A fundamental problem in combinatorial optimization is identifying equivalent formulations. Despite the growing need for automated equivalence checks -- driven, for example, by optimization copilots, which generate problem formulations from natural language descriptions -- current approaches rely on simple heuristics that fail to reliably check formulation equivalence. Inspired by Karp reductions, in this work we introduce Quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings for scalable, reliable equivalence checking, with a verification stage that ensures mapped solutions preserve feasibility and optimality without additional solver calls. To evaluate our approach, we construct EquivaFormulation, the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.
The assessment of argument quality depends on well-established logical, rhetorical, and dialectical properties that are unavoidably subjective: multiple valid assessments may exist, there is no unequivocal ground truth. This aligns with recent paths in machine learning, which embrace the co-existence of different perspectives. However, this potential remains largely unexplored in NLP research on argument quality. One crucial reason seems to be the yet unexplored availability of suitable datasets. We fill this gap by conducting a systematic review of argument quality datasets. We assign them to a multi-layered categorization targeting two aspects: (a) What has been annotated: we collect the quality dimensions covered in datasets and consolidate them in an overarching taxonomy, increasing dataset comparability and interoperability. (b) Who annotated: we survey what information is given about annotators, enabling perspectivist research and grounding our recommendations for future actions. To this end, we discuss datasets suitable for developing perspectivist models (i.e., those containing individual, non-aggregated annotations), and we showcase the importance of a controlled selection of annotators in a pilot study.
Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using Levy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations. We provide a self-contained overview of LP ambiguity sets and their connections to popular metrics such as Wasserstein and Total Variation. We show that the link between conformal prediction and LP ambiguity sets is a natural one: by propagating the LP ambiguity set through the scoring function, we reduce complex high-dimensional distribution shifts to manageable one-dimensional distribution shifts, enabling exact quantification of worst-case quantiles and coverage. Building on this analysis, we construct robust conformal prediction intervals that remain valid under distribution shifts, explicitly linking LP parameters to interval width and confidence levels. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.
Training Large Language Models (LLMs) with synthetic data is a prevalent practice in code generation. A key approach is self-training, where LLMs are iteratively trained on self-generated correct code snippets. In this case, the self-generated codes are drawn from a conditional distribution, conditioned on a specific seed description. However, the seed description is not the only valid representation that aligns with its intended meaning. With all valid descriptions and codes forming a joint space, codes drawn from the conditional distribution would lead to an underrepresentation of the full description-code space. As such, we propose Gibbs Fine-Tuning (GiFT), a novel self-training method inspired by Gibbs sampling. GiFT allows self-generated data to be drawn from the marginal distribution of the joint space, thereby mitigating the biases inherent in conditional sampling. We provide a theoretical analysis demonstrating the potential benefits of fine-tuning LLMs with code derived from the marginal distribution. Furthermore, we propose a perplexity-based code selection method to mitigate the imbalanced long-tail distribution of the self-generated codes. Empirical evaluation of two LLMs across four datasets demonstrates that GiFT achieves superior performance, particularly on more challenging benchmarks. Source code is available at https://github.com/Alex-HaochenLi/GiFT.
In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical constraints of SAT problems by factoring their CNF representations into simplified multi-level, multi-output Boolean functions. It then leverages gradient-based optimization to guide the search for a diverse set of valid solutions. Our method operates directly on the circuit structure of refactored SAT instances, reinterpreting the SAT problem as a supervised multi-output regression task. This differentiable technique enables independent bit-wise operations on each tensor element, allowing parallel execution of learning processes. As a result, we achieve GPU-accelerated sampling with significant runtime improvements ranging from $33.6\times$ to $523.6\times$ over state-of-the-art heuristic samplers. We demonstrate the superior performance of our sampling method through an extensive evaluation on $60$ instances from a public domain benchmark suite utilized in previous studies.
Federated Learning presents a nascent approach to machine learning, enabling collaborative model training across decentralized devices while safeguarding data privacy. However, its distributed nature renders it susceptible to adversarial attacks. Integrating blockchain technology with Federated Learning offers a promising avenue to enhance security and integrity. In this paper, we tackle the potential of blockchain in defending Federated Learning against adversarial attacks. First, we test Proof of Federated Learning, a well known consensus mechanism designed ad-hoc to federated contexts, as a defense mechanism demonstrating its efficacy against Byzantine and backdoor attacks when at least one miner remains uncompromised. Second, we propose Krum Federated Chain, a novel defense strategy combining Krum and Proof of Federated Learning, valid to defend against any configuration of Byzantine or backdoor attacks, even when all miners are compromised. Our experiments conducted on image classification datasets validate the effectiveness of our proposed approaches.
Estimating associations between spatial covariates and responses - rather than merely predicting responses - is central to environmental science, epidemiology, and economics. For instance, public health officials might be interested in whether air pollution has a strictly positive association with a health outcome, and the magnitude of any effect. Standard machine learning methods often provide accurate predictions but offer limited insight into covariate-response relationships. And we show that existing methods for constructing confidence (or credible) intervals for associations fail to provide nominal coverage in the face of model misspecification and distribution shift - despite both being essentially always present in spatial problems. We introduce a method that constructs valid frequentist confidence intervals for associations in spatial settings. Our method requires minimal assumptions beyond a form of spatial smoothness. In particular, we do not require model correctness or covariate overlap between training and target locations. Our approach is the first to guarantee nominal coverage in this setting and outperforms existing techniques in both real and simulated experiments.
