Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable; many applications require a single output to act on, not several. To overcome this limitation, prediction sets can be provided to a human who then makes an informed decision. In any such system it is crucial to ensure the fairness of outcomes across protected groups, and researchers have proposed that Equalized Coverage be used as the standard for fairness. By conducting experiments with human participants, we demonstrate that providing prediction sets can lead to disparate impact in decisions. Disquietingly, we find that providing sets that satisfy Equalized Coverage actually increases disparate impact compared to marginal coverage. Instead of equalizing coverage, we propose to equalize set sizes across groups which empirically leads to lower disparate impact.

As deep generative models have progressed, recent work has shown them to be capable of memorizing and reproducing training datapoints when deployed. These findings call into question the usability of generative models, especially in light of the legal and privacy risks brought about by memorization. To better understand this phenomenon, we propose the *manifold memorization hypothesis* (MMH), a geometric framework which leverages the manifold hypothesis into a clear language in which to reason about memorization. We propose to analyze memorization in terms of the relationship between the dimensionalities of $(i)$ the ground truth data manifold and $(ii)$ the manifold learned by the model. This framework provides a formal standard for "how memorized" a datapoint is and systematically categorizes memorized data into two types: memorization driven by overfitting and memorization driven by the underlying data distribution. By analyzing prior work in the context of the MMH, we explain and unify assorted observations in the literature. We empirically validate the MMH using synthetic data and image datasets up to the scale of Stable Diffusion, developing new tools for detecting and preventing generation of memorized samples in the process.

Satya Krishna Gorti, Ilan Gofman, Zhaoyan Liu, Jiapeng Wu, Noël Vouitsis, Guangwei Yu, Jesse C. Cresswell, Rasa Hosseinzadeh. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Automatic summarization systems have advanced rapidly with large language models (LLMs), yet they still lack reliable guarantees on inclusion of critical content in high-stakes domains like healthcare, law, and finance. In this work, we introduce Conformal Importance Summarization, the first framework for importance-preserving summary generation which uses conformal prediction to provide rigorous, distribution-free coverage guarantees. By calibrating thresholds on sentence-level importance scores, we enable extractive document summarization with user-specified coverage and recall rates over critical content. Our method is model-agnostic, requires only a small calibration set, and seamlessly integrates with existing black-box LLMs. Experiments on established summarization benchmarks demonstrate that Conformal Importance Summarization achieves the theoretically assured information coverage rate. Our work suggests that Conformal Importance Summarization can be combined with existing techniques to achieve reliable, controllable automatic summarization, paving the way for safer deployment of AI summarization tools in critical applications. Code is available at github.com/layer6ai-labs/conformal-importance-summarization.

Tabular data is one of the most ubiquitous sources of information worldwide, spanning a wide variety of domains. This inherent heterogeneity has slowed the development of Tabular Foundation Models (TFMs) capable of fast generalization to unseen datasets. In-Context Learning (ICL) has recently emerged as a promising solution for TFMs, enabling dynamic adaptation to new tasks without additional tuning. While many studies have attempted to re-purpose large language models for tabular ICL, they have had limited success, so recent works have focused on developing tabular-specific foundation models. In this work, we propose an approach to combine ICL-based retrieval with self supervised learning to train tabular foundation models. We also investigate the utility of real vs. synthetic data for model pre-training, and show that real data can contain useful signal not easily captured in synthetic training. Specifically, we show that incorporating real data during the pre-training phase can lead to significantly faster training and better downstream generalization to unseen data. Our resulting model, **TabDPT**, achieves strong performance on both regression (CTR23) and classification (CC18) benchmarks. Importantly, we also demonstrate that with our pre-training procedure, scaling both model and data size leads to consistent performance improvements that follow power laws. This echoes scaling laws in LLMs and other foundation models, and suggests that large-scale TFMs can be achievable. We open-source our full pipeline: inference code including trained model weights can be found [here](https://github.com/layer6ai-labs/TabDPT-inference), and the training code to reproduce experiments can be found [here](https://github.com/layer6ai-labs/TabDPT-training).

Causal effect estimation from observational data is fundamental across various applications. However, selecting an appropriate estimator from dozens of specialized methods demands substantial manual effort and domain expertise. We present CausalPFN, a single transformer that *amortizes* this workflow: trained once on a large library of simulated data-generating processes that satisfy ignorability, it infers causal effects for new observational datasets out of the box. CausalPFN combines ideas from Bayesian causal inference with the large-scale training protocol of prior-fitted networks (PFNs), learning to map raw observations directly to causal effects without any task-specific adjustment. Our approach achieves superior average performance on heterogeneous and average treatment effect estimation benchmarks (IHDP, Lalonde, ACIC). Moreover, it shows competitive performance for real-world policy making on uplift modeling tasks. CausalPFN provides calibrated uncertainty estimates to support reliable decision-making based on Bayesian principles. This ready-to-use model requires no further training or tuning and takes a step toward automated causal inference (https://github.com/vdblm/CausalPFN/).

Existing research on Retrieval-Augmented Generation (RAG) primarily focuses on improving overall question-answering accuracy, often overlooking the quality of sub-claims within generated responses.Recent methods that attempt to improve RAG trustworthiness, such as through auto-evaluation metrics, lack probabilistic guarantees or require ground truth answers.To address these limitations, we propose Conformal-RAG, a novel framework inspired by recent applications of conformal prediction (CP) on large language models (LLMs).Conformal-RAG leverages CP and internal information from the RAG mechanism to offer statistical guarantees on response quality.It ensures group-conditional coverage spanning multiple sub-domains without requiring manual labelling of conformal sets, making it suitable for complex RAG applications.Compared to existing RAG auto-evaluation methods, Conformal-RAG offers statistical guarantees on the quality of refined sub-claims, ensuring response reliability without the need for ground truth answers.Additionally, our experiments demonstrate that by leveraging information from the RAG system, Conformal-RAG retains up to 60% more high-quality sub-claims from the response compared to direct applications of CP to LLMs, while maintaining the same reliability guarantee.

The goal of multimodal alignment is to learn a single latent space that is shared between multimodal inputs. The most powerful models in this space have been trained using massive datasets of paired inputs and large-scale computational resources, making them prohibitively expensive to train in many practical scenarios. We surmise that existing unimodal encoders pre-trained on large amounts of unimodal data should provide an effective bootstrap to create multimodal models from unimodal ones at much lower costs. We therefore propose FuseMix, a multimodal augmentation scheme that operates on the latent spaces of arbitrary pre-trained unimodal encoders. Using FuseMix for multimodal alignment, we achieve competitive performance - and in certain cases outperform state-of-the art methods - in both image-text and audio-text retrieval, with orders of magnitude less compute and data: for example, we outperform CLIP on the Flickr30K text-to-image retrieval task with ~600 × fewer GPU days and ~80 × fewer image-text pairs. Additionally, we show how our method can be applied to convert pre-trained text-to-image generative models into audio-to-image ones. Code is available at: https://github.com/layer6ai-labs/fusemix.

Self-supervised representation learning (SSRL) has advanced considerably by exploiting the transformation invariance assumption under artificially designed data augmentations. While augmentation-based SSRL algorithms push the boundaries of performance in computer vision and natural language processing, they are often not directly applicable to other data modalities, and can conflict with application-specific data augmentation constraints. This paper presents an SSRL approach that can be applied to any data modality and network architecture because it does not rely on augmentations or masking. Specifically, we show that high-quality data representations can be learned by reconstructing random data projections. We evaluate the proposed approach on a wide range of representation learning tasks that span diverse modalities and real-world applications. We show that it outperforms multiple state-of-the-art SSRL baselines. Due to its wide applicability and strong empirical results, we argue that learning from randomness is a fruitful research direction worthy of attention and further study.

In response to everyday queries, humans explicitly signal uncertainty and offer alternative answers when they are unsure. Machine learning models that output calibrated prediction sets through conformal prediction mimic this human behaviour; larger sets signal greater uncertainty while providing alternatives. In this work, we study the usefulness of conformal prediction sets as an aid for human decision making by conducting a pre-registered randomized controlled trial with conformal prediction sets provided to human subjects. With statistical significance, we find that when humans are given conformal prediction sets their accuracy on tasks improves compared to fixed-size prediction sets with the same coverage guarantee. The results show that quantifying model uncertainty with conformal prediction is helpful for human-in-the-loop decision making and human-AI teams.

