Current LLM evaluation relies on two complementary but often disconnected signals: static benchmarks with objective correctness labels and arena-style preference data that better reflect open-ended user interactions. We introduce DualEval, a latent model-item calibration framework that represents models and evaluation items in a shared space, jointly estimating model ability together with item difficulty and sharpness. We apply DualEval across four domains: coding, math, miscellaneous domain-knowledge tasks, and generic everyday user queries. Our evaluation uses 18 frontier LLMs, static benchmark labels, and reward-model scores validated against held-out human preferences for open-ended model responses. Empirically, our framework produces reliable and balanced model rankings, and its learned item-level profiles support downstream applications such as benchmark compression for sample-efficient evaluation and anomaly detection for contamination or outlier analysis. Overall, DualEval unifies static and arena-style evaluation through joint model-item calibration, producing model rankings and item-level diagnostics that support more sample-efficient, interpretable, and auditable evaluation pipelines.

Large language models (LLMs) are increasingly deployed, yet their outputs can be highly sensitive to routine, non-adversarial variation in how users phrase queries, a gap not well addressed by existing red-teaming efforts. We propose Green Shielding, a user-centric agenda for building evidence-backed deployment guidance by characterizing how benign input variation shifts model behavior. We operationalize this agenda through the CUE criteria: benchmarks with authentic Context, reference standards and metrics that capture true Utility, and perturbations that reflect realistic variations in the Elicitation of model behavior. Guided by the PCS framework and developed with practicing physicians, we instantiate Green Shielding in medical diagnosis through HealthCareMagic-Diagnosis (HCM-Dx), a benchmark of patient-authored queries, together with structured reference diagnosis sets and clinically grounded metrics for evaluating differential diagnosis lists. We also study perturbation regimes that capture routine input variation and show that prompt-level factors shift model behavior along clinically meaningful dimensions. Across multiple frontier LLMs, these shifts trace out Pareto-like tradeoffs. In particular, neutralization, which removes common user-level factors while preserving clinical content, increases plausibility and yields more concise, clinician-like differentials, but reduces coverage of highly likely and safety-critical conditions. Together, these results show that interaction choices can systematically shift task-relevant properties of model outputs and support user-facing guidance for safer deployment in high-stakes domains. Although instantiated here in medical diagnosis, the agenda extends naturally to other decision-support settings and agentic AI systems.

We study post-calibration uncertainty for trained ensembles of classifiers. Specifically, we consider both aleatoric (label noise) and epistemic (model) uncertainty. Among the most popular and widely used calibration methods in classification are temperature scaling (i.e., pool-then-calibrate) and conformal methods. However, the main shortcoming of these calibration methods is that they do not balance the proportion of aleatoric and epistemic uncertainty. Not balancing these uncertainties can severely misrepresent predictive uncertainty, leading to overconfident predictions in some input regions while being underconfident in others. To address this shortcoming, we present a simple but powerful calibration algorithm Joint Uncertainty Calibration (JUCAL) that jointly calibrates aleatoric and epistemic uncertainty. JUCAL jointly calibrates two constants to weight and scale epistemic and aleatoric uncertainties by optimizing the negative log-likelihood (NLL) on the validation/calibration dataset. JUCAL can be applied to any trained ensemble of classifiers (e.g., transformers, CNNs, or tree-based methods), with minimal computational overhead, without requiring access to the models' internal parameters. We experimentally evaluate JUCAL on various text classification tasks, for ensembles of varying sizes and with different ensembling strategies. Our experiments show that JUCAL significantly outperforms SOTA calibration methods across all considered classification tasks, reducing NLL and predictive set size by up to 15

One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic regression, the feedback can be either soft labels, corresponding to the true conditional probability of the data (as in distillation), or sampled hard labels (taking values ± 1). We point out a fundamental problem that arises even in a particularly favorable setting, where the goal is to learn a noise-free soft target of the form σ(𝐱^⊤𝐰^⋆). In the over-constrained case (i.e. the number of samples n exceeds the input dimension d) with examples (𝐱_i,σ(𝐱_i^⊤𝐰^⋆)), it is sufficient to recover 𝐰^⋆ and hence achieve the Bayes risk. However, we prove that when the examples are labeled by hard labels y_i sampled from the same conditional distribution σ(𝐱_i^⊤𝐰^⋆) and 𝐰^⋆ is s-sparse, then rotation-invariant algorithms are provably suboptimal: they incur an excess risk Ω(d-1/n), while there are simple non-rotation invariant algorithms with excess risk O(slog d/n). The simplest rotation invariant algorithm is gradient descent on the logistic loss (with early stopping). A simple non-rotation-invariant algorithm for sparse targets that achieves the above upper bounds uses gradient descent on the weights u_i,v_i, where now the linear weight w_i is reparameterized as u_iv_i.

