Fairness Metrics

Fairness impossibility results often look like distinct scalar incompatibility statements. We show that several share one RKHS geometry: fairness criteria are linear constraints on conditional mean embeddings, and unequal base rates make the law of total expectation overdetermine those constraints. This view yields four results. The Kleinberg--Mullainathan--Raghavan dichotomy needs only group-conditional unbiasedness, not full calibration. The \emph{Pok\'emon theorem} shows that a distinct group pair satisfying any finite collection of linear mean-fairness criteria leaves a residual violation witnessed by the MMD, decaying at the Kolmogorov $m$-width rate under spectral regularity. The same tools prove an impossibility for fair feature learning: parity and class-conditional separation in representation space force class collapse under unequal base rates. The approximate relaxations yield signal and error frontiers, allowing a trade-off between real-world estimators and fairness goals. Experiments on standard fairness benchmarks are consistent with our bounds.

The standard rule in unconstrained causal policy learning is simple: treat individuals with nonnegative CATE. We show that this rule can fail when treatment eligibility is strategically manipulable. Agents may move or report covariates after a policy is announced, so treatment is assigned using manipulated covariates while welfare remains determined by baseline CATEs. This creates a mismatch between who receives treatment and who benefits from treatment. We formalize this setting as strategic causal policy learning and show that strategic welfare equals the CATE-weighted mass of baseline types that can reach the treatment region. This access-burden representation leads to three distinct strategic thresholds: a welfare threshold, a safe threshold, and a fair threshold. For linear CATE models, we derive closed-form threshold corrections. Homogeneous costs admit a single buffer correction that recovers the ideal positive-CATE allocation, while heterogeneous costs make welfare maximization, no-exploit safety, and subgroup fairness select different policies. Experiments illustrate these tradeoffs and show when group-specific corrections can restore the ideal allocation.

Diffusion models steer conditional generation with a tunable guidance scale, which users routinely adjust to trade off prompt alignment and diversity. However, these models often reflect and amplify social biases, whose mitigation has been a long-standing concern. Current debiasing techniques are often optimized for a single guidance scale, leaving them vulnerable to fairness degradation when that scale is adjusted. We trace this behavior to a previously overlooked source by decomposing total bias into two components: a model bias and a guidance bias. While prior work primarily targets the former, we show that the guidance bias grows monotonically with the guidance scale, eventually dominating the high-guidance regimes users prefer. To address this, we extend Strong Demographic Parity to guidance and derive a condition under which the target guided distribution retains its group ratio across guidance scales. We propose StayFair, which leverages this condition to design fair guidance algorithms in both regimes. For classifier guidance, it equalizes the classifier's output distributions across groups; for classifier-free guidance, it shifts the null embedding by a prompt-dependent offset. Since StayFair modifies only guidance, it is orthogonal to model debiasing and can be layered onto existing fair diffusion models to extend their fairness across guidance scales. Across class-conditional and text-to-image generation, StayFair decouples fairness from the guidance scale without sacrificing image quality.

Post-hoc image explanations usually reveal *where* a model looks through spatial heatmaps, or *which channels* matter through global channel scores. This separation is limiting for multi-spectral data, where channel relevance is often spatially localized and physically meaningful. We introduce **Spectral-Spatial Interpretation (SSI)**, a full-grid attribution method over position-channel players (g, c). For each spatial position, SSI fixes the observed surrounding context, defines a conditional game over the channels at that position, and applies the Shapley value to this local game. The result is a full spectral-spatial attribution matrix rather than a single heatmap or a global channel ranking. SSI has a clear local semantics: it satisfies Shapley fairness within each position, and its channel aggregation exactly recovers the position-level contextual contrast obtained by replacing that entire position with the baseline. We also distinguish SSI from context-averaged Owen-style hierarchical accounting, which respects the same position-channel grouping but averages over external spatial coalitions. On HLS Burn Scar, SSI outperforms an MC-Owen estimator across retained attribution metrics while using only about 6% of its evaluation budget. Across CUB-200, EuroSAT, and HLS Burn Scar under both per-channel mean and zero baselines, SSI achieves the best joint deletion and insertion AUC over dense, flat, and rank-1 baselines, yields the strongest spectral hit rates and channel deletion, and leads spatial localization on both annotated datasets.

