Large language model (LLM) systems suffer from the models' unstable ability to generate valid and factual content, resulting in hallucination generation. Current hallucination detection methods heavily rely on out-of-model information sources, such as RAG to assist the detection, thus bringing heavy additional latency. Recently, internal states of LLMs' inference have been widely used in numerous research works, such as prompt injection detection, etc. Considering the interpretability of LLM internal states and the fact that they do not require external information sources, we introduce such states into LLM hallucination detection. In this paper, we systematically analyze different internal states' revealing features during inference forward and comprehensively evaluate their ability in hallucination detection. Specifically, we cut the forward process of a large language model into three stages: understanding, query, generation, and extracting the internal state from these stages. By analyzing these states, we provide a deep understanding of why the hallucinated content is generated and what happened in the internal state of the models. Then, we introduce these internal states into hallucination detection and conduct comprehensive experiments to discuss the advantages and limitations.
We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away from the manifold. At the same time, we are still able to leverage a nice distribution structure. We derive non-asymptotic bounds on the approximation and generalization errors of the denoising score matching estimate. The rates of convergence are determined by the intrinsic dimension. Furthermore, our bounds remain valid even if we allow the ambient dimension grow polynomially with the sample size.
Multi-View Representation Learning (MVRL) aims to derive a unified representation from multi-view data by leveraging shared and complementary information across views. However, when views are irregularly missing, the incomplete data can lead to representations that lack sufficiency and consistency. To address this, we propose Multi-View Permutation of Variational Auto-Encoders (MVP), which excavates invariant relationships between views in incomplete data. MVP establishes inter-view correspondences in the latent space of Variational Auto-Encoders, enabling the inference of missing views and the aggregation of more sufficient information. To derive a valid Evidence Lower Bound (ELBO) for learning, we apply permutations to randomly reorder variables for cross-view generation and then partition them by views to maintain invariant meanings under permutations. Additionally, we enhance consistency by introducing an informational prior with cyclic permutations of posteriors, which turns the regularization term into a similarity measure across distributions. We demonstrate the effectiveness of our approach on seven diverse datasets with varying missing ratios, achieving superior performance in multi-view clustering and generation tasks.
Language Models (LMs) have shown substantial improvements in handling factual knowledge, yet their capability to consistently represent temporal facts, which are valid only within specific timeframes, remains underexplored. To investigate this, we introduce TimeStress, a novel dataset comprising 521K statements on 2003 of the most popular temporal facts in Wikidata. Each statement contextualizes a fact with correct and incorrect dates across three precisions (Day, Month, Year). This setup allows us to evaluate LMs' ability to discern between correct and incorrect temporal statements based on their probability of being generated. We assess 18 LMs across various architectures using two metrics: the win rate, indicating how often correct dates outperform incorrect ones, and robustness, reflecting consistent performance across all dates. Our findings reveal that while some LMs achieve a win rate exceeding 80\%, robustness remains low, with the best model achieving only 6\%. Furthermore, robust knowledge at one date precision does not reliably transfer to others, highlighting a significant generalization gap. These results underscore the struggle of LMs to maintain a consistent temporal representation, supporting their limitations as reliable sources of temporal knowledge. We provide all data and code for further research.
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences are a nonparametric tool showing under which high-level assumptions asymptotic coverage is achieved so that they also give a certain robustness guarantee against distributional deviations. In this paper, we propose a new flexible class of confidence sequences yielding sharp asymptotic time-uniform confidence sequences under mild assumptions. Furthermore, we highlight the connection to corresponding sequential testing problems and detail the underlying limit theorem.
This paper proposes valid inference tools, based on self-normalization, in time series expected shortfall regressions and, as a corollary, also in quantile regressions. Extant methods for such time series regressions, based on a bootstrap or direct estimation of the long-run variance, are computationally more involved, require the choice of tuning parameters and have serious size distortions when the regression errors are strongly serially dependent. In contrast, our inference tools only require estimates of the (quantile, expected shortfall) regression parameters that are computed on an expanding window, and are correctly sized as we show in simulations. Two empirical applications to stock return predictability and to Growth-at-Risk demonstrate the practical usefulness of the developed inference tools.