Data science is a pillar of artificial intelligence (AI), which is transforming nearly every domain of human activity, from the social and physical sciences to engineering and medicine. While data-driven findings in AI offer unprecedented power to extract insights and guide decision-making, many are difficult or impossible to replicate. A key reason for this challenge is the uncertainty introduced by the many choices made throughout the data science life cycle (DSLC). Traditional statistical frameworks often fail to account for this uncertainty. The Predictability-Computability-Stability (PCS) framework for veridical (truthful) data science (VDS) offers a principled approach to addressing this challenge throughout the DSLC. This paper presents an updated and streamlined PCS workflow, tailored for practitioners and enhanced with guided use of generative AI (GenAI). We include a running example to display the PCS framework in action and conduct a related case study that showcases the uncertainty in downstream predictions caused by judgement calls in the data cleaning stage. This article is part of the theme issue 'Statistical workflow'.

Empirical scaling laws for language models have encouraged the development of ever-larger LLMs, despite their growing computational and memory costs. Sparse Mixture-of-Experts (MoEs) offer a promising alternative by activating only a subset of experts per forward pass, improving efficiency without sacrificing performance. However, the large number of expert parameters still leads to substantial memory consumption. Existing pruning methods typically allocate budgets uniformly across layers, overlooking the heterogeneous redundancy that arises in sparse MoEs. We propose GRAPE (Global Redundancy-Aware Pruning of Experts, a global pruning strategy that dynamically allocates pruning budgets based on cross-layer redundancy. Experiments on Mixtral-8x7B, Mixtral-8x22B, DeepSeek-MoE, Qwen-MoE, and GPT-OSS show that, under the same pruning budget, GRAPE consistently achieves the best average performance. On the three main models reported in the paper, it improves average accuracy over the strongest local baseline by 1.40

Agentic data science (ADS) pipelines have grown rapidly in both capability and adoption, with systems such as OpenAI Codex now able to directly analyze datasets and produce answers to statistical questions. However, these systems can reach falsely optimistic conclusions that are difficult for users to detect. To address this, we propose a pair of lightweight sanity checks grounded in the Predictability-Computability-Stability (PCS) framework for veridical data science. These checks use reasonable perturbations to screen whether an agent can reliably distinguish signal from noise, acting as a falsifiability constraint that can expose affirmative conclusions as unsupported. Together, the two checks characterize the trustworthiness of an ADS output, e.g. whether it has found stable signal, is responding to noise, or is sensitive to incidental aspects of the input. We validate the approach on synthetic data with controlled signal-to-noise ratios, confirming that the sanity checks track ground-truth signal strength. We then demonstrate the checks on 11 real-world datasets using OpenAI Codex, characterizing the trustworthiness of each conclusion and finding that in 6 of the datasets an affirmative conclusion is not well-supported, even though a single ADS run may support one. We further analyze failure modes of ADS systems and find that ADS self-reported confidence is poorly calibrated to the empirical stability of its conclusions.

Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regression and online stochastic gradient descent (SGD) are polynomially suboptimal for certain categories of such problems. Moving beyond minimax theory, this work provides instance-wise comparisons of the finite-sample risks for these algorithms on any well-specified linear regression problem. Our analysis yields three key findings. First, GD dominates ridge regression: with comparable regularization, the excess risk of GD is always within a constant factor of that of ridge, but ridge can be polynomially worse even when tuned optimally. Second, GD is incomparable with SGD. While it is known that for certain problems GD can be polynomially better than SGD, the reverse is also true: we construct problems, inspired by benign overfitting theory, where optimally stopped GD is polynomially worse. Finally, GD dominates SGD for a significant subclass of problems – those with fast and continuously decaying covariance spectra – which includes all problems satisfying the standard capacity condition.