Inorganic crystals are periodic, highly symmetric arrangements of atoms in three-dimensional space. Their structures are constrained by the symmetry operations of a crystallographic \emph{space group} and restricted to lie in specific affine subspaces known as \emph{Wyckoff positions}. The frequency an atom appears in the crystal and its rough positioning are determined by its Wyckoff positions. Most generative models that predict atomic coordinates overlook these symmetry constraints, leading to unrealistically high populations of proposed crystals exhibiting limited symmetry. We introduce Space Group Conditional Flow Matching (SGFM), a novel generative framework that samples significantly closer to the target population of highly symmetric, stable crystals. We achieve this by conditioning the entire generation process on a given space group and set of Wyckoff positions; specifically, we define a conditionally symmetric noise distribution and a group-conditioned, equivariant, parametric vector field that restricts the motion of atoms to their initial Wyckoff position. Our form of group-conditioned equivariance is achieved using an efficient reformulation of \emph{group averaging} tailored for symmetric crystals. It reduces the computational overhead of symmetrization to a negligible level. SGFM achieves state-of-the-art performance in \textit{De Novo Generation} on the MP-$20$ benchmark.

Covering problems are fundamental combinatorial optimization problems with broad connections to clustering, facility location, and various applications such as machine learning and controlling disease outbreaks. In this work we study a variant of the set cover problem that generalizes the partition set cover problem~\citep{bera2014approximation}. In partition set cover, given an instance $(P, S)$ with a universe $P = \cup_{c \in [\ell]} P_c$ (where $[\ell]$ denotes $\{1, 2, \ldots, \ell\}$), a collection of subsets \(S\) (each with associated costs), and coverage requirements $k_1,k_2,\dots,k_\ell$, the objective is to find a subcollection with minimum cost that covers at least $k_c$ elements from each group $c \in [\ell]$. We generalize this problem by allowing for the groups $P = \cup_{c \in [\ell]} P_c$ to be overlapping thus capturing both \emph{group fairness} and \emph{multigroup fairness}. We further allow for probabilistic coverage requirements for each element in the ground set thus capturing the notion of \emph{individual fairness}. Our main result is a randomized iterated-rounding-based algorithm with provable guarantees. Our main result is a randomized iterated rounding based algorithm with provable guarantees. We supplement our theoretical results by showing that algorithm has significantly running times and outperforms the best known algorithm of \citep{inamdar18PartitionSetCover}.

A standard way to enforce group fairness in machine learning models is to add a fairness regularizer to the training loss. Existing dependence-based regularizers, however, are often computationally expensive, with per-batch costs that are typically quadratic or higher in the batch size $B$. We propose a novel group-fairness regularizer based on the Cramér-von-Mises (CvM) sensitivity index, which penalizes statistical dependence between model predictions and a sensitive attribute during training. Our method combines a rank-based CvM estimator with differentiable soft ranking, yielding a bounded training penalty with $\Oc(B \log B)$ per-batch complexity. This is the first sub-quadratic in-processing fairness method that targets genuine joint-distribution dependence. We further establish theoretical connections between the CvM regularizer and standard fairness metrics such as demographic parity and equality of opportunity. Experiments on tabular and image datasets show competitive fairness-utility trade-offs while substantially lowering training overhead compared to existing dependence-based regularizers.

Peer review at ML conferences increasingly relies on reviewer scores as the primary decision instrument. As submissions have scaled from thousands to tens of thousands per year, no systematic audit has examined whether this instrument functions uniformly across research areas, or whether acceptance outcomes are in practice shaped by forces that reviewer scores neither capture nor control. This position paper argues that acceptance outcomes are shaped by forces beyond reviewer scores, and that the underlying cause is a measurement design failure, not individual bias. When a fixed numerical scale aggregates quality judgments across communities with structurally non-uniform reviewer pools, absolute scores become incomparable across areas, and area chairs must substitute community priors for score-based decisions. Using ICLR 2021--2026 data covering 50,289 papers across 219 research topics, we show that at any given reviewer score, a paper's acceptance probability varies by up to 8$\times$ depending on its topic. We rule out scoring culture, expert reviewer standards, rational area chair reweighting, and quality dilution as alternative explanations. We call on program committees to adopt inherently calibrated review signals and publish topic-stratified, score-conditional acceptance rates as a first-class fairness metric.

