Authors: Eric Eaton, Surbhi Goel, Marcel Hussing, Michael Kearns, Aaron Roth, Sikata Bela Sengupta, Jessica Sorrell
Organizations: Department of Computer and Information Sciences, University of Pennsylvania · Department of Computer Science, The Johns Hopkins University
Numerous lines of aim to control model disagreement -- the extent to which two machine learning models disagree in their predictions. We adopt a simple and standard notion of model disagreement in real-valued prediction problems, namely the expected squared difference in predictions between two models trained on independent samples, without any coordination of the training processes. We would like to be able to drive disagreement to zero with some natural parameter(s) of the training procedure using analyses that can be applied to existing training methodologies. We develop a simple general technique for proving bounds on independent model disagreement based on anchoring to the average of two models within the analysis. We then apply this technique to prove disagreement bounds for four commonly used machine learning algorithms: (1) stacked aggregation over an arbitrary model class (where disagreement is driven to 0 with the number of models k being stacked) (2) gradient boosting (where disagreement is driven to 0 with the number of iterations k) (3) neural network training with architecture search (where disagreement is driven to 0 with the size n of the architecture being optimized over) and (4) regression tree training over all regression trees of fixed depth (where disagreement is driven to 0 with the depth d of the tree architecture). For clarity, we work out our initial bounds in the setting of one-dimensional regression with squared error loss -- but then show that all of our results generalize to multi-dimensional regression with any strongly convex loss.
Statistical learning theory studies when data-driven algorithms generalize, how many samples they need, and what statistical or computational limits apply.
Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes. In this paper, we tackle these issues by providing new disagreement-based certificates for the gap between the true risk of any two predictors. We then bound the true risk of the predictor of interest via a surrogate model that enjoys tight generalization guarantees, and by evaluating our disagreement bound on an unlabeled dataset.We empirically demonstrate the tightness of the obtained certificates and showcase the versatility of the approach by training surrogate models leveraging three different frameworks: sample compression, model compression and PAC-Bayes theory. Importantly, such guarantees are achieved without modifying the target model, nor adapting the training procedure to the generalization framework.
Language-model judges and reward models enable scalable supervision, but finite optimization can exploit evaluator errors rather than improve response quality. We characterize this failure through the covariance geometry of evaluator ensembles. For calibrated judges, the ensemble mean retains common-mode error along the all-ones direction, whereas cross-judge disagreement captures only orthogonal error. Consequently, disagreement can be high despite robust aggregation, or low while shared response-dependent errors persist. We prove that common-mode error is not identifiable from internal judge scores alone. Under a joint sub-Gaussian model, we bound best-of-K selection overstatement and target-quality regret, extending the guarantees to predictably adaptive search under conditional calibration. The resulting search terms scale as the square root of log K and are asymptotically tight for Gaussian projected errors. We further show that noisy quality proxies introduce artificial rank-one covariance without changing disagreement, and propose a bounded two-anchor Bernstein certificate for finite-search error and regret. Fixed-seed Gaussian stress tests over 120 (J, rho, K) configurations and real-model audits validate the theory while revealing the limits of disagreement-based diagnostics under increasing search pressure.
Fariya Afrin, Ibne Farabi Shihab
Department of Computer Science, Kalinga Institute of Industrial Technology · Department of Computer Science, Iowa State University
Foundation models are increasingly adopted across a wide range of applications, often serving as core blocks within AI systems. Yet different foundation models may encode the same input from multiple different views, leading to substantial representation disagreement, which we term Rashomon Representation. Such disagreement often signals inputs that a given model encodes in a way inconsistent with other models, offering a valuable yet underexplored signal for input reliability estimation. While prior work has largely focused on measuring disagreement across multiple models with a representation set, we instead focus on predicting disagreement from a single representation. We hypothesize that this disagreement follows some consistent, input-dependent patterns rather than occurring at random. To test this, we quantify disagreement by comparing each sample's nearest neighbors across different models' representation spaces, then train a lightweight predictor that estimates disagreement from a single model's representation. At inference time, given a new input, the predictor uses that input's representation to tell whether it aligns with or diverges from those of other models. Extensive experiments across diverse foundation models and datasets show that representational disagreement is indeed input-dependent, predictable, and generalizable, enabling efficient reliability estimation of foundation models.
Mingyue Ma, Zongbo Han, Changqing Zhang +1
Beijing University of Posts and Telecommunications · Tianjin University