Safety-critical perception systems require both reliable uncertainty quantification and principled abstention mechanisms to maintain safety under diverse operational conditions. We present a novel dual-threshold conformalization framework that provides statistically-guaranteed uncertainty estimates while enabling selective prediction in high-risk scenarios. Our approach uniquely combines a conformal threshold ensuring valid prediction sets with an abstention threshold optimized through ROC analysis, providing distribution-free coverage guarantees (>= 1 - alpha) while identifying unreliable predictions. Through comprehensive evaluation on CIFAR-100, ImageNet1K, and ModelNet40 datasets, we demonstrate superior robustness across camera and LiDAR modalities under varying environmental perturbations. The framework achieves exceptional detection performance (AUC: 0.993 to 0.995) under severe conditions while maintaining high coverage (>90.0%) and enabling adaptive abstention (13.5% to 63.4% +/- 0.5) as environmental severity increases. For LiDAR-based perception, our approach demonstrates particularly strong performance, maintaining robust coverage (>84.5%) while appropriately abstaining from unreliable predictions. Notably, the framework shows remarkable stability under heavy perturbations, with detection performance (AUC: 0.995 +/- 0.001) significantly outperforming existing methods across all modalities. Our unified approach bridges the gap between theoretical guarantees and practical deployment needs, offering a robust solution for safety-critical autonomous systems operating in challenging real-world conditions.
Uncertainty quantification in time series prediction is challenging due to the temporal dependence and distribution shift on sequential data. Conformal inference provides a pivotal and flexible instrument for assessing the uncertainty of machine learning models through prediction sets. Recently, a series of online conformal inference methods updated thresholds of prediction sets by performing online gradient descent on a sequence of quantile loss functions. A drawback of such methods is that they only use the information of revealed non-conformity scores via miscoverage indicators but ignore error quantification, namely the distance between the non-conformity score and the current threshold. To accurately leverage the dynamic of miscoverage error, we propose \textit{Error-quantified Conformal Inference} (ECI) by smoothing the quantile loss function. ECI introduces a continuous and adaptive feedback scale with the miscoverage error, rather than simple binary feedback in existing methods. We establish a long-term coverage guarantee for ECI under arbitrary dependence and distribution shift. The extensive experimental results show that ECI can achieve valid miscoverage control and output tighter prediction sets than other baselines.
Generating novel crystalline materials has the potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in determining their physical properties. However, existing crystal generation methods either fail to generate materials that display the symmetries of real-world crystals, or simply replicate the symmetry information from examples in a database. To address this limitation, we propose SymmCD, a novel diffusion-based generative model that explicitly incorporates crystallographic symmetry into the generative process. We decompose crystals into two components and learn their joint distribution through diffusion: 1) the asymmetric unit, the smallest subset of the crystal which can generate the whole crystal through symmetry transformations, and; 2) the symmetry transformations needed to be applied to each atom in the asymmetric unit. We also use a novel and interpretable representation for these transformations, enabling generalization across different crystallographic symmetry groups. We showcase the competitive performance of SymmCD on a subset of the Materials Project, obtaining diverse and valid crystals with realistic symmetries and predicted properties.
Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models offer a cost-effective alternative that can potentially attain higher statistical precision. However, the benefits of in silico experiments come with a significant risk: statistical inferences are not valid if the models fail to accurately predict experimental responses to interventions. In this paper, we propose a novel approach that integrates the predictions from multiple foundation models with experimental data while preserving valid statistical inference. Our estimator is consistent and asymptotically normal, with asymptotic variance no larger than the standard estimator based on experimental data alone. Importantly, these statistical properties hold even when model predictions are arbitrarily biased. Empirical results across several randomized experiments show that our estimator offers substantial precision gains, equivalent to a reduction of up to 20% in the sample size needed to match the same precision as the standard estimator based on experimental data alone.
Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for high-dimensional and non-polynomial systems. Given the analytical nature of the candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature. Full implementation is available on \href{https://github.com/JieFeng-cse/Analytical-Lyapunov-Function-Discovery}{Github}
Machine learning models are increasingly used to produce predictions that serve as input data in subsequent statistical analyses. For example, computer vision predictions of economic and environmental indicators based on satellite imagery are used in downstream regressions; similarly, language models are widely used to approximate human ratings and opinions in social science research. However, failure to properly account for errors in the machine learning predictions renders standard statistical procedures invalid. Prior work uses what we call the Predict-Then-Debias estimator to give valid confidence intervals when machine learning algorithms impute missing variables, assuming a small complete sample from the population of interest. We expand the scope by introducing bootstrap confidence intervals that apply when the complete data is a nonuniform (i.e., weighted, stratified, or clustered) sample and to settings where an arbitrary subset of features is imputed. Importantly, the method can be applied to many settings without requiring additional calculations. We prove that these confidence intervals are valid under no assumptions on the quality of the machine learning model and are no wider than the intervals obtained by methods that do not use machine learning predictions.
