Fine-tuning aligned language models on entirely benign tasks (e.g. math tutoring) unpredictably degrades safety guardrails, even when training data contains no harmful content and developers have no adversarial intent. We show that the prevailing explanation, that fine-tuning updates should be orthogonal to safety-critical directions in high-dimensional parameter space, offers false reassurance: we show that this orthogonality is structurally unstable and collapses under the very dynamics of gradient descent. We then resolve this through a novel geometric analysis, proving that alignment concentrates in low-dimensional subspaces with sharp curvature, creating a brittle structure that first- order methods cannot detect or defend. While initial fine-tuning updates may indeed avoid these subspaces, the curvature of the fine-tuning loss generates second-order acceleration that systematically steers trajectories into alignment-sensitive regions—an effect invisible to all existing defenses. We formalize this mechanism through the Alignment Instability Condition (AIC), three geometric properties that, when jointly satisfied, lead to safety degradation. Our main result establishes a quartic scaling law: alignment loss grows with the fourth power of training time, governed by the sharpness of alignment geometry and the strength of curvature coupling between the fine-tuning task and safety- critical parameters. These results expose a structural blind spot in the current safety paradigm. The dominant approaches to safe fine-tuning of null-space projections, gradient filtering, and first-order constraints address only the initial snapshot of a fundamentally dynamic problem. Alignment fragility is not a bug to be patched; it is an intrinsic geometric property of gradient descent on curved manifolds. Our results motivate the development of curvature-aware methods, and we hope will further enable a shift in alignment safety analysis from reactive red-teaming to predictive diagnostics for open-weight model deployment.

Machine learning systems are increasingly deployed in settings where failures to uphold safety or fairness can have significant consequences. In such settings, practitioners may want assurances that these systems satisfy safety or fairness criteria despite the statistical uncertainty induced by training with finite data. We study an existing framework for providing safety and fairness guarantees with high confidence under finite-sample uncertainty, and provide a unifying proof framework that identifies sufficient conditions for these guarantees to hold. We then consider settings in which the data available for training consist of a mixture of ground-truth and inferred data, such as model-generated proxy labels. These composite-data regimes arise naturally in modern alignment pipelines, but can violate the statistical assumptions required for high-confidence guarantees on system behavior to hold. As a result, a machine learning system may only appear to satisfy safety or fairness criteria. We characterize how this failure arises, and derive sufficient conditions under which finite-sample guarantees can be recovered.

Resume screening is perceived as a particularly suitable task for LLMs, given their ability to analyze natural language; thus many individuals rely on general purpose LLMs without further adapting them to the task. While researchers have shown that some LLMs are biased in their selection rates of different demographics, studies measuring the validity of LLM decisions are limited. One of the difficulties in externally measuring validity stems from lack of access to a large corpus of resumes for whom the ground truth in their ranking is known and that has not already been used for training. In this work, we overcome this challenge by systematically constructing a large dataset of resumes tailored to particular jobs that are directly comparable, with a known ground truth of superiority. We then use the constructed dataset to measure the validity of ranking decisions made by various LLMs at scale, finding that many models are unable to consistently select the resumes describing more qualified candidates. Furthermore, when measuring the fairness of decisions, we find that models do not reliably abstain when ranking equally-qualified candidates, and select candidates from different demographic groups at different rates, generally prioritizing historically-marginalized candidates. In conclusion, our framework provides a principled audit of LLM resume screeners in the absence of ground truth, offering a crucial tool to independent auditors and developers to ensure the validity of these systems as they are deployed at scale.

Machine learning models are often designed to maximize a primary goal, such as accuracy. However, as these models are increasingly used to inform decisions that affect people’s lives or well-being, it is often unclear what the real-world repercussions of their deployment might be—making it crucial to understand and manage such repercussions effectively. Models maximizing user engagement on social media platforms, e.g., may inadvertently contribute to the spread of misinformation and content that deepens political polarization. This issue is not limited to social media—it extends to other applications where machine learning-informed decisions can have real-world repercussions, such as education, employment, and lending. Existing methods addressing this issue require prior knowledge or estimates of analytical models describing the relationship between a classifier’s predictions and their corresponding repercussions. We introduce THEIA, a novel classification algorithm capable of optimizing a primary objective, such as accuracy, while providing high-confidence guarantees about its potential repercussions. Importantly, THEIA solves the open problem of providing such guarantees based solely on existing data with observations of previous repercussions. We prove that it satisfies constraints on a model’s repercussions with high confidence and that it is guaranteed to identify a solution, if one exists, given sufficient data. We empirically demonstrate, using real-life data, that THEIA can identify models that achieve high accuracy while ensuring, with high confidence, that constraints on their repercussions are satisfied.

