Fairness Metrics

In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To address this challenge, we construct structure-preserving metrics that are geodesically complete while ensuring that every stationary point under the new metric remains stationary under the original one. Building on this foundation, we revisit the classical symmetric two-point zeroth-order estimator and analyze its mean-squared error from an intrinsic perspective, depending only on the manifold’s geometry rather than any ambient embedding. Leveraging this intrinsic analysis, we establish convergence guarantees for stochastic gradient descent (SGD) with this intrinsic estimator. Under additional suitable conditions, an $\epsilon$-stationary point under the constructed metric $g'$ also corresponds to an $\epsilon$-stationary point under the original metric $g$, thereby matching the best-known complexity in the geodesically complete setting. Empirical studies on synthetic problems confirm our theoretical findings, and experiments on a practical mesh optimization task demonstrate that our framework maintains stable convergence even in the absence of geodesic completeness.

Fairness in machine learning has emerged as a central concern, as predictive models frequently inherit or even amplify biases present in training data. Such biases often manifest as unintended correlations between model outcomes and sensitive attributes, leading to systematic disparities across demographic groups. Existing approaches to fair learning largely fall into two directions: incorporating fairness constraints tailored to specific definitions, which limits their generalizability, or reducing the statistical dependence between predictions and sensitive attributes, which is more flexible but highly sensitive to the choice of distance measure. The latter strategy in particular raises the challenge of finding a principled and reliable measure of dependence that can perform consistently across tasks. In this work, we present a general and model-agnostic approach to address this challenge. The method is based on encouraging independence between predictions and sensitive features through an optimization framework that leverages the Cauchy–Schwarz (CS) Divergence as a principled measure of dependence. Prior studies suggest that CS Divergence provides a tighter theoretical bound compared to alternative distance measures used in earlier fairness methods, offering a stronger foundation for fairness-oriented optimization. Our framework, therefore, unifies prior efforts under a simple yet effective principle and highlights the value of carefully chosen statistical measures in fair learning. Through extensive empirical evaluation on four tabular datasets and one image dataset, we show that our approach consistently improves multiple fairness metrics while maintaining competitive accuracy.

With the growing importance of trustworthy AI, algorithmic fairness has emerged as a critical concern. Among various fairness notions, group fairness - which measures the model bias between sensitive groups - has received significant attention. While many group-fair models have focused on satisfying group fairness constraints, model uncertainty has received relatively little attention, despite its importance for robust and trustworthy decision-making. To address this, we adopt a Bayesian framework to capture model uncertainty in fair model training. We first define group-fair posterior distributions and then introduce a fair variational Bayesian inference. Then we propose a novel distribution termed matched Gibbs posterior, as a proxy distribution for the fair variational Bayesian inference by employing a new group fairness measure, the matched deviation. A notable feature of matched Gibbs posterior is that it approximates the posterior distribution well under the fairness constraint without requiring heavy computation. Theoretically, we show that the matched deviation has a strong relation to existing group fairness measures, highlighting desirable fairness guarantees. Computationally, by treating the matching function in the matched deviation as a learnable parameter, we develop an efficient MCMC algorithm. Experiments on real-world datasets demonstrates that matched Gibbs posterior outperforms other methods in balancing uncertainty–fairness and utility–fairness trade-offs, while also offering additional desirable properties.

Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of semantic ambiguity, where classifiers are particularly prone to unwarranted high-confidence predictions. Motivated by this observation, we propose a principled framework to mitigate OOD overconfidence by leveraging the geometry of OT-induced singular boundaries. Specifically, we formulate an OT problem between a continuous base distribution and the latent embeddings of training data, and identify the resulting singular boundaries. By sampling near these boundaries, we construct a class of OOD inputs, termed optimal transport-induced OOD samples (OTIS), which are geometrically grounded and inherently semantically ambiguous. During training, a confidence suppression loss is applied to OTIS to guide the model toward more calibrated predictions in structurally uncertain regions. Extensive experiments show that our method significantly alleviates OOD overconfidence and outperforms state-of-the-art methods.