Low-Rank Adaptation (LoRA) is a widely used finetuning method for large models. Its small memory footprint allows practitioners to adapt large models to specific tasks at a fraction of the cost of full finetuning. Different modifications have been proposed to enhance its efficiency by, for example, setting the learning rate, the rank, and the initialization. Another improvement axis is adapter placement strategy: when using LoRA, practitioners usually pick module types to adapt with LoRA, such as Query and Key modules. Few works have studied the problem of adapter placement, with nonconclusive results: original LoRA paper suggested placing adapters in attention modules, while other works suggested placing them in the MLP modules. Through an intuitive theoretical analysis, we introduce PLoP (Precise LoRA Placement), a lightweight method that allows automatic identification of module types where LoRA adapters should be placed, given a pretrained model and a finetuning task. We demonstrate that PLoP consistently outperforms, and in the worst case competes, with commonly used placement strategies through comprehensive experiments on supervised finetuning and reinforcement learning for reasoning.

In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD with a constant step size successfully finds a global minimum for any batch size choice. However, the particular global minimum found depends upon the batch size. In the full-batch setting, we show that the solution is dense (i.e., not sparse) and is highly aligned with its initialized direction, showing that relatively little feature learning occurs. On the other hand, for any batch size strictly smaller than the number of samples, SGD finds a global minimum which is sparse and nearly orthogonal to its initialization, showing that the randomness of stochastic gradients induces a qualitatively different type of "feature selection" in this setting. Moreover, if we measure the sharpness of the minimum by the trace of the Hessian, the minima found with full batch gradient descent are flatter than those found with strictly smaller batch sizes, in contrast to previous works which suggest that large batches lead to sharper minima. To prove convergence of SGD with a constant step size, we introduce a powerful tool from the theory of non-homogeneous random walks which may be of independent interest.

Tree-based ensembles such as random forests remain the go-to for tabular data over deep learning models due to their prediction performance and computational efficiency. These advantages have led to their widespread deployment in high-stakes domains, where interpretability is essential for ensuring trustworthy predictions. This has motivated the development of popular local feature importance methods such as LIME and TreeSHAP. However, these approaches rely on approximations that ignore the model's internal structure and instead depend on potentially unstable perturbations. These issues are addressed in the global setting by MDI+, a global feature importance method which combines tree-based and linear feature importances by exploiting an equivalence between decision trees and least squares on a transformed node basis. However, the global MDI+ scores are not able to explain predictions when faced with heterogeneous individual characteristics. To address this gap, we propose Local MDI+ (LMDI+), a novel extension of the MDI+ framework that quantifies feature importances for each particular sample. Across twelve real-world benchmark datasets, LMDI+ outperforms existing baselines at identifying instance-specific predictive features, yielding an average 10

Large language models (LLMs) have revolutionized machine learning due to their ability to capture complex interactions between input features. Popular post-hoc explanation methods like SHAP provide marginal feature attributions, while their extensions to interaction importances only scale to small input lengths (approximate to 20). We propose Spectral Explainer (SPEX), a model-agnostic interaction attribution algorithm that efficiently scales to large input lengths (approximate to 1000). SPEX exploits underlying natural sparsity among interactions-common in real-world data-and applies a sparse Fourier transform using a channel decoding algorithm to efficiently identify important interactions. We perform experiments across three difficult long-context datasets that require LLMs to utilize interactions between inputs to complete the task. For large inputs, SPEX outperforms marginal attribution methods by up to 20% in terms of faithfully reconstructing LLM outputs. Further, SPEX successfully identifies key features and interactions that strongly influence model output. For one of our datasets, HotpotQA, SPEX provides interactions that align with human annotations. Finally, we use our model-agnostic approach to generate explanations to demonstrate abstract reasoning in closed-source LLMs (GPT-4o mini) and compositional reasoning in vision-language models.

Concept bottleneck models (CBM) aim to improve model interpretability by predicting human level "concepts" in a bottleneck within a deep learning model architecture. However, how the predicted concepts are used in predicting the target still either remains black-box or is simplified to maintain interpretability at the cost of prediction performance. We propose to use Fast Interpretable Greedy Sum-Trees (FIGS) to obtain Binary Distillation (BD). This new method, called FIGS-BD, distills a binary-augmented concept-to-target portion of the CBM into an interpretable tree-based model, while maintaining the competitive prediction performance of the CBM teacher. FIGS-BD can be used in downstream tasks to explain and decompose CBM predictions into interpretable binary-concept-interaction attributions and guide adaptive test-time intervention. Across 4 datasets, we demonstrate that our adaptive test-time intervention identifies key concepts that significantly improve performance for realistic human-in-the-loop settings that only allow for limited concept interventions.