Recent works have studied fair resource allocation in social settings, where fairness is judged by the impact of allocation decisions rather than more traditional minimum or maximum thresholds on the allocations themselves. Our work significantly adds to this literature by developing continuous resource allocation strategies that adhere to equality of impact, a generalization of equality of opportunity. We derive methods to maximize total welfare across groups subject to minimal violation of equality of impact, in settings where the outcomes of allocations are unknown but have a diminishing marginal effect. While focused on a two-group setting, our study addresses a broader class of welfare dynamics than explored in prior work. Our contributions are three-fold. First, we provide an algorithm designed for non-noisy continuous-resource environments that achieves sublinear fairness regret. Second, we propose a meta-algorithm for noisy settings building on the first contribution, and third, we empirically demonstrate that our approach consistently achieves fair, welfare-maximizing allocations.

Existing approaches to language model alignment often treat safety as a tradeoff against helpfulness which can lead to unacceptable actions in sensitive domains. To ensure reliable performance in such settings, we propose High-Confidence Safe Reinforcement Learning from Human Feedback (HC-RLHF), a method that provides high-confidence safety guarantees while maximizing helpfulness. Similar to previous methods, HC-RLHF explicitly decouples human preferences regarding helpfulness and harmlessness (safety) and trains separate reward and cost models, respectively. It then employs a two-step process to find safe solutions. In the first step, it optimizes the reward function while ensuring that a specific upper-confidence bound on the cost constraint is satisfied. In the second step, the trained model undergoes a safety test to verify whether its performance satisfies a separate upper-confidence bound on the cost constraint. We provide a theoretical analysis of HC-RLHF, including a proof that it will not return an unsafe solution with a probability greater than a user-specified threshold. For our empirical analysis, we apply HC-RLHF to align three different language models (Qwen2-1.5B, Qwen2.5-3B, and LLaMa-3.2-3B) with human preferences. Our results demonstrate that HC-RLHF produces safe models with high probability while also improving helpfulness and harmlessness compared to previous methods.

In research studying the fairness of machine learning algorithms and models, fairness often means that a metric is the same when computed for two different groups of people. For example, one might define fairness to mean that the false positive rate of a classifier is the same for people of different genders, ages, or races. However, it is usually not possible to make this metric identical for all groups. Instead, algorithms ensure that the metric is similar—for example, that the false positive rates are similar. Researchers usually measure this similarity or dissimilarity using either the difference or ratio between the metric values for different groups of people. Although these two approaches are known to be different, there has been little work analyzing their differences and respective benefits. In this paper we examine this relationship analytically and empirically, and conclude that unless there are application-specific reasons to prefer the difference approach, the ratio approach should be preferred.

Recent studies found that using machine learning for social applications can lead to injustice in the form of racist, sexist, and otherwise unfair and discriminatory outcomes. To address this challenge, recent machine learning algorithms have been designed to limit the likelihood such unfair behavior occurs. However, these approaches typically assume the data used for training is representative of what will be encountered in deployment, which is often untrue. In particular, if certain subgroups of the population become more or less probable in deployment (a phenomenon we call demographic shift), prior work’s fairness assurances are often invalid. In this paper, we consider the impact of demographic shift and present a class of algorithms, called Shifty algorithms, that provide high-confidence behavioral guarantees that hold under demographic shift when data from the deployment environment is unavailable during training. Shifty, the first technique of its kind, demonstrates an effective strategy for designing algorithms to overcome demographic shift’s challenges. We evaluate Shifty using the UCI Adult Census dataset (Kohavi and Becker, 1996), as well as a real-world dataset of university entrance exams and subsequent student success. We show that the learned models avoid bias under demographic shift, unlike existing methods. Our experiments demonstrate that our algorithm’s high-confidence fairness guarantees are valid in practice and that our algorithm is an effective tool for training models that are fair when demographic shift occurs.

The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not capture the setting where the set of available decisions (actions) at each time step is stochastic. Recently, the stochastic action set Markov decision process (SAS-MDP) formulation has been proposed, which captures the concept of a stochastic action set. In this paper we argue that existing RL algorithms for SAS-MDPs suffer from divergence issues, and present new algorithms for SAS-MDPs that incorporate variance reduction techniques unique to this setting, and provide conditions for their convergence. We conclude with experiments that demonstrate the practicality of our approaches using several tasks inspired by real-life use cases wherein the action set is stochastic.

We present RobinHood, an offline contextual bandit algorithm designed to satisfy a broad family of fairness constraints. Unlike previous work, our algorithm accepts multiple fairness definitions and allows users to construct their own unique fairness definitions for the problem at hand. We provide a theoretical analysis of RobinHood, which includes a proof that it will not return an unfair solution with probability greater than a user-specified threshold. We validate our algorithm on three applications: a tutoring system in which we conduct a user study and consider multiple unique fairness definitions; a loan approval setting (using the Statlog German credit data set) in which well-known fairness definitions are applied; and criminal recidivism (using data released by ProPublica). In each setting, our algorithm is able to produce fair policies that achieve performance competitive with other offline and online contextual bandit algorithms.