Abstention

Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labels with design parameters, exhibits strong sensitivity to their arbitrary ordering and scaling, leading to unstable training. We introduce Diagonal Flow Matching (Diag--CFM), which resolves this through a zero-anchoring strategy that pairs design coordinates with noise and labels with zero, making the learning problem provably invariant to coordinate permutations. This yields substantially lower round-trip error than CFM and invertible neural network baselines across design dimensions up to $P{=}784$, including order-of-magnitude gains on several benchmarks. We develop two architecture-intrinsic uncertainty metrics, Zero-Deviation and Self-Consistency, that enable three practical capabilities: selecting the best candidate among multiple generations, abstaining from unreliable predictions, and detecting out-of-distribution targets; consistently outperforming ensemble and general-purpose alternatives across all tasks. We validate on airfoil, gas turbine combustor, scalable analytical benchmarks, a photonics inverse-design task, and an image-statistics benchmark.

Uncertainty in artificial intelligence (AI) predictions raises pressing legal and ethical questions for AI-assisted decision-making. This article examines two uncertainty-based algorithmic interventions that act as guardrails for human-AI interaction: selective abstention, which withholds high-uncertainty predictions from human decision-makers, and selective friction, which presents such predictions together with salient warnings about the model's uncertainty. Prior work suggests that uncertainty-based abstention can exacerbate disparities where under-represented groups are more likely to receive uncertain predictions. We provide, to our knowledge, the first doctrinal analysis of uncertainty-based algorithmic interventions under laws from the United Kingdom and examine their consequences through two AI-assisted case studies: consumer credit and risk of reoffending. We show that the use of uncertainty thresholds, though formally neutral, can generate discriminatory effects. We argue that both interventions pose risks of unlawful discrimination, but that selective friction is legally preferable. It preserves access to the prediction and is more likely to satisfy proportionality under the Equality Act 2010. Whether selective friction also improves decision quality in practice is uncertain. We identify conditions under which it may improve or worsen decision quality.

Large language models (LLMs) increasingly generate citation-backed responses, yet citation hallucination remains a major challenge for trustworthy scientific information access. We introduce REASONS, a benchmark of 12,723 sentence-level citation instances spanning 12 arXiv subject categories, designed to evaluate scientific citation attribution under varying evidence conditions. We propose a dual-metric framework consisting of Abstention Rate (AR) and Hallucination Rate (HR) to characterize the trade-off between reliability and responsiveness. Using author-attribution and title-attribution tasks, we evaluate proprietary and open-source LLMs under zero-context, metadata-augmented, cascaded metadata-augmented prompting (CMP), retrieval-augmented, and adversarial settings. Advanced RAG lowers HR relative to Naive RAG (65.4% vs. 87.6%) but reduces AR from 5.0% to 0%. Under adversarial metadata, several systems exceed 85% HR, while retrieval-augmented variants frequently maintain near-zero abstention. Human evaluation of 1,000 outputs ($κ=0.78$) finds a 12.7:1 ratio of factual hallucinations to acceptable paraphrases. Our findings demonstrate that citation attribution systems should be evaluated not only for correctness but also for their ability to abstain appropriately under uncertainty. REASONS provides a benchmark and evaluation framework for studying attribution reliability in citation generation.