A Fixed-Radius Distance-Band Benchmark for Dimensionality-Reduction Fidelity

Dimensionality-reduction (DR) methods are routinely judged by how well each point's k nearest neighbors survive the 2-D embedding (recall@k, trustworthiness, continuity). We argue this family is a biased measure of distance fidelity: its per-point variable radius and hard inclusion threshold favor neighbor-graph methods (t-SNE, UMAP) and penalize methods that preserve absolute distances. We instead score DR fidelity with a fixed-radius distance-band Shepard rho: the Spearman correlation between high-D and 2-D pairwise distances, restricted to cumulative distance bands so that near and global structure are reported separately, with every point judged on the same absolute radius. On synthetic datasets with known ground-truth geometry (non-uniform density, dense clusters, a closed-loop transition, off-subspace outliers, imbalanced two-population data) at realistic noise (SNR=1, D=768, N=1000), we benchmark eight methods -- PCA, Isomap, t-SNE, UMAP, PyMDE, PCC, DREAMS, and the closed-source toorPIA -- and show that (i) high global Shepard rho can coexist with a ~93x collapse of within-cluster scale, invisible to rank-based scores but obvious in a value-based over-compression metric; (ii) recall@k and the fixed-radius band disagree systematically, in the direction the bias predicts; (iii) a membership-restricted Shepard rho resolves single-point and minority-population questions that many-pair statistics cannot -- questions on which even DREAMS, a recent local-plus-global hybrid, fails silently. A supplementary out-of-sample (addplot) test asks whether a never-seen anomaly lands outside the normal region and whether its direction identifies its source. All metrics are computed exactly on all pairwise distances, independently of any method's internals, and every number is reproducible offline: the closed-source method's output coordinates (not its algorithm) are committed to the artifact.

Evaluating the Diversity of AI-Generated Content with Diversity Profiles

Diversity is a fundamental criterion for evaluating generative artificial intelligence (AI) systems, yet its measurement remains inherently ambiguous. Existing approaches typically represent generated samples in an embedding space, compute pairwise distances or similarities, and aggregate them into a single scalar score. Such scalar summaries are convenient, but they often encode different inductive biases and may yield contradictory rankings of the same sample sets. In this paper, we argue that diversity evaluation for AI-generated content is intrinsically under-specified when reduced to a single number. We first review representative diversity metrics, and then diagnose their limitations from two complementary perspectives: an axiomatic analysis showing that no representative scalar metric satisfies all desirable properties simultaneously, and an empirical analysis showing that high-dimensional representation spaces can induce concentrated, modality-dependent distance distributions. To address these issues, we propose diversity profiles: curve-valued, condition-aware summaries that evaluate a parameterized diversity family across a range of thresholds, scales, exponents, or orders under a specified representation and distance or kernel function. Diversity profiles reveal whether a comparison is robust across resolutions or instead depends on an arbitrary parameter choice. We instantiate profiles for several representative metric families and demonstrate their practical use in generative AI evaluation. Overall, diversity profiles provide a more transparent and resolution-aware framework for comparing the diversity of AI-generated content.

FinVerse: Financial Time-Series Benchmark

As time-series foundation models have emerged, the need for benchmarks that can evaluate their forecasting ability in meaningful ways has become increasingly important. Existing time-series forecasting benchmarks provide useful standardized comparisons, but they often evaluate heterogeneous series with uniform error-based metrics. Strong performance under such metrics does not necessarily imply that a model's forecasts will support the best real-world decisions across domains. For example, in stock forecasting, correctly predicting whether a price will rise or fall can be more directly relevant to realized returns than minimizing point-wise forecast error alone. To this end, we introduce FinVerse, a finance-domain time-series forecasting benchmark that takes a first step toward more realistic evaluation. The released FinVerse data artifact contains 116,897 financial time series with 171.1M observations, of which 60,232 series with 17.4M observations are selected as evaluated targets based on their economic relevance to financial decisions. Unlike generic forecasting benchmarks that primarily emphasize uniform point-forecast or probabilistic accuracy, FinVerse defines 11 metric families comprising 78 evaluation metrics and assigns the most appropriate evaluation metrics to each individual time series based on its underlying economic meaning. Our analysis of 43 public time-series forecasting foundation models shows that strong performance under generic forecasting criteria does not necessarily translate into useful financial forecasts. This finding highlights the need for domain-aware benchmarks that evaluate models under objectives closer to real-world decision making.