Data-Free Robustness Distillation (DFRD) aims to transfer the robustness from the teacher to the student without accessing the training data. While existing methods focus on overall robustness, they overlook the robust fairness issues, leading to severe disparity of robustness across different categories. In this paper, we find two key problems: (1) student model distilled with equal class proportion data behaves significantly different across distinct categories; and (2) the robustness of student model is not stable across different attacks target. To bridge these gaps, we present the first Fairness Enhanced data-free Robustness Distillation (FERD) framework to adjust the proportion and distribution of adversarial examples. For the proportion, FERD adopts a robustness guided class reweighting strategy to synthesize more samples for the less robust categories, thereby improving robustness of them. For the distribution, FERD generates complementary data samples for advanced robustness distillation. It generates Fairness-Aware Examples (FAEs) by enforcing a uniformity constraint on feature-level predictions, which suppress the dominance of class-specific non-robust features, providing a more balanced representation across all categories. Then, FERD constructs Uniform-Target Adversarial Examples (UTAEs) from FAEs by applying a uniform target class constraint to avoid biased attack directions, which distribute the attack targets across all categories and prevents overfitting to specific vulnerable categories. Extensive experiments on three public datasets show that FERD achieves state-of-the-art worst-class robustness under all adversarial attack (e.g., the worst-class robustness under FGSM and AutoAttack are improved by 15.1% and 6.4% using MobileNetV2 on CIFAR-10), demonstrating superior performance in both robustness and fairness aspects. Our code is available at: [https://anonymous.4open.science/r/FERD-2A48/](https://anonymous.4open.science/r/FERD-2A48/).

On two-sided matching platforms such as online dating and recruiting, recommendation algorithms often aim to maximize the total number of matches. However, this objective creates an imbalance, where some users receive far too many matches while many others receive very few and eventually abandon the platform. Retaining users is crucial for many platforms, such as those that depend heavily on subscriptions. Some may use fairness objectives to solve the problem of match maximization. However, fairness in itself is not the ultimate objective for many platforms, as users do not suddenly reward the platform simply because exposure is equalized. In practice, where user retention is often the ultimate goal, casually relying on fairness will leave the optimization of retention up to luck. In this work, instead of maximizing matches or axiomatically defining fairness, we formally define the new problem setting of maximizing user retention in two-sided matching platforms. To this end, we introduce a dynamic learning-to-rank (LTR) algorithm called Matching for Retention (MRet). Unlike conventional algorithms for two-sided matching, our approach models user retention by learning personalized retention curves from each user’s profile and interaction history. Based on these curves, MRet dynamically adapts recommendations by jointly considering the retention gains of both the user receiving recommendations and those who are being recommended, so that limited matching opportunities can be allocated where they most improve overall retention. Naturally but importantly, empirical evaluations on synthetic and real-world datasets from a major online dating platform show that MRet achieves higher user retention, since conventional methods optimize matches or fairness rather than retention.

Aligning AI with human values is a pressing unsolved problem. To address the lack of quantitative metrics for value alignment, we propose EigenBench: a black-box method for comparatively benchmarking language models’ values. Given an ensemble of models, a constitution describing a value system, and a dataset of scenarios, our method returns a vector of scores quantifying each model’s alignment to the given constitution. To produce these scores, each model judges the outputs of other models across many scenarios, and these judgments are aggregated with EigenTrust (Kamvar et al., 2003), yielding scores that reflect a weighted consensus judgment of the whole ensemble. EigenBench uses no ground truth labels, as it is designed to quantify subjective traits for which reasonable judges may disagree on the correct label. Hence, to validate our method, we collect human judgments on the same ensemble of models and show that EigenBench’s judgments align closely with those of human evaluators. We further demonstrate that EigenBench can recover model rankings on the GPQA benchmark without access to objective labels, supporting its viability as a framework for evaluating subjective values for which no ground truths exist.

Protecting the intellectual property of large language models (LLMs) is crucial, given the substantial resources required for their training. Consequently, there is an urgent need for both model owners and third parties to determine whether a suspect LLM is trained from scratch or derived from an existing base model. However, the intensive post-training processes that models typically undergo—such as supervised fine-tuning, extensive continued pretraining, reinforcement learning, multi-modal extension, pruning, and upcycling—pose significant challenges to reliable identification. In this work, we propose a training-free fingerprinting method based on weight matrices. We leverage the Linear Assignment Problem (LAP) and an unbiased Centered Kernel Alignment (CKA) similarity to neutralize the effects of parameter manipulations, yielding a highly robust and high-fidelity similarity metric. On a comprehensive testbed of 60 positive and 90 negative model pairs, our method demonstrates exceptional robustness against all six aforementioned post-training categories while exhibiting a near-zero risk of false positives. By achieving perfect scores on all classification metrics, our approach establishes a strong basis for reliable model lineage verification. Moreover, the entire computation completes within 30s on an NVIDIA 3090 GPU.