As machine learning (ML) enters high-stakes domains, trustworthy uncertainty quantification (UQ) is essential for safety. In this paper we introduce PCS-UQ, a framework based on the Predictability, Computability, and Stability (PCS) principles for veridical data science. Starting with a candidate set of models or algorithms, PCS-UQ integrates a rigorous prediction-check to screen out unsuitable models in the set and utilizes bootstrap samples, in order to capture both inter-sample variability and algorithmic instability for the prediction-checked algorithms. We then introduce a novel multiplicative calibration scheme to enhance local adaptivity, which basically corresponds to a new score in conformal prediction. Moreover, we produce a compilation of 17 real-world regression datasets with manually-constructed subgroups. On this benchmark, PCS-UQ maintains the target coverage while outperforming or matching conformal methods equipped with oracle-selected algorithms in interval width. PCS-UQ achieves consistent subgroup coverage, outperforming these oracle-selected conformal methods. Notably, PCS-UQ stands out in achieving both competitive interval widths and consistent subgroup coverage.Across 6 classification datasets, PCS-UQ reduces prediction set sizes by 20%. To scale the framework for deep learning, we propose computationally efficient variants that bypass expensive retraining. On three computer vision benchmarks, these variants reduce prediction set sizes by 20% over conformal baselines. Finally, we provide theoretical proof that a modified PCS-UQ algorithm preserves valid coverage under exchangeability as a form of split conformal inference.

Data science is a pillar of artificial intelligence (AI), which is transforming nearly every domain of human activity, from the social and physical sciences to engineering and medicine. While data-driven findings in AI offer unprecedented power to extract insights and guide decision-making, many are difficult or impossible to replicate. A key reason for this challenge is the uncertainty introduced by the many choices made throughout the data science life cycle (DSLC). Traditional statistical frameworks often fail to account for this uncertainty. The Predictability-Computability-Stability (PCS) framework for veridical (truthful) data science offers a principled approach to addressing this challenge throughout the DSLC. This paper presents an updated and streamlined PCS workflow, tailored for practitioners and enhanced with guided use of generative AI. We include a running example to display the PCS framework in action, and conduct a related case study which showcases the uncertainty in downstream predictions caused by judgment calls in the data cleaning stage.

In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum l(2)-margin solution-a phenomenon known as the implicit bias of GD. This work investigates additional regularization effects induced by early stopping in well-specified high-dimensional logistic regression. We first demonstrate that the excess logistic risk vanishes for early-stopped GD but diverges to infinity for GD iterates at convergence. This suggests that early-stopped GD is well-calibrated, whereas asymptotic GD is statistically inconsistent. Second, we show that to attain a small excess zero-one risk, polynomially many samples are sufficient for early-stopped GD, while exponentially many samples are necessary for any interpolating estimator, including asymptotic GD. This separation underscores the statistical benefits of early stopping in the overparameterized regime. Finally, we establish nonasymptotic bounds on the norm and angular differences between early-stopped GD and l(2)-regularized empirical risk minimizer, thereby connecting the implicit regularization of GD with explicit l(2)-regularization.

Modern machine learning has achieved impressive prediction performance, but often sacrifices interpretability, a critical consideration in high-stakes domains such as medicine. In such settings, practitioners often use highly interpretable decision tree models, but these suffer from inductive bias against additive structure. To overcome this bias, we propose Fast Interpretable Greedy-Tree Sums (FIGS), which generalizes the Classification and Regression Trees (CART) algorithm to simultaneously grow a flexible number of trees in summation. By combining logical rules with addition, FIGS adapts to additive structure while remaining highly interpretable. Experiments on real-world datasets show FIGS achieves state-of-the-art prediction performance. To demonstrate the usefulness of FIGS in high-stakes domains, we adapt FIGS to learn clinical decision instruments (CDIs), which are tools for guiding decision-making. Specifically, we introduce a variant of FIGS known as Group Probability-Weighted Tree Sums (G-FIGS) that accounts for heterogeneity in medical data. G-FIGS derives CDIs that reflect domain knowledge and enjoy improved specificity (by up to 20% over CART) without sacrificing sensitivity or interpretability. Theoretically, we prove that FIGS learns components of additive models, a property we refer to as disentanglement. Further, we show (under oracle conditions) that tree-sum models leverage disentanglement to generalize more efficiently than single tree models when fitted to additive regression functions. Finally, to avoid overfitting with an unconstrained number of splits, we develop Bagging-FIGS, an ensemble version of FIGS that borrows the variance reduction techniques of random forests. Bagging-FIGS performs competitively with random forests and XGBoost on real-world datasets.