UpliftBench: Revealing Outcome-Regime and Objective Mismatch in Uplift Evaluation

Uplift modeling (conditional-average-treatment-effect estimation) drives personalized targeting, yet published uplift benchmarks frequently disagree on which estimator performs best; we show the disagreement is substantially about metrics, not models. UpliftBench evaluates 12 uplift estimators under an outer-test-isolated, multi-objective protocol across seven dataset families; its two findings are identified where a reference objective exists -- F1 on the standard continuous benchmark (IHDP), F2 in a within-sample case study on Jobs. On that benchmark, Qini shows no detectable alignment with effect accuracy -- across all 100 IHDP realizations its mean rank correlation with effect accuracy is +0.07, 95% CI [-0.03, +0.16] -- while AUUC is consistently more aligned (paired prefix-mean-AUUC-over-Qini gap +0.49 [+0.40, +0.59]; the shipped cumulative-gain AUUC aligns better still, +0.73). On Jobs, ranking metrics are structurally insufficient for a sign-threshold policy because they discard the score level; empirically, within the released split-rotation analysis direct policy-risk selection yields lower benchmark regret than random model selection while Qini, AUUC, and uplift-at-$k$ do not (14-15% regret). Calibrating the decision threshold removes 81% of the Qini-selection regret. Both findings are bounded, not universal: F1 is not detected on either validation family (the ACIC and Revenue-Synthetic gaps are both indistinguishable from zero), and F2 vanishes under a budgeted-value objective where rank suffices. UpliftBench releases versioned loaders, fixed protocols, result artifacts, and a reproducible living leaderboard; the public repository accompanies the paper.

An Insight on Evaluation Metrics Under the Imbalanced Case of Anomaly Detection

Anomaly detection is inherently characterised by severe class imbalance, making the interpretation of evaluation metrics challenging. Although metrics such as AUROC, AUPR, F1-score, and MCC are widely used, their values convey different meanings depending on the anomaly ratio. In this work, we analyse the behaviour of those four common anomaly detection metrics under varying levels of imbalance. We focus on the study of metric landscapes, visualisations that relate metric values to true positive and true negative rates, providing an intuitive view of metric preferences and stability. Our analysis offers practical guidance for interpreting and comparing anomaly detection results across datasets with different imbalance ratios.

Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learning

Current evaluation of epistemic uncertainty relies on tasks such as out-ofdistribution detection and active learning. However, the Bayes-optimal decision strategies for these tasks do not coincide with the scores commonly used to quantify epistemic uncertainty. Building on the epistemic reject-option framework, we evaluate epistemic uncertainty using its ability to identify regret, the reducible error. Formulating selective prediction as a constrained optimization over coverage, expected risk, and regret, we prove the optimal selector is a thresholded convex combination of the ground-truth aleatoric and epistemic uncertainties. This theoretical unification exposes a weakness in recent uncertainty disentanglement literature: we demonstrate that standard correlation metrics between learned components do not necessarily predict their actual operational utility. We instead propose to evaluate the achievable risk, regret, coverage surface of the decomposition as a diagnostic for joint disentanglement and utility. Benchmarking standard methods on datasets with dense human annotations reveals that decision-theoretic rankings can disagree substantially with proxy-task rankings, including pairwise rank inversions between methods that are top-ranked on one criterion and bottom-ranked on other.