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.
Autonomous agents are often required to plan under multiple objectives whose preference ordering varies based on context. The agent may encounter multiple contexts during its course of operation, each imposing a distinct lexicographic ordering over the objectives, with potentially different reward functions associated with each context. Existing approaches to multi-objective planning typically consider a single preference ordering over the objectives, across the state space, and do not support planning under multiple objective orderings within an environment. We present Contextual Lexicographic Markov Decision Process (CLMDP), a framework that enables planning under varying lexicographic objective orderings, depending on the context. In a CLMDP, both the objective ordering at a state and the associated reward functions are determined by the context. We employ a Bayesian approach to infer a state-context mapping from expert trajectories. Our algorithm to solve a CLMDP first computes a policy for each objective ordering and then combines them into a single context-aware policy that is valid and cycle-free. The effectiveness of the proposed approach is evaluated in simulation and using a mobile robot.
Existing algorithms for online conformal prediction -- guaranteeing marginal coverage in adversarial settings -- are variants of online gradient descent (OGD), but their analyses of worst-case coverage do not follow from the regret guarantee of OGD. What is the relationship between no-regret learning and online conformal prediction? We observe that although standard regret guarantees imply marginal coverage in i.i.d. settings, this connection fails as soon as we either move to adversarial environments or ask for group conditional coverage. On the other hand, we show a tight connection between threshold calibrated coverage and swap-regret in adversarial settings, which extends to group-conditional (multi-valid) coverage. We also show that algorithms in the follow the perturbed leader family of no regret learning algorithms (which includes online gradient descent) can be used to give group-conditional coverage guarantees in adversarial settings for arbitrary grouping functions. Via this connection we analyze and conduct experiments using a multi-group generalization of the ACI algorithm of Gibbs & Candes [2021] (arXiv:2106.00170).
Overfitting is a well-known issue in machine learning that occurs when a model struggles to generalize its predictions to new, unseen data beyond the scope of its training set. Traditional techniques to mitigate overfitting include early stopping, data augmentation, and regularization. In this work, we demonstrate that the degree of overfitting of a trained model is correlated with the ability to generate counterfactual examples. The higher the overfitting, the easier it will be to find a valid counterfactual example for a randomly chosen input data point. Therefore, we introduce CF-Reg, a novel regularization term in the training loss that controls overfitting by ensuring enough margin between each instance and its corresponding counterfactual. Experiments conducted across multiple datasets and models show that our counterfactual regularizer generally outperforms existing regularization techniques.
The correct way to quantify predictive uncertainty in neural networks remains a topic of active discussion. In particular, it is unclear whether the state-of-the art entropy decomposition leads to a meaningful representation of model, or epistemic, uncertainty (EU) in the light of a debate that pits ignorance against disagreement perspectives. We aim to reconcile the conflicting viewpoints by arguing that both are valid but arise from different learning situations. Notably, we show that the presence of shortcuts is decisive for EU manifesting as disagreement.
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.
Inference in linear panel data models is complicated by the presence of fixed effects when (some of) the regressors are not strictly exogenous. Under asymptotics where the number of cross-sectional observations and time periods grow at the same rate, the within-group estimator is consistent but its limit distribution features a bias term. In this paper we show that a panel version of the moving block bootstrap, where blocks of adjacent cross-sections are resampled with replacement, replicates the limit distribution of the within-group estimator. Confidence ellipsoids and hypothesis tests based on the reverse-percentile bootstrap are thus asymptotically valid without the need to take the presence of bias into account.
Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.
Estimating the expectation of a Bernoulli random variable based on N independent trials is a classical problem in statistics, typically addressed using Binomial Proportion Confidence Intervals (BPCI). In the control systems community, many critical tasks-such as certifying the statistical safety of dynamical systems-can be formulated as BPCI problems. Conformal Prediction (CP), a distribution-free technique for uncertainty quantification, has gained significant attention in recent years and has been applied to various control systems problems, particularly to address uncertainties in learned dynamics or controllers. A variant known as training-conditional CP was recently employed to tackle the problem of safety certification. In this note, we highlight that the use of training-conditional CP in this context does not provide valid safety guarantees. We demonstrate why CP is unsuitable for BPCI problems and argue that traditional BPCI methods are better suited for statistical safety certification.
