoid weights trained on the same target label without recalibration, because data-dependent weights can invalidate the expectation bound. 4. First cheap experiment: train five small MLPs or CNNs on CIFAR-10, calibrate each on a held-out split, and compare one model, unweighted fusion, and uncertainty-weighted fusion at alpha=0.1. Measure marginal coverage, average set size, and abstention while varying the graph from disconnected to complete. The prediction is coverage at least 0.90 up to sampling error for every graph and noise distribution, while denser graphs reduce ambiguous prediction sets. The empirical rejection frequency should track the Markov boundary e_F>=10. Falsification occurs if coverage is below 0.90 despite valid local calibration or if abstention does not generally decrease with neighborhood size.