Inspired by the success of Large Language Models (LLMs), the development of Large Atom Models (LAMs) has gained significant momentum in scientific computation. Since 2022, the Deep Potential team has been actively pretraining LAMs and launched the OpenLAM Initiative to develop an open-source foundation model spanning the periodic table. A core objective is establishing comprehensive benchmarks for reliable LAM evaluation, addressing limitations in existing datasets. As a first step, the LAM Crystal Philately competition has collected over 19.8 million valid structures, including 1 million on the OpenLAM convex hull, driving advancements in generative modeling and materials science applications.
The Handbook of Combinatorial Designs catalogs many types of combinatorial designs, together with lists of open instances for which existence has not yet been determined. We develop a constructive protocol CPro1, which uses Large Language Models (LLMs) to generate code that constructs combinatorial designs and resolves some of these open instances. The protocol starts from a definition of a particular type of design, and a verifier that reliably confirms whether a proposed design is valid. The LLM selects strategies and implements them in code, and scaffolding provides automated hyperparameter tuning and execution feedback using the verifier. Most generated code fails, but by generating many candidates, the protocol automates exploration of a variety of standard methods (e.g. simulated annealing, genetic algorithms) and experimentation with variations (e.g. cost functions) to find successful approaches. Testing on 16 different types of designs, CPro1 constructs solutions to open instances for 6 of them: Symmetric and Skew Weighing Matrices, Equidistant Permutation Arrays, Packing Arrays, Balanced Ternary Designs, and Florentine Rectangles.
Benchmarking and establishing proper statistical validation metrics for reinforcement learning (RL) remain ongoing challenges, where no consensus has been established yet. The emergence of quantum computing and its potential applications in quantum reinforcement learning (QRL) further complicate benchmarking efforts. To enable valid performance comparisons and to streamline current research in this area, we propose a novel benchmarking methodology, which is based on a statistical estimator for sample complexity and a definition of statistical outperformance. Furthermore, considering QRL, our methodology casts doubt on some previous claims regarding its superiority. We conducted experiments on a novel benchmarking environment with flexible levels of complexity. While we still identify possible advantages, our findings are more nuanced overall. We discuss the potential limitations of these results and explore their implications for empirical research on quantum advantage in QRL.
We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.
De novo generation of hit-like molecules is a challenging task in the drug discovery process. Most methods in previous studies learn the semantics and syntax of molecular structures by analyzing molecular graphs or simplified molecular input line entry system (SMILES) strings; however, they do not take into account the drug responses of the biological systems consisting of genes and proteins. In this study we propose a hybrid neural network, HNN2Mol, which utilizes gene expression profiles to generate molecular structures with desirable phenotypes for arbitrary target proteins. In the algorithm, a variational autoencoder is employed as a feature extractor to learn the latent feature distribution of the gene expression profiles. Then, a long short-term memory is leveraged as the chemical generator to produce syntactically valid SMILES strings that satisfy the feature conditions of the gene expression profile extracted by the feature extractor. Experimental results and case studies demonstrate that the proposed HNN2Mol model can produce new molecules with potential bioactivities and drug-like properties.
The problem of evaluating the effectiveness of a treatment or policy commonly appears in causal inference applications under network interference. In this paper, we suggest the new method of high-dimensional network causal inference (HNCI) that provides both valid confidence interval on the average direct treatment effect on the treated (ADET) and valid confidence set for the neighborhood size for interference effect. We exploit the model setting in Belloni et al. (2022) and allow certain type of heterogeneity in node interference neighborhood sizes. We propose a linear regression formulation of potential outcomes, where the regression coefficients correspond to the underlying true interference function values of nodes and exhibit a latent homogeneous structure. Such a formulation allows us to leverage existing literature from linear regression and homogeneity pursuit to conduct valid statistical inferences with theoretical guarantees. The resulting confidence intervals for the ADET are formally justified through asymptotic normalities with estimable variances. We further provide the confidence set for the neighborhood size with theoretical guarantees exploiting the repro samples approach. The practical utilities of the newly suggested methods are demonstrated through simulation and real data examples.
Test Input Generators (TIGs) are crucial to assess the ability of Deep Learning (DL) image classifiers to provide correct predictions for inputs beyond their training and test sets. Recent advancements in Generative AI (GenAI) models have made them a powerful tool for creating and manipulating synthetic images, although these advancements also imply increased complexity and resource demands for training. In this work, we benchmark and combine different GenAI models with TIGs, assessing their effectiveness, efficiency, and quality of the generated test images, in terms of domain validity and label preservation. We conduct an empirical study involving three different GenAI architectures (VAEs, GANs, Diffusion Models), five classification tasks of increasing complexity, and 364 human evaluations. Our results show that simpler architectures, such as VAEs, are sufficient for less complex datasets like MNIST. However, when dealing with feature-rich datasets, such as ImageNet, more sophisticated architectures like Diffusion Models achieve superior performance by generating a higher number of valid, misclassification-inducing inputs.