Although generative models have made remarkable progress in recent years, their use in critical applications has been hindered by an inability to reliably evaluate the quality of their generated samples. Quality refers to at least two complementary concepts: fidelity and coverage. Current quality metrics often lack reliable, interpretable values due to an absence of calibration or insufficient robustness to outliers. To address these shortcomings, we introduce two novel metrics: $\textit{Clipped Density}$ and $\textit{Clipped Coverage}$. By clipping individual sample contributions, as well as the radii of nearest neighbor balls for fidelity, our metrics prevent out-of-distribution samples from biasing the aggregated values. Through analytical and empirical calibration, these metrics demonstrate linear score degradation as the proportion of bad samples increases. Thus, they can be straightforwardly interpreted as equivalent proportions of good samples. Extensive experiments on synthetic and real-world datasets demonstrate that $\textit{Clipped Density}$ and $\textit{Clipped Coverage}$ outperform existing methods in terms of robustness, sensitivity, and interpretability when evaluating generative models.

Large Language Models (LLMs) pose a significant risk of safety misalignment after finetuning, as models can be compromised by both explicitly and implicitly harmful data. Even some seemingly benign data can inadvertently steer a model towards unsafe behaviors. To address this, we introduce GradShield, a principled filtering method that safeguards LLMs during finetuning by identifying and removing harmful data points before they corrupt the model's alignment. It removes potentially harmful data by computing a Finetuning Implicit Harmfulness Score (FIHS) for each data point and employs an adaptive thresholding algorithm.We apply GradShield to multiple utility fine-tuning tasks combined with different levels of harmful data, and evaluate the safety and utility performance of the resulting LLMs under various metrics. Our results show that GradShield outperforms all baseline methods, as it consistently maintains a low Attack Success Rate (ASR) of under $6\%$, while preserving the utility performance.

Navigating dilemmas involving conflicting values is challenging even for humans in high-stakes domains, let alone for AI, yet prior work has been limited to everyday scenarios. To close this gap, we introduce CLASH (Character perspective-based LLM Assessments in Situations with High-stakes), a meticulously curated dataset consisting of 345 high-impact dilemmas along with 3,795 individual perspectives of diverse values. CLASH enables the study of critical yet underexplored aspects of value-based decision-making processes, including understanding of decision ambivalence and psychological discomfort as well as capturing the temporal shifts of values in the perspectives of characters. By benchmarking 14 non-thinking and thinking models, we uncover several key findings. (1) Even strong proprietary models, such as GPT-5 and Claude-4-Sonnet, struggle with ambivalent decisions, achieving only 24.06 and 51.01 accuracy. (2) Although LLMs reasonably predict psychological discomfort, they do not adequately comprehend perspectives involving value shifts. (3) Cognitive behaviors that are effective in the math-solving and game strategy domains do not transfer to value reasoning. Instead, new failure patterns emerge, including early commitment and overcommitment. (4) The steerability of LLMs towards a given value is significantly correlated with their value preferences. (5) Finally, LLMs exhibit greater steerability when reasoning from a third-party perspective, although certain values (e.g., safety) benefit uniquely from first-person framing.

We develop new classifiers under group fairness in the attribute-aware setting for binary classification with multiple group fairness constraints (e.g., demographic parity (DP), equalized odds (EO), and predictive parity (PP)). We propose a novel approach based on directly intervening on the operating characteristics of a pre-trained base classifier, by: (i) identifying optimal operating characteristics using the base classifier's group-wise ROC convex hulls; (ii) post-processing the base classifier to match those targets. As practical post-processors, we consider randomizing a mixture of group-wise thresholding rules subject to minimizing the expected number of interventions. We further extend our approach to handle multiple protected attributes and multiple linear fractional constraints. On standard datasets (COMPAS and ACSIncome), our method simultaneously satisfies approximate DP, EO, and PP with few interventions and a nearly optimal drop in accuracy; and compare favorably to previous methods.

