Symbolic regression is a fundamental tool for discovering interpretable mathematical expressions from data, with broad applications across scientific and engineering domains. Recently, large language models (LLMs) have demonstrated strong performance in this task, leveraging embedded scientific priors and reasoning capabilities to surpass traditional methods. However, existing LLM-based approaches, such as LLM-SR, often over-rely on internal priors, lacking explicit data understanding and systematic reflection during equation generation. To address these limitations, we propose DrSR (Dual Reasoning Symbolic Regression), a framework that combines data-driven insight with reflective learning to enhance both robustness and discovery capability. Specifically, DrSR guides LLMs to analyze structural relationships (e.g., monotonicity, nonlinearity, and correlation) within the data to generate structured descriptions. Simultaneously, it monitors equation performance and establishes a feedback loop to refine subsequent generations. By integrating data understanding and generation reflection in a closed loop, DrSR enables more efficient exploration of the symbolic expression space. Experiments across interdisciplinary datasets in physics, chemistry, biology, and materials science demonstrate that DrSR substantially improves the valid equation rate and consistently outperforms both classical and recent LLM-based methods in terms of accuracy, generalization, and search efficiency. These results underscore its potential for scientific equation discovery.
Large language models (LLMs) exhibit compelling linguistic behaviour, and sometimes offer self-reports, that is to say statements about their own nature, inner workings, or behaviour. In humans, such reports are often attributed to a faculty of introspection and are typically linked to consciousness. This raises the question of how to interpret self-reports produced by LLMs, given their increasing linguistic fluency and cognitive capabilities. To what extent (if any) can the concept of introspection be meaningfully applied to LLMs? Here, we present and critique two examples of apparent introspective self-report from LLMs. In the first example, an LLM attempts to describe the process behind its own "creative" writing, and we argue this is not a valid example of introspection. In the second example, an LLM correctly infers the value of its own temperature parameter, and we argue that this can be legitimately considered a minimal example of introspection, albeit one that is (presumably) not accompanied by conscious experience.
Large Language Models (LLMs) excel at many tasks but struggle with ambiguous scenarios where multiple valid responses exist, often yielding unreliable results. Conversely, Small Language Models (SLMs) demonstrate robustness in such scenarios but are susceptible to misleading or adversarial inputs. We observed that LLMs handle negative examples effectively, while SLMs excel with positive examples. To leverage their complementary strengths, we introduce SLIDE (Small and Large Integrated for Dialogue Evaluation), a method integrating SLMs and LLMs via adaptive weighting. Building on SLIDE, we further propose a Dual-Refinement Evaluation (DRE) method to enhance SLM-LLM integration: (1) SLM-generated insights guide the LLM to produce initial evaluations; (2) SLM-derived adjustments refine the LLM's scores for improved accuracy. Experiments demonstrate that DRE outperforms existing methods, showing stronger alignment with human judgment across diverse benchmarks. This work illustrates how combining small and large models can yield more reliable evaluation tools, particularly for open-ended tasks such as dialogue evaluation.
Text-to-SQL systems translate natural language (NL) questions into SQL queries, enabling non-technical users to interact with structured data. While large language models (LLMs) have shown promising results on the text-to-SQL task, they often produce semantically incorrect yet syntactically valid queries, with limited insight into their reliability. We propose SQLens, an end-to-end framework for fine-grained detection and correction of semantic errors in LLM-generated SQL. SQLens integrates error signals from both the underlying database and the LLM to identify potential semantic errors within SQL clauses. It further leverages these signals to guide query correction. Empirical results on two public benchmarks show that SQLens outperforms the best LLM-based self-evaluation method by 25.78% in F1 for error detection, and improves execution accuracy of out-of-the-box text-to-SQL systems by up to 20%.