Likelihood-based deep generative models (DGMs) commonly exhibit a puzzling behaviour: when trained on a relatively complex dataset, they assign higher likelihood values to out-of-distribution (OOD) data from simpler sources. Adding to the mystery, OOD samples are never generated by these DGMs despite having higher likelihoods. This two-pronged paradox has yet to be conclusively explained, making likelihood-based OOD detection unreliable. Our primary observation is that high-likelihood regions will not be generated if they contain minimal probability mass. We demonstrate how this seeming contradiction of large densities yet low probability mass can occur around data confined to low-dimensional manifolds. We also show that this scenario can be identified through local intrinsic dimension (LID) estimation, and propose a method for OOD detection which pairs the likelihoods and LID estimates obtained from a *pre-trained* DGM. Our method can be applied to normalizing flows and score-based diffusion models, and obtains results which match or surpass state-of-the-art OOD detection benchmarks using the same DGM backbones. Our code is available at our [GitHub repository](https://github.com/layer6ai-labs/dgm_ood_detection).

High-dimensional data commonly lies on low-dimensional submanifolds, and estimating the local intrinsic dimension (LID) of a datum -- i.e. the dimension of the submanifold it belongs to -- is a longstanding problem. LID can be understood as the number of local factors of variation: the more factors of variation a datum has, the more complex it tends to be. Estimating this quantity has proven useful in contexts ranging from generalization in neural networks to detection of out-of-distribution data, adversarial examples, and AI-generated text. The recent successes of deep generative models present an opportunity to leverage them for LID estimation, but current methods based on generative models produce inaccurate estimates, require more than a single pre-trained model, are computationally intensive, or do not exploit the best available deep generative models: diffusion models (DMs). In this work, we show that the Fokker-Planck equation associated with a DM can provide an LID estimator which addresses the aforementioned deficiencies. Our estimator, called FLIPD, is easy to implement and compatible with all popular DMs. Applying FLIPD to synthetic LID estimation benchmarks, we find that DMs implemented as fully-connected networks are highly effective LID estimators that outperform existing baselines. We also apply FLIPD to natural images where the true LID is unknown. Despite being sensitive to the choice of network architecture, FLIPD estimates remain a useful measure of relative complexity; compared to competing estimators, FLIPD exhibits a consistently higher correlation with image PNG compression rate and better aligns with qualitative assessments of complexity. Notably, FLIPD is orders of magnitude faster than other LID estimators, and the first to be tractable at the scale of Stable Diffusion.

We systematically study a wide variety of generative models spanning semantically-diverse image datasets to understand and improve the feature extractors and metrics used to evaluate them. Using best practices in psychophysics, we measure human perception of image realism for generated samples by conducting the largest experiment evaluating generative models to date, and find that no existing metric strongly correlates with human evaluations. Comparing to 17 modern metrics for evaluating the overall performance, fidelity, diversity, rarity, and memorization of generative models, we find that the state-of-the-art perceptual realism of diffusion models as judged by humans is not reflected in commonly reported metrics such as FID. This discrepancy is not explained by diversity in generated samples, though one cause is over-reliance on Inception-V3. We address these flaws through a study of alternative self-supervised feature extractors, find that the semantic information encoded by individual networks strongly depends on their training procedure, and show that DINOv2-ViT-L/14 allows for much richer evaluation of generative models. Next, we investigate data memorization, and find that generative models do memorize training examples on simple, smaller datasets like CIFAR10, but not necessarily on more complex datasets like ImageNet. However, our experiments show that current metrics do not properly detect memorization: none in the literature is able to separate memorization from other phenomena such as underfitting or mode shrinkage. To facilitate further development of generative models and their evaluation we release all generated image datasets, human evaluation data, and a modular library to compute 17 common metrics for 9 different encoders at https://github.com/layer6ai-labs/dgm-eval.

Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data supported on an unknown low-dimensional manifold, a common occurrence in real-world domains such as image data. Recent attempts to remedy this limitation have introduced geometric complications that defeat a central benefit of normalizing flows: exact density estimation. We recover this benefit with Conformal Embedding Flows, a framework for designing flows that learn manifolds with tractable densities. We argue that composing a standard flow with a trainable conformal embedding is the most natural way to model manifold-supported data. To this end, we present a series of conformal building blocks and apply them in experiments with synthetic and real-world data to demonstrate that flows can model manifold-supported distributions without sacrificing tractable likelihoods.