Multi-view evidential learning aims to integrate information from multiple views to improve prediction performance and provide trustworthy uncertainty estimation. Most previous methods assume that view-specific evidence learning is naturally reliable. However, in practice, the evidence learning process tends to be biased. Through empirical analysis on real-world data, we reveal that samples tend to be assigned more evidence to support data-rich classes, thereby leading to unreliable uncertainty estimation in predictions. This motivates us to delve into a new Biased Evidential Multi-view Learning (BEML) problem. To this end, we propose Fairness-Aware Multi-view Evidential Learning (FAML). FAML first introduces an adaptive prior based on training trajectories, which acts as a regularization strategy to flexibly calibrate the biased evidence learning process. Furthermore, we explicitly incorporate a fairness constraint based on class-wise evidence variance to promote balanced evidence allocation. In the multi-view fusion stage, we propose an opinion alignment mechanism to mitigate view-specific bias across views, thereby encouraging the integration of consistent and mutually supportive evidence. Theoretical analysis shows that FAML enhances fairness in the evidence learning process. Extensive experiments on six real-world multi-view datasets demonstrate that FAML achieves more balanced evidence allocation and improves both prediction performance and the reliability of uncertainty estimation compared to state-of-the-art methods.

Sparse autoencoders (SAEs) are widely used to extract sparse, interpretable latents from transformer activations. We test whether commonly used SAE quality metrics and automatic explanation pipelines can distinguish trained transformers from randomly initialized ones (e.g., where parameters are sampled i.i.d. from a Gaussian). Over a wide range of Pythia model sizes and multiple randomization schemes, we find that, in many settings, SAEs trained on randomly initialized transformers produce auto-interpretability scores and reconstruction metrics that are similar to those from trained models. These results show that high aggregate auto-interpretability scores do not, by themselves, guarantee that learned, computationally relevant features have been recovered. We therefore recommend treating common SAE metrics as useful but insufficient proxies for mechanistic interpretability and argue for routine randomized baselines and targeted measures of feature 'abstractness'.

Large Language Models (LLMs) are widely deployed in reasoning, planning, and decision-making tasks, making their trustworthiness critical. A significant and underexplored risk is intentional deception, where an LLM deliberately fabricates or conceals information to serve a hidden objective. Existing studies typically induce deception by explicitly setting a hidden objective through prompting or fine-tuning, which may not reflect real-world human-LLM interactions. Moving beyond such human-induced deception, we investigate LLMs' self-initiated deception on benign prompts. To address the absence of ground truth, we propose a framework based on Contact Searching Questions~(CSQ). This framework introduces two statistical metrics derived from psychological principles to quantify the likelihood of deception. The first, the *Deceptive Intention Score*, measures the model's bias toward a hidden objective. The second, the *Deceptive Behavior Score*, measures the inconsistency between the LLM's internal belief and its expressed output. Evaluating 16 leading LLMs, we find that both metrics rise in parallel and escalate with task difficulty for most models. Moreover, increasing model capacity does not always reduce deception, posing a significant challenge for future LLM development.

Fairness has become an arising concern in machine learning with its prevalence in decision-making processes, and the trade-offs between various fairness notions and between fairness and accuracy has been empirically observed. However, the inheritance of such trade-offs, as well as the quantification of the best achievable trade-offs, i.e., the Pareto optimal trade-offs, under varied constraints on fairness notions has been rarely and improperly discussed. Owing to the sub-optimality of fairness interventions, existing work fails to provide informative characterization regarding these trade-offs. In light of existing limitations, in this work, we propose a reformulation of the model-specific (MS) Pareto optimal trade-off, where we frame it as convex optimization problems involving fairness notions and accuracy w.r.t. the confusion vector. Our formulation provides an efficient approximation of the best achievable accuracy under dynamic fairness constraints, and yields systematical analysis regarding the fairness-accuracy trade-off. Going beyond the discussion on fairness-accuracy trade-offs, we extend the discussion to the trade-off between fairness notions, which characterizes the impact of accuracy on the compatibility between fairness notions. Inspired by our reformulation, we propose a last-layer retraining framework with group-dependent bias, and we prove theoretically the superiority of our method over existing baselines. Experimental results demonstrate the effectiveness of our method in achieving better fairness-accuracy trade-off, and that our MS Pareto frontiers sufficiently quantify the two trade-offs.