Automating the enrichment of UML class diagrams with behavioral methods from natural language use cases is a significant challenge. This study evaluates nine large language models (LLMs) in augmenting a methodless UML diagram (21 classes, 17 relationships) using 21 structured waste-management use cases. A total of 90 diagrams (3,373 methods) were assessed across six metrics: method quantity, signature richness (visibility, names, parameters, return types), annotation completeness (linking to use cases/actions), structural fidelity, syntactic correctness (PlantUML compilation), and naming convergence (across models). All LLMs produced valid PlantUML diagrams adhering to UML conventions. Some models excelled in method coverage and annotation accuracy, while others showed richer parameterization but weaker traceability. These results demonstrate that LLMs can generate well-structured methods with consistent naming, advancing automated behavioral modeling. However, inconsistencies in annotations and signatures highlight the need for improved prompt engineering and model selection. The rapid generation of these methods supports Agile practices by enabling faster design iterations. Despite their capabilities, human oversight is essential to ensure accuracy, appropriateness, and semantic alignment. This positions LLMs as collaborative partners in software design. All experimental artifacts (\texttt{.puml}, \texttt{.png}, \texttt{.csv}) are publicly available for reproducibility.
Stuttering is a complex disorder that requires specialized expertise for effective assessment and treatment. This paper presents an effort to enhance the FluencyBank dataset with a new stuttering annotation scheme based on established clinical standards. To achieve high-quality annotations, we hired expert clinicians to label the data, ensuring that the resulting annotations mirror real-world clinical expertise. The annotations are multi-modal, incorporating audiovisual features for the detection and classification of stuttering moments, secondary behaviors, and tension scores. In addition to individual annotations, we additionally provide a test set with highly reliable annotations based on expert consensus for assessing individual annotators and machine learning models. Our experiments and analysis illustrate the complexity of this task that necessitates extensive clinical expertise for valid training and evaluation of stuttering assessment models.
The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated approximation methods like entropy-regularized optimal transport, downsampling, and subsampling, which trade accuracy for computational efficiency. In this paper, we consider the challenge of computing efficient approximations to the Wasserstein metric that also serve as strict upper or lower bounds. Focusing on discrete measures on regular grids, our approach involves formulating and exactly solving a Kantorovich problem on a coarse grid using a quantized measure and specially designed cost matrix, followed by an upscaling and correction stage. This is done either in the primal or dual space to obtain valid upper and lower bounds on the Wasserstein metric of the full-resolution inputs. We evaluate our methods on the DOTmark optimal transport images benchmark, demonstrating a 10x-100x speedup compared to entropy-regularized OT while keeping the approximation error below 2%.
Recent advances in object detectors have led to their adoption for industrial uses. However, their deployment in critical applications is hindered by the inherent lack of reliability of neural networks and the complex structure of object detection models. To address these challenges, we turn to Conformal Prediction, a post-hoc procedure which offers statistical guarantees that are valid for any dataset size, without requiring prior knowledge on the model or data distribution. Our contribution is manifold: first, we formally define the problem of Conformal Object Detection (COD) and introduce a novel method, Sequential Conformal Risk Control (SeqCRC), that extends the statistical guarantees of Conformal Risk Control (CRC) to two sequential tasks with two parameters, as required in the COD setting. Then, we propose loss functions and prediction sets suited to applying CRC to different applications and certification requirements. Finally, we present a conformal toolkit, enabling replication and further exploration of our methods. Using this toolkit, we perform extensive experiments, yielding a benchmark that validates the investigated methods and emphasizes trade-offs and other practical consequences.
Vision-Language Models (VLMs) have demonstrated remarkable progress in multimodal understanding, yet their capabilities for scientific reasoning remains inadequately assessed. Current multimodal benchmarks predominantly evaluate generic image comprehension or text-driven reasoning, lacking authentic scientific contexts that require domain-specific knowledge integration with visual evidence analysis. To fill this gap, we present CSVQA, a diagnostic multimodal benchmark specifically designed for evaluating scientific reasoning through domain-grounded visual question answering.Our benchmark features 1,378 carefully constructed question-answer pairs spanning diverse STEM disciplines, each demanding domain knowledge, integration of visual evidence, and higher-order reasoning. Compared to prior multimodal benchmarks, CSVQA places greater emphasis on real-world scientific content and complex reasoning.We additionally propose a rigorous evaluation protocol to systematically assess whether model predictions are substantiated by valid intermediate reasoning steps based on curated explanations. Our comprehensive evaluation of 15 VLMs on this benchmark reveals notable performance disparities, as even the top-ranked proprietary model attains only 49.6\% accuracy.This empirical evidence underscores the pressing need for advancing scientific reasoning capabilities in VLMs. Our CSVQA is released at https://huggingface.co/datasets/Skywork/CSVQA.
