What FID Hides: Detecting, Ranking, and Diagnosing Deviations in Generative Evaluation

Generative models are commonly ranked by Fréchet Inception Distance (FID) and Kernel Inception Distance (KID), yet FID's first-two-moment summary can miss distributional differences, and a reported scalar gap alone is not a calibrated test against sampling variation. FID's moment restriction has concrete consequences: on ImageNet, visually unrecognizable images optimized only to match the reference Inception mean and covariance obtain FID $24.7$ versus $58.6$ for held-out real images (lower is better). Moreover, FID and KID are scalar discrepancies that are unchanged when the two samples are exchanged and therefore do not encode the direction of a dispersion change: under-dispersion, as can occur in mode collapse, versus over-dispersion. We introduce \textbf{ZID} (\emph{Z-resolved Integrated Diagnostic}), which combines six standardized location- and dispersion-sensitive arms from a rank graph (RISE) and Gaussian kernels (GPK at two bandwidths). Rather than asking one scalar to serve incompatible roles, ZID reports three linked outputs: an index for ranking departure magnitude, a permutation $p$-value for testing distributional equality, and a signed dispersion readout for diagnosis. In controlled experiments, ZID detects a broad range of departures, and its score tracks increasing severity along the corresponding sweeps, including cases in which FID is flat or reversed. On DiT-XL/2 and SiT-XL/2 guidance sweeps, ZID detects departure from real data, and its signed readout labels the high-guidance diversity collapse as under-dispersion.

Beyond Effective Sample Size: Effective Number of Proposals for Adaptive Importance Sampling

Population-based adaptive importance sampling (AIS) methods use a set of proposal densities to approximate complex target distributions. Their performance is commonly assessed through effective sample size (ESS) and related weight-based diagnostics, which measure the concentration of normalized importance weights. However, a large ESS only indicates that the normalized sample weights are not strongly concentrated; it does not describe how the proposal components are arranged in the sampling space. In population-based AIS, several proposal components may generate samples in the same region of the target, so the sample weights can appear well balanced even though the effective number of distinct proposal components is small. This letter introduces the effective number of proposals (ENP), a similarity-aware proposal-level diagnostic for population-based AIS. ENP combines the total normalized weight assigned to each proposal with a redundancy measure computed from similarities among target-weighted samples, estimating the number of non-redundant empirical proposal contributions to the approximation. We establish basic effective-number properties and show that ENP detects proposal collapse and duplication missed by standard ESS. We also illustrate its use as a targeted feedback signal for proposal rejuvenation.

Detecting Explanatory Insufficiency in Learned Representations: A Framework for Representational Vigilance

Learned representations are central to modern machine learning and are commonly evaluated through predictive performance, robustness, uncertainty estimation, or generalization. However, a learned representation may remain operationally successful while progressively failing to organize persistent residual structures that are not fully captured by conventional evaluation metrics. This article introduces VER, the Vigilant Evaluator of Representations, a conceptual framework for monitoring representational adequacy in learned representations. VER does not propose a new learning algorithm, loss function, or model architecture. Instead, it formalizes a diagnostic process through which persistent residual structures may be identified, analyzed, and interpreted as potential indicators of explanatory insufficiency. The framework distinguishes representational inadequacy from ordinary prediction error, uncertainty, noise, and distribution shift. It introduces a monitoring sequence based on representation identification, explanatory-domain delimitation, residual-structure detection, explanatory-resistance evaluation, and vigilance signaling. VER is intended as a contribution to representation diagnostics in machine learning. Its objective is not to replace existing evaluation methods but to complement them by treating representational adequacy as an explicit object of inquiry. A path toward empirical evaluation through representational-vigilance benchmarks is also outlined.