Deep models often exploit spurious correlations (e.g., backgrounds or dataset artifacts), hurting worst-group performance. We propose \textbf{Evidence-Gated Suppression (EGS)}, a lightweight, plug-in regularizer that intervenes inside the network during training. EGS tracks a class-conditional, confidence-weighted contribution for each neuron (more negative $\Leftrightarrow$ stronger support) and applies a percentile-based, multiplicative decay to the most extreme contributors, reducing overconfident shortcut pathways while leaving other features relatively more influential. EGS integrates with standard ERM, requires no group labels, and adds $<5\%$ training overhead. We provide analysis linking EGS to minority-margin gains, path-norm-like capacity control, and stability benefits via EMA-smoothed gating. Empirically, EGS improves worst-group accuracy and calibration vs.\ ERM and is competitive with state-of-the-art methods across spurious-correlation benchmarks (e.g., Waterbirds, CelebA, BAR, COCO), while maintaining strong average accuracy. These results suggest that regulating internal evidence flow is a simple and scalable route to robustness without group labels.

The ability to train Deep Neural Networks (DNNs) with constraints is instrumental in improving the fairness of modern machine-learning models. Many algorithms have been analysed in recent years, and yet there is no standard, widely accepted method for the constrained training of DNNs. In this paper, we provide a challenging benchmark of real-world large-scale fairness-constrained learning tasks, built on top of the US Census (Folktables, Ding et al, 2021). We point out the theoretical challenges of such tasks and review the main approaches in stochastic approximation algorithms. Finally, we demonstrate the use of the benchmark by implementing and comparing three recently proposed, but as-of-yet unimplemented, algorithms both in terms of optimization performance, and fairness improvement. We will release the code of the benchmark as a Python package after peer-review.

Machine learning models trained on real-world data often inherit and amplify biases against certain social groups, raising urgent concerns about their deployment at scale. While numerous bias mitigation methods have been proposed, comparing the effectiveness of bias mitigation methods remains difficult due to heterogeneous datasets, inconsistent fairness metrics, isolated evaluation of vision versus multi-modal models, and insufficient hyperparameter tuning that undermines fair comparisons. We introduce NH-Fair, a unified benchmark for fairness without harm that spans both vision models and large vision–language models (LVLMs) under standardized data, metrics, and training protocols, covering supervised and zero-shot regimes. Our key contributions are: (1) a systematic ERM tuning study that identifies training choices with large influence on both utility and disparities, yielding empirically grounded guidelines to help practitioners reduce expensive hyperparameter tuning space in achieving strong fairness and accuracy; (2) evidence that many debiasing methods do not reliably outperform a well-tuned ERM baseline, whereas a composite data-augmentation method consistently delivers parity gains without sacrificing utility, emerging as a promising practical strategy. (3) an analysis showing that while LVLMs achieve higher average accuracy, they still exhibit subgroup disparities, and gains from scaling are typically smaller than those from architectural or training-protocol choices. NH-Fair provides a reproducible, tuning-aware pipeline for rigorous, harm-aware fairness evaluation.

Large Language Models (LLMs) reproduce social biases, yet prevailing evaluations score models in isolation, obscuring how biases persist across families and releases. We introduce Bias Similarity Measurement (BSM), which treats fairness as a relational property between models, unifying scalar, distributional, behavioral, and representational signals into a single similarity space. Evaluating 30 LLMs on 1M+ prompts, we find that instruction tuning primarily enforces abstention rather than altering internal representations; small models gain little accuracy and can become less fair under forced choice; and open-weight models can match or exceed proprietary systems. Family signatures diverge: Gemma favors refusal, LLaMA 3.1 approaches neutrality with fewer refusals, and converges toward abstention-heavy behavior overall. Counterintuitively, Gemma 3 Instruct matches GPT-4–level fairness at far lower cost, whereas Gemini’s heavy abstention suppresses utility. Beyond these findings, BSM offers an auditing workflow for procurement, regression testing, and lineage screening, and extends naturally to code and multilingual settings. Our results reframe fairness not as isolated scores but as comparative bias similarity, enabling systematic auditing of LLM ecosystems. Code is available at https://anonymous.4open.science/r/bias_llm-0A8E.