When benchmark examples overlap with a model’s training data, benchmark contamination can substantially inflate reported evaluation metrics, yet training provenance is often unavailable. We study post-hoc recovery of uncontaminated evaluation metrics in supervised tabular classification and regression using only prediction–label pairs from a potentially contaminated benchmark. We introduce MILAN (Metric Integrity via Leakage-Aware Normalization), a meta-trained framework that models a contaminated benchmark as a mixture of training-origin and clean evaluation examples and estimates soft posterior weights for the clean component to correct evaluation metrics. MILAN supports a broad class of metrics through weighted estimators and metric-specific correction procedures, and can optionally incorporate contamination-rate priors and sample-wise difficulty scores. To quantify uncertainty, MILAN additionally provides split-conformal prediction intervals with marginal coverage across exchangeable recovery problems. Across a large suite of simulated recovery problems with held-out datasets and model families, MILAN consistently improves clean-metric recovery over thresholding, clustering, mixture-model, anomaly-detection, and membership-inference baselines. In a polygenic risk score case study using UK Biobank evaluation data, MILAN improves agreement with independent FinnGen reference metrics. We provide a scikit-learn-style implementation at \url{hidden-for-submission}.

There is a fundamental limit to the best prediction error of any model for a given data distribution. In classification, the Bayes error quantifies this limit and serves as both a benchmark for trained models and a criterion to detect overfitting. The state-of-the-art Bayes error estimation techniques for binary classification use only soft labels (positive class probabilities) and require no input features or auxiliary training. We extend such notions to constrained classification problems, such as fairness. Fair classification is an important case of constrained or multi-objective classification. It requires a model not only to be accurate but also to yield fair outcomes (equal or near-equal true positive rates) across different demographic groups (e.g., race and gender). This leads to an inherent fairness-accuracy tradeoff or a Pareto frontier that is used to compare fair classifiers against each other. The focus of our work is to estimate the fundamental limit for this fairness-accuracy tradeoff. We derive an explicit expression for the fair Bayes error rate (i.e., best achievable error rate subject to given fairness constraints), and construct consistent, instance-free estimators for it using only soft labels and group information. We provably bound the bias and the sample complexity of our estimators. Empirically, our method produces a robust, low-variance estimate of the optimal fairness-accuracy trade-off curve, even when the soft labels are noisy and derived from a classification model on hard labels.

This paper studies binary classification under generalized performance metrics, going beyond standard misclassification error. We focus on linear-fractional measures—including the $F$-score and Jaccard index—which are widely used in class-imbalanced settings. We first provide a unified characterization of the optimal classifier, showing that it admits a thresholding structure on the regression function. This reduces the original infinite-dimensional, non-decomposable optimization problem to the estimation of a single scalar parameter. Building on this result, we analyze plug-in classifiers that combine a regression estimator with a data-driven estimate of the optimal threshold. We show that this threshold is characterized as the solution of a fixed-point equation depending only on the marginal distribution, enabling its estimation using unlabeled data and avoiding standard validation-based procedures. Our main contribution is a finite-sample analysis of this approach. We derive excess risk bounds that decompose the error into contributions from regression estimation, threshold estimation, and sampling effects, providing a modular understanding of learning under non-decomposable metrics. Under standard margin assumptions, we further establish fast convergence rates. Our results yield a unified theoretical framework for plug-in classification under linear-fractional metrics, extending prior analyses beyond specific measures such as the $F$-score. Empirical results on synthetic and real datasets support our theoretical findings.

Intersectional fairness requires evaluating models across fine-grained subgroups. However, as group definitions become more granular, the sample size per subgroup shrinks, causing fairness estimates to become increasingly unstable. Existing in-processing methods are _certainty-blind_: they penalize observed disparities without distinguishing statistically certified unfairness from sampling noise. This leads to _fairness overfitting_, where models sacrifice utility to "fix" spurious disparities in sparse regimes. To address this, we introduce the _significant-excess_ metric family, a continuous, uncertainty-aware fairness score that measures only the portion of a subgroup’s disparity exceeding what sampling variation can explain at a specific confidence level. Leveraging this, we propose SAFER (Significance-Aware Fairness Regularizer), a differentiable in-processing method that gates fairness penalties using a soft-count likelihood-ratio significance test. SAFER satisfies a _provable safety property_: when no subgroup disparity is statistically certifiable, its fairness gradient is exponentially small and training reduces to unconstrained optimization. Mechanism ablations across three benchmark datasets and purpose-built stress variants confirm that each component of SAFER – threshold smoothing, the significance gate, and a dense-tail term – is empirically necessary in its theoretically predicted operating regime. SAFER consistently achieves a superior fairness-utility Pareto frontier, compared to baselines methods in sparse intersectional settings while preserving utility when certified unfairness is absent.