LLM providers typically offer multiple LLM tiers, varying in performance and price. As NLP tasks become more complex and modularized, selecting the suitable LLM tier for each subtask is a key challenge to balance between cost and performance. To address the problem, we introduce LLM Automatic Transmission (LLM-AT) framework that automatically selects LLM tiers without training. LLM-AT consists of Starter, Generator, and Judge. The starter selects the initial LLM tier expected to solve the given question, the generator produces a response using the LLM of the selected tier, and the judge evaluates the validity of the response. If the response is invalid, LLM-AT iteratively upgrades to a higher-tier model, generates a new response, and re-evaluates until a valid response is obtained. Additionally, we propose accuracy estimator, which enables the suitable initial LLM tier selection without training. Given an input question, accuracy estimator estimates the expected accuracy of each LLM tier by computing the valid response rate across top-k similar queries from past inference records. Experiments demonstrate that LLM-AT achieves superior performance while reducing costs, making it a practical solution for real-world applications.
We consider the problem of statistical inference when the data is collected via a Thompson Sampling-type algorithm. While Thompson Sampling (TS) is known to be both asymptotically optimal and empirically effective, its adaptive sampling scheme poses challenges for constructing confidence intervals for model parameters. We propose and analyze a variant of TS, called Stable Thompson Sampling, in which the posterior variance is inflated by a logarithmic factor. We show that this modification leads to asymptotically normal estimates of the arm means, despite the non-i.i.d. nature of the data. Importantly, this statistical benefit comes at a modest cost: the variance inflation increases regret by only a logarithmic factor compared to standard TS. Our results reveal a principled trade-off: by paying a small price in regret, one can enable valid statistical inference for adaptive decision-making algorithms.
Large language models (LLMs) are increasingly used for data generation. However, creating evaluation benchmarks raises the bar for this emerging paradigm. Benchmarks must target specific phenomena, penalize exploiting shortcuts, and be challenging. Through two case studies, we investigate whether LLMs can meet these demands by generating reasoning over-text benchmarks and comparing them to those created through careful crowdsourcing. Specifically, we evaluate both the validity and difficulty of LLM-generated versions of two high-quality reading comprehension datasets: CondaQA, which evaluates reasoning about negation, and DROP, which targets reasoning about quantities. We find that prompting LLMs can produce variants of these datasets that are often valid according to the annotation guidelines, at a fraction of the cost of the original crowdsourcing effort. However, we show that they are less challenging for LLMs than their human-authored counterparts. This finding sheds light on what may have been lost by generating evaluation data with LLMs, and calls for critically reassessing the immediate use of this increasingly prevalent approach to benchmark creation.
We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian latents explaining statistical dependence between observations at different time steps, combining the intuition of contrastive methods with the flexible tools of probabilistic generative models. Unlike contrastive approaches, the RP-GSSM is a valid probabilistic model learned via maximum likelihood. Unlike generative approaches, the RP-GSSM has no need for an explicit network mapping from latents to observations, allowing it to focus model capacity on inference of latents. The model is both tractable and expressive: it admits exact inference thanks to its jointly Gaussian latent prior, while maintaining expressivity with an arbitrarily nonlinear neural network link between observations and latents. These qualities allow the RP-GSSM to learn task-relevant latents without ad-hoc regularization, auxiliary losses, or optimizer scheduling. We show how this approach outperforms alternatives on problems that include learning nonlinear stochastic dynamics from video, with or without background distractors. Our results position the RP-GSSM as a useful foundation model for a variety of downstream applications.
In this work, we investigate the relationship between model generalization and counterfactual explainability in supervised learning. We introduce the notion of $\varepsilon$-valid counterfactual probability ($\varepsilon$-VCP) -- the probability of finding perturbations of a data point within its $\varepsilon$-neighborhood that result in a label change. We provide a theoretical analysis of $\varepsilon$-VCP in relation to the geometry of the model's decision boundary, showing that $\varepsilon$-VCP tends to increase with model overfitting. Our findings establish a rigorous connection between poor generalization and the ease of counterfactual generation, revealing an inherent trade-off between generalization and counterfactual explainability. Empirical results validate our theory, suggesting $\varepsilon$-VCP as a practical proxy for quantitatively characterizing overfitting.