Did We Actually Fix It? An Independent Adversarial Stress-Test of Post-Point-Adjustment Evaluation Metrics for Time-Series Anomaly Detection

Point-adjustment (PA), for years the default scoring protocol in time-series anomaly detection (TSAD), was shown by Kim et al. (2022) to award near-perfect F1 to random anomaly scores. The field adopted a suite of replacement metrics (PA%K, range-based precision/recall, affiliation precision/recall, and Volume-Under-the-Surface, VUS, ROC/PR). We ask, independently and adversarially, whether these resist no-skill detectors on real benchmarks, and find the answer turns entirely on one overlooked variable: N, the number of random attempts an adversary reports the best of. Under a single honest run (N=1), not one replacement metric is gameable on any of six benchmarks (UCR, SMD, SMAP, MSL, NAB, PSM): a random detector reaches 90% of the best real detector's score on at most 11% of series for affiliation-F1, 5% for the ROC family, and 2% for the PR-based metrics and PA%K. But under best-of-N reporting, the seed-shopping endemic to ML, the metrics split sharply. affiliation-F1 and every ROC-based metric inflate steeply, affiliation crossing gameable (25% of series) by N=3 and reaching 0.98 at the full pool (N=41), the ROC family crossing by N=9-11; the PR-based metrics and PA%K stay near-flat at every N, floored near the anomaly prevalence (the lone exception is NAB at large N). A paired test finds VUS-ROC inflated on 131 series where its sibling VUS-PR is not, and never the reverse. The ROC-vs-PR split follows from the order-statistic behaviour of AUC under extreme class imbalance (a random PR-AUC is floored at prevalence); affiliation inflates by a second route, its extreme single-run leniency (already fragile at N=1). We release a pip-installable stress-test harness, and recommend reporting single-run scores or disclosing N and preferring PR-based metrics, which resist best-of-N inflation on nearly every benchmark.

Decision-Aligned Evaluation of Uncertainty Quantification

Uncertainty estimates in machine learning are typically evaluated using generic metrics such as the negative log-likelihood and expected calibration error, yet good performance on such metrics does not necessarily imply high utility in downstream decisions. We introduce decision-alignment, a criterion that reveals which evaluation metrics meaningfully align with downstream utilities. Applying this framework, we show that many widely used uncertainty metrics are either misaligned with common decision problems or encode pathological prior beliefs about the downstream task. We then propose prior-weighted utility metrics, a special class of proper scoring rules that provides decision-aligned uncertainty evaluation. Across benchmark experiments and real-world case studies, our metrics consistently align with realized decision utility, while conventional metrics do not. Our results surface flaws in the current UQ evaluation protocol and offer a principled extension of existing metrics toward decision-relevant UQ evaluation.

TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting

Deep learning-based models have achieved state-of-the-art performance in Time Series Forecasting (TSF), yet their evaluation remains dominated by pointwise error metrics such as Mean Squared Error (MSE), which quantify numerical accuracy but overlook structural properties of the forecast signal, including recurrent dynamics, oscillatory behavior, and phase alignment. As a result, forecasts exhibiting over-smoothing, phase shifts, or frequency distortions may achieve favorable error scores despite substantial structural degradation. To address this limitation, we propose TopoCast, a topology-driven framework for evaluating structural fidelity in TSF. TopoCast reconstructs phase-space representations of forecast and ground-truth sequences using Takens delay embedding and applies persistent homology to characterize their intrinsic dynamics. We derive four complementary topological fidelity measures from persistence diagrams and aggregate them into a Topological Fidelity Score (TFS). We further introduce dominant cycle overlap, a novel metric that maps persistent topological features to the temporal domain to assess whether dominant oscillatory patterns occur at the correct time points. Combined with TFS, this yields the Localized Topological Fidelity Score (LTFS), a phase-aware measure that captures temporal localization errors invisible to existing evaluation metrics. Experiments on five Transformer architectures across three real-world benchmark datasets demonstrate that models with similar forecasting errors can exhibit markedly different structural fidelity profiles, revealing failure modes overlooked by conventional evaluation and highlighting the value of topology-aware forecast assessment.