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.
Tokenization is a fundamental preprocessing step in NLP, directly impacting large language models' (LLMs) ability to capture syntactic, morphosyntactic, and semantic structures. This paper introduces a novel framework for systematically evaluating tokenization strategies, addressing challenges in morphologically rich and low-resource languages. Using a Turkish dataset of 6,200 multiple-choice questions from the Massive Multitask Language Understanding (MMLU) benchmark, the framework assesses tokenizers across five key metrics: vocabulary size, token count, processing time, language-specific token percentages (\%TR), and token purity. These metrics provide a structured approach to evaluating how well tokenizers preserve linguistic structures. While \%TR measures the proportion of valid words in the target language, \%Pure assesses the alignment of tokens with meaningful linguistic units, such as roots and valid morphemes, minimizing semantic fragmentation. The findings reveal that \%TR, introduced as a critical metric, exhibits a stronger correlation with downstream performance (e.g., MMLU scores) than token purity, emphasizing its role in improving model accuracy. Additionally, larger model parameters do not necessarily yield better tokenization quality or enhanced results, highlighting the importance of tailored tokenization strategies that prioritize linguistic alignment. This framework sets a new standard for developing robust tokenization methods optimized for morphologically complex and low-resource languages. Future work will refine morphological analysis, explore domain-specific customizations, and conduct cross-linguistic evaluations to further enhance tokenization practices.
The development of robust safety benchmarks for large language models requires open, reproducible datasets that can measure both appropriate refusal of harmful content and potential over-restriction of legitimate scientific discourse. We present an open-source dataset and testing framework for evaluating LLM safety mechanisms across mainly controlled substance queries, analyzing four major models' responses to systematically varied prompts. Our results reveal distinct safety profiles: Claude-3.5-sonnet demonstrated the most conservative approach with 73% refusals and 27% allowances, while Mistral attempted to answer 100% of queries. GPT-3.5-turbo showed moderate restriction with 10% refusals and 90% allowances, and Grok-2 registered 20% refusals and 80% allowances. Testing prompt variation strategies revealed decreasing response consistency, from 85% with single prompts to 65% with five variations. This publicly available benchmark enables systematic evaluation of the critical balance between necessary safety restrictions and potential over-censorship of legitimate scientific inquiry, while providing a foundation for measuring progress in AI safety implementation. Chain-of-thought analysis reveals potential vulnerabilities in safety mechanisms, highlighting the complexity of implementing robust safeguards without unduly restricting desirable and valid scientific discourse.
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.
The nonlinear, non-convex AC Optimal Power Flow (AC-OPF) problem is fundamental for power systems operations. The intrinsic complexity of AC-OPF has fueled a growing interest in the development of optimization proxies for the problem, i.e., machine learning models that predict high-quality, close-to-optimal solutions. More recently, dual conic proxy architectures have been proposed, which combine machine learning and convex relaxations of AC-OPF, to provide valid certificates of optimality using learning-based methods. Building on this methodology, this paper proposes, for the first time, a dual conic proxy architecture for the semidefinite (SDP) relaxation of AC-OPF problems. Although the SDP relaxation is stronger than the second-order cone relaxation considered in previous work, its practical use has been hindered by its computational cost. The proposed method combines a neural network with a differentiable dual completion strategy that leverages the structure of the dual SDP problem. This approach guarantees dual feasibility, and therefore valid dual bounds, while providing orders of magnitude of speedups compared to interior-point algorithms. The paper also leverages self-supervised learning, which alleviates the need for time-consuming data generation and allows to train the proposed models efficiently. Numerical experiments are presented on several power grid benchmarks with up to 500 buses. The results demonstrate that the proposed SDP-based proxies can outperform weaker conic relaxations, while providing several orders of magnitude speedups compared to a state-of-the-art interior-point SDP solver.