Natural gradient descent is a theoretical pillar of second-order optimization for neural networks. Existing implementations either rely on structural approximations of the curvature matrix or incur substantial computational and memory overhead. Direct application remains difficult at deep-network scale. We build an optimizer based on an unbiased stochastic estimator of the Fisher information matrix. It employs a truncated exponential moving average metric with damping, which we call the Stochastic Truncated Metric (STM), and is otherwise closely aligned with the original natural gradient. This gives a matrix-free parameter update with strictly $O(Kd)$ time and memory per step, where $K$ is a small constant. It is applicable across network architectures without layer-wise assumptions. We bound the error induced by the finite-memory truncation. We show that STM is stable and efficient on vision and language benchmarks.

Graph Neural Networks (GNNs) have shown remarkable effectiveness across diverse graph-related tasks. However, existing studies reveal that their fairness is highly vulnerable to adversarial manipulation, which can substantially exacerbate inherent biases toward sensitive attributes, such as gender in demographic prediction. Although prior work has shown that fairness poisoning attacks can be launched via malicious node injection, whether this strategy can support the more challenging fairness evasion attacks remains open. Moreover, existing methods have not directly addressed fairness attacks on multi-class datasets with multi-valued sensitive attributes. To bridge this gap, we propose a universal fairness attack framework (UFA) that injects malicious nodes to perform both poisoning and evasion attacks against GNNs while minimally affecting model utility. UFA first identifies nodes most susceptible to being pushed across the decision boundary. It then targets core mechanisms shared by diverse GNN architectures to manipulate node representations, thereby maximizing outcome disparities across sensitive groups. Comprehensive experiments on five real-world datasets demonstrate the effectiveness of UFA. By injecting fewer than 0.2\% malicious nodes, UFA severely degrades the fairness of both mainstream and fairness-aware GNNs, proving effective in both poisoning and evasion settings. Our findings expose the fragility of fairness in GNNs and underscore the urgent need for robust fairness-aware models.

A major goal in computational neuroscience is to understand how animals learn to perform a new behavior from a sequence of actions and rewards. Recent work from Liebana et al. (2025) has argued that animal learning trajectories are inconsistent with learning in shallow (1-layer) networks and are better explained by gradient descent (GD) in a deep neural network (DNN). However, previous work on inferring animal learning rules from behavioral data has focused on either 1-layer networks or fits to group behavior, highlighting the need for methods to fit DNN learning rules to individual animal learning trajectories. To address this gap, we develop a method for inferring single-animal DNN-based learning rules, parametrized by a set of initial weights, a learning rate, and a softmax parameter governing stochasticity in choice behavior. We first prove that GD in a shallow network can be arbitrarily well approximated by GD in a deep network, establishing a theoretical limit on network identifiability. Using this result to refine our inference method, we analyze two behavioral datasets from mice learning a sensory decision-making task. Specifically, we compare three model architectures: 1-layer linear (1L) and 2-layer linear (2L) models considered in Liebana et al., as well as a 2-layer nonlinear network (2NL) with a sigmoidal nonlinearity after the first layer. The 2NL model achieved the best fit for 84 out of 88 mice in both datasets (by AIC). Moreover, simulated learning trajectories from the fitted 2NL model closely matched the timecourse of key behavioral metrics such as bias, stimulus sensitivity, and accuracy. These results show that both depth and nonlinearity are critical for capturing individual learning trajectories. Strikingly, we found that the inferred learning rate and initial layer-1 weights of the 2NL model systematically predicted individual differences in accuracy and task bias, linking network initialization and learning rate to individual differences in learning performance across mice.

Post-training pruning reduces the memory and computation costs of large language models (LLMs), and N:M semi-structured sparsity provides a hardware-friendly pruning pattern for efficient inference. However, pruned models are often evaluated mainly by perplexity and average downstream accuracy, which are useful aggregate metrics but do not fully explain how pruning changes individual candidate-level decisions. We evaluate magnitude pruning, Wanda, SparseGPT, Wanda++, and our proposed MR-GOBS across multiple model families and sparsity settings. We further conduct a paired decision-level evaluation that measures true-label confidence, answer margin, prediction flips, candidate-level distribution shift, and near-boundary vulnerability. Our results show that pruning weakens decision reliability by lowering confidence in the correct answer, shrinking answer margins, and increasing correct-to-wrong flips, especially on near-boundary examples. To examine whether reconstruction-oriented improvements reliably improve decision reliability, we revisit SparseGPT through its local least-squares reconstruction formulation and refine its N:M mask-selection step. MR-GOBS uses GroupOBS, a set-level OBS reconstruction cost for jointly pruning a group of weights, to score each legal local N:M mask. It then selects masks using a minimax-regret criterion over multiple calibration views. Although MR-GOBS often improves average perplexity over SparseGPT, these gains do not always translate into better downstream accuracy or decision-level metrics. Our findings suggest that reliable evaluation of pruned LLMs requires both aggregate performance metrics and decision-level diagnostics.