Fitting Gaussian Processes (GPs) provides interpretable aleatoric uncertainty quantification for estimation of spatio-temporal fields. Spatio-temporal deep learning models, while scalable, typically assume a simplistic independent covariance matrix for the response, failing to capture the underlying correlation structure. However, spatio-temporal GPs suffer from issues of scalability and various forms of approximation bias resulting from restrictive assumptions of the covariance kernel function. We propose STACI, a novel framework consisting of a variational Bayesian neural network approximation of non-stationary spatio-temporal GP along with a novel spatio-temporal conformal inference algorithm. STACI is highly scalable, taking advantage of GPU training capabilities for neural network models, and provides statistically valid prediction intervals for uncertainty quantification. STACI outperforms competing GPs and deep methods in accurately approximating spatio-temporal processes and we show it easily scales to datasets with millions of observations.
We study the problem of estimating the average treatment effect (ATE) in adaptive experiments where treatment can only be encouraged--rather than directly assigned--via a binary instrumental variable. Building on semiparametric efficiency theory, we derive the efficiency bound for ATE estimation under arbitrary, history-dependent instrument-assignment policies, and show it is minimized by a variance-aware allocation rule that balances outcome noise and compliance variability. Leveraging this insight, we introduce AMRIV--an \textbf{A}daptive, \textbf{M}ultiply-\textbf{R}obust estimator for \textbf{I}nstrumental-\textbf{V}ariable settings with variance-optimal assignment. AMRIV pairs (i) an online policy that adaptively approximates the optimal allocation with (ii) a sequential, influence-function-based estimator that attains the semiparametric efficiency bound while retaining multiply-robust consistency. We establish asymptotic normality, explicit convergence rates, and anytime-valid asymptotic confidence sequences that enable sequential inference. Finally, we demonstrate the practical effectiveness of our approach through empirical studies, showing that adaptive instrument assignment, when combined with the AMRIV estimator, yields improved efficiency and robustness compared to existing baselines.
Construction of confidence intervals and hypothesis tests for functionals based on asymptotically normal estimators is a classical topic in statistical inference. The simplest and in many cases optimal inference procedure is the Wald interval or the likelihood ratio test, both of which require an estimator and an estimate of the asymptotic variance of the estimator. Estimators obtained from online/sequential algorithms forces one to consider the computational aspects of the inference problem, i.e., one cannot access all of the data as many times as needed. Several works on this topic explored the online estimation of asymptotic variance. In this article, we propose computationally efficient, rate-optimal, and asymptotically valid confidence regions based on the output of online algorithms {\em without} estimating the asymptotic variance. As a special case, this implies inference from any algorithm that yields an asymptotically normal estimator. We focus our efforts on stochastic gradient descent with Polyak averaging to understand the practical performance of the proposed method.
Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of standard confidence interval procedures based solely on labelled data, while preserving their fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.
Designing metal-organic frameworks (MOFs) with novel chemistries is a long-standing challenge due to their large combinatorial space and the complex 3D arrangements of building blocks. While recent deep generative models have enabled scalable MOF generation, they assume (1) a fixed set of building blocks and (2) known ground-truth local block-wise 3D coordinates. However, this limits their ability to (1) design novel MOFs and (2) generate the structure using novel building blocks. We propose a two-stage de novo MOF generation framework that overcomes these limitations by modeling both chemical and geometric degrees of freedom. First, we train a SMILES-based autoregressive model to generate novel metal and organic building blocks, paired with cheminformatics for 3D structure initialization. Second, we introduce a flow-matching model that predicts translations, rotations, and torsional angles to assemble flexible blocks into valid 3D frameworks. Our experiments demonstrate improved reconstruction accuracy, the generation of valid, novel, and unique MOFs, and the ability of our model to create novel building blocks.
In the previous article, we presented a quantum-inspired framework for modeling semantic representation and processing in Large Language Models (LLMs), drawing upon mathematical tools and conceptual analogies from quantum mechanics to offer a new perspective on these complex systems. In this paper, we clarify the core assumptions of this model, providing a detailed exposition of six key principles that govern semantic representation, interaction, and dynamics within LLMs. The goal is to justify that a quantum-inspired framework is a valid approach to studying semantic spaces. This framework offers valuable insights into their information processing and response generation, and we further discuss the potential of leveraging quantum computing to develop significantly more powerful and efficient LLMs based on these principles.