The Gentle Collapse: Distributional Metrics for Continual Learning

Accuracy degradation is the standard metric for Catastrophic Forgetting (CF), however, it records only whether forgetting occurred or not. It saturates at the extremes and collapses discretely at task boundaries, hiding the internal structure of what is being forgotten. We introduce six softmax-derived metrics spanning true-label rank (TLR), predictive confidence, and distributional divergence that characterize forgetting continuously, each normalized to [0, 1] with no modification to training. On CIFAR-100, these metrics carry information where accuracy does not: at 0% accuracy, the Confusion Margin spans an IQR of [0.32, 0.50] across classes that accuracy treats identically. We demonstrate that this richer signal is actionable in mitigating catastrophic forgetting. Per-sample metric scores used as loss weights reduce forgetting by 1.3 percentage points over uniform experience replay (ER) on CIFAR-100. Furthermore, the slope of a metric over a small window provides a stable sampling criterion: at a small-window size (e.g. 3 epochs), accuracy-trend degrades to 34.79% (std. = 2.32) while log-TLR achieves 41.07% (std. = 0.57). This gap is structural since reliable small-window trend estimation requires a continuous signal. On TinyImageNet, log-TLR trend sampling reduces forgetting by 7.7 percentage points over the ER baseline.

Not all Jensen-Shannon Divergence Estimators are Equal

The Jensen-Shannon divergence is widely reported as a scalar measure of fidelity for synthetic tabular data. Yet, in practice, it is estimated from finite samples using protocols that are often underspecified. This creates a measurement problem. Although the population divergence is well defined, the empirical value depends on the estimator family, sampling protocol, calibration, dimensionality, and class balance. We show that different protocols can yield non-comparable values: marginal-based estimators ignore dependencies in the joint distribution and can severely underestimate divergence, while classifier-based estimators capture joint structure but exhibit strong estimator dependence. We systematically study this behavior across controlled settings with reference divergences and real-world synthetic tabular benchmarks. Our analysis reveals dependence blindness in marginal estimators, prior-shift bias under class imbalance, and estimator sensitivity in high dimensions. To address prior shift, we derive a closed-form posterior correction for classifier-based Jensen-Shannon estimation. Our results show that empirical Jensen-Shannon divergence values are inherently protocol-dependent, making explicit specification of the estimation procedure necessary for meaningful comparison. We provide practical guidelines and an open-source tool for estimator-aware Jensen-Shannon evaluation.

Expectations vs. Realities: The Cost of MSE-Optimal Forecasting Under Conditional Uncertainty

Multi-step time series forecasting (MSF) is commonly evaluated using point-wise error metrics such as mean squared error (MSE), implicitly treating the conditional mean as a sufficient target. We show that this can be misleading under conditional uncertainty, where the conditional expectation becomes unrepresentative of typical realized values at longer horizons. We formalize this effect through a conditional uncertainty gap and prove that whenever this gap is nonzero, no deterministic predictor can simultaneously minimize MSE and match the marginal distribution of realized futures. This establishes a fundamental, model-agnostic trade-off between point accuracy and marginal realism in MSF evaluation. Using controlled stochastic dynamical systems and nine real-world forecasting benchmarks, we empirically characterize the resulting accuracy--realism frontier and \textbf{quantify the practical cost of MSE-only model selection}. As conditional uncertainty increases with forecast horizon, the attainable set expands into a pronounced Pareto front, separating MSE-optimal but under-dispersed predictors from methods that trade accuracy for realistic marginal variability. \textbf{Across benchmarks, we find that small relaxations in MSE ($\boldsymbol{\le 5\%}$) frequently unlock disproportionate gains in marginal realism, with median improvements of $\mathbf{17.3\%}$ and gains exceeding $\mathbf{30\%}$ in some datasets.} We further show that common forecasting strategies systematically occupy different regions of this frontier: direct multi-output predictors concentrate near the accuracy-optimal extreme, while recursive strategies and sample-based inference favors marginal realism. Together, these results expose a structural failure mode of MSE-based evaluation in long-horizon forecasting and recast strategy and inference selection as navigation of an unavoidable accuracy--realism trade-off.