Similarity measures such as canonical correlation analysis (CCA), representational similarity analysis (RSA) and center kernel alignment (CKA), are widely used to compare the representational geometries used by different neural networks to solve the same task. Yet, because existing methods compare the *extrinsic geometry* of neural representations in state space, rather than their *intrinsic geometry*, they may fail to capture subtle yet crucial distinctions between fundamentally different computations performed by biological and artificial neural networks. Here, we introduce metric similarity analysis (MSA), a novel method which leverages tools from Riemannian geometry to compare the intrinsic geometry of neural manifolds. Within our mathematical framework, we derive several properties of MSA, including coordinate, scale and rotation invariances. We show that MSA can be used to i) disentangle neural computations of deep networks in rich vs. lazy learning regimes, ii) compare the computation-through-dynamics of recurrent neural networks and state-space models during neuroscience working memory tasks, and iii) investigate the statistical manifolds of diffusion models. Overall, we introduce a mathematically grounded and broadly applicable framework to understand the mechanisms behind neural computations by contrasting their Riemannian geometries, with broad applicability to both neuroscience and machine learning.

Progress in language model development is often driven by comparative decisions: which architecture to adopt, which pretraining corpus to use, or which training recipe to apply. Making these decisions well requires reliable performance forecasts, yet the two commonly used signals are fundamentally limited. Cross-entropy loss is poorly aligned with downstream capabilities, and direct downstream evaluation is expensive, sparse, and often uninformative at early training stages. Instead, we propose to construct proxy metrics by aggregating token-level statistics, such as entropy, top-k accuracy, and expert token rank, from a candidate model's next token distribution over expert-written solutions. Across three settings, our proxies consistently outperform loss- and compute-based baselines: 1) For cross-family model selection, they rank a heterogeneous population of reasoning models with mean Spearman $\rho = 0.81$ (vs. $\rho = 0.36$ for cross-entropy loss); 2) For pretraining data selection, they reliably rank 25 candidate corpora for a target model at roughly $10{,}000\times$ less compute than direct evaluation, pushing the Pareto frontier beyond existing methods; and 3) for training-time forecasting, they extrapolate downstream accuracy across an $18\times$ compute horizon with roughly half the error of existing alternatives. Together, these results suggest that expert trajectories are a broadly useful source of signal for assessing model capabilities, enabling reliable performance forecasting throughout the model development lifecycle.

Chains of thought (CoTs) have become central in interpreting and auditing behaviors of large language models. Yet growing evidence suggests that these traces often fail to faithfully represent the computations behind a model's predictions. Several faithfulness metrics have been proposed, but whether they indeed measure faithfulness remains unknown. Answering this requires ground-truth labels, which are hard to obtain since internal computations are not directly observable. Consequently, most works proposing metrics report only absolute scores or comparisons to prior metrics, and the few existing benchmarks rely on proxies like plausibility or importance, properties orthogonal to faithfulness that can mislead about whether a CoT can be trusted. We address this challenge by constructing tasks whose outputs reveal which intermediate computations must have produced them, and developing an automated labeling pipeline that yields ground-truth faithfulness labels at both the step and CoT level. Building on this methodology, we present **BonaFide**, a benchmark of 3,066 labeled CoTs across 13 tasks and 10 models, and use it to conduct the first systematic evaluation of prominent faithfulness metrics. Our experiments show that most metrics perform near chance, exhibit strong prediction biases and degrade on longer CoTs. The best metric reaches only 0.71 AUROC at the CoT level while another reaches 0.59 at the step level, with neither transferring across settings, while entailing prohibitively high computational cost. Our results expose fundamental gaps in current faithfulness evaluation and call for the development of more reliable and efficient metrics.

Gradient-based attribution methods are model-faithful and scalable, but Integrated Gradients (IG) can be brittle because explanations depend on heuristic baselines, straight-line paths, discretization, and saturation. We propose Fisher--Rao Integrated Gradients (FRInGe), which defines both the reference and interpolation schedule in predictive distribution space. FRInGe replaces input baselines with a maximum-entropy predictive reference and follows a Fisher--Rao geodesic on the probability simplex. The corresponding input-space trajectory is realized through the pullback Fisher metric and stabilized by KL and Euclidean trust regions; attributions are obtained by integrating input gradients along this trajectory. Across six ImageNet architectures, FRInGe most clearly improves calibration-oriented attribution metrics, especially MAS scores, while remaining competitive on perturbation AUC and infidelity.