We develop Latent Exploration Score (LES) to mitigate over-exploration in Latent Space Optimization (LSO), a popular method for solving black-box discrete optimization problems. LSO utilizes continuous optimization within the latent space of a Variational Autoencoder (VAE) and is known to be susceptible to over-exploration, which manifests in unrealistic solutions that reduce its practicality. LES leverages the trained decoder’s approximation of the data distribution, and can be employed with any VAE decoder–including pretrained ones–without additional training, architectural changes or access to the training data. Our evaluation across five LSO benchmark tasks and twenty-two VAE models demonstrates that LES always enhances the quality of the solutions while maintaining high objective values, leading to improvements over existing solutions in most cases. We believe that new avenues to LSO will be opened by LES’ ability to identify out of distribution areas, differentiability, and computational tractability.

Domain adaptation (DA) is a statistical learning problem that arises when the distribution of the source data used to train a model differs from that of the target data used to evaluate the model. While many DA algorithms have demonstrated considerable empirical success, blindly applying these algorithms can often lead to worse performance on new datasets. To address this, it is crucial to clarify the assumptions under which a DA algorithm has good target performance. In this work, we focus on the assumption of the presence of conditionally invariant components (CICs), which are relevant for prediction and remain conditionally invariant across the source and target data. We demonstrate that CICs, which can be estimated through conditional invariant penalty (CIP), play three prominent roles in providing target risk guarantees in DA. First, we propose a new algorithm based on CICs, importance-weighted conditional invariant penalty (IW-CIP), which has target risk guarantees beyond simple settings such as covariate shift and label shift. Second, we show that CICs help identify large discrepancies between source and target risks of other DA algorithms. Finally, we demonstrate that incorporating CICs into the domain invariant projection (DIP) algorithm can address its failure scenario caused by label-flipping features. We support our new algorithms and theoretical findings via numerical experiments on synthetic data, MNIST, CelebA, Camelyon17, and DomainNet datasets.

The Madden-Julian Oscillation (MJO) is a large-scale tropical phenomenon where fluctuations of clouds, rainfall, winds, and pressure propagate eastward around the globe every 30 to 90 days on average. The MJO has significant impacts on weather and climate both locally and globally. Despite its importance, forecasting the MJO remains challenging due to the limitations of traditional numerical and statistical methods. To address this, machine learning has emerged as a promising avenue for MJO forecasting (Martin et al. 2022, Silini et al. 2021, Delaunay and Christensen 2022). Apart from accurate forecasts emphasized in previous research, our study aims to get more physical insights: we build a predictive and interpretable convolution neural network (CNN) and unravel what tropical waves at which spatial scales are essential for MJO forecasting. Our CNN model takes tropical reanalysis maps as input and predicts the MJO index, achieving forecast skills comparable to NCEP Climate Forecast System (CFSv2). This level of skill is state-of-art in interpretable neural networks. To understand what information is crucial to our MJO forecast, we decompose the output of each convolution layer into tropical waves at different zonal scales. We find that the CNN focuses on large-scale patterns whose zonal scale is above 2500 km. In fact, even when fed exclusively with large-scale features as input, the CNN achieves MJO forecasts akin to the skill of the original model. Furthermore, the CNN chooses to reconstruct large-scale features from input containing solely small-scale features instead of relying directly on small scales for forecasting. This reconstruction further emphasizes the critical role of large-scale patterns in MJO predictions. In future research, we plan to perform a systematic analysis to evaluate the contribution of different tropical waves to MJO forecasting. We will also simplify the model architecture to facilitate better understanding. Additionally, we plan to incorporate more previous time steps as input memories to enhance forecast accuracy. This work represents a promising advance towards economic yet precise MJO forecasting.