Estimating question difficulty is a critical component in evaluating and improving large language models (LLMs) for question answering (QA). Existing approaches often rely on readability formulas, retrieval-based signals, or popularity statistics, which may not fully capture the reasoning challenges posed to modern LLMs. In this paper, we introduce Q-DAPS (Question Difficulty based on Answer Plausibility Scores) method, a novel approach that estimates question difficulty by computing the entropy of plausibility scores over candidate answers. We systematically evaluate Q-DAPS across four prominent QA datasets—TriviaQA, NQ, MuSiQue, and QASC—demonstrating that it consistently outperforms baselines. Moreover, Q-DAPS shows strong robustness across hyperparameter variations and question types. Extensive ablation studies further show that Q-DAPS remains robust across different plausibility estimation paradigms, model sizes, and realistic settings. Human evaluations further confirm strong alignment between Q-DAPS’s difficulty estimates and human judgments of question difficulty. Overall, Q-DAPS provides an interpretable, scalable, and bias-resilient approach to question difficulty estimation in modern QA systems.
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Evaluating whether large language models (LLMs) capture the structureof natural language beyond local fluency remains an open challenge.Existing evaluation methods, largely based on task performance orshort-context behavior, provide limited insight into the long-rangestatistical organization of generated text.We propose a complementary evaluation framework based on repeatedsubsequences. By analyzing their distribution across scales andrelating it to higher-order Rényi entropies, we probe how textsreuse previously established structure under finite-lengthconditions. Experiments on human-written texts and length-matchedGPT-generated texts show that,while power-law models can describerestricted ranges of block length, the observed entropy growth isoften equally or better characterized by logarithmic–power forms.Across datasets, natural language exhibits stable entropy-growthpatterns over accessible ranges, with consistent average behavior despite variability across individual texts. In contrast,GPT-generated texts show systematic and statistically significantshifts in estimated exponents with model size.These results demonstrate that repeated-subsequence entropyprovides a quantitative structural diagnostic that revealssystematic differences in long-range organization,distinguishing natural language from state-of-the-art LLM outputsbeyond surface-level fluency.
A fundamental obstacle to causal discovery from text is the lack of causally annotated text data for use as ground truth, due to high annotation costs. This motivates an important task of generating text with causal graph annotations. Early template-based generation methods sacrifice text naturalness in exchange for high causal graph annotation accuracy. Recent Large Language Model (LLM)-dependent methods directly generate natural text from target graphs through LLMs, but do not guarantee causal graph annotation accuracy. Therefore, we propose iTAG, which performs real-world concept assignment to nodes before converting causal graphs into text in existing LLM-dependent methods. iTAG frames this process as an inverse problem with the causal graph as the target, iteratively examining and refining concept selection through Chain-of-Thought (CoT) reasoning so that the induced relations between concepts are as consistent as possible with the target causal relationships described by the causal graph. iTAG demonstrates both extremely high annotation accuracy and naturalness across extensive tests, and the results of testing text-based causal discovery algorithms with the generated data show high statistical correlation with real-world data. This suggests that iTAG-generated data can serve as a practical surrogate for scalable benchmarking of text-based causal discovery algorithms.
Structured pruning offers a hardware-friendly approach for efficient LLM inference. Early static methods determine fixed subnetworks through offline calibration, suffering from performance degradation and calibration sensitivity. Recent methods explore input-adaptive pruning by selecting a subset of tokens as probes to estimate hidden activations for online pruning decisions.However, existing probe selection strategies fail to identify outlier-triggering tokens, and uniform layer-wise sparsity misaligns with heterogeneous outlier distributions, leading to critical channels being incorrectly pruned. Therefore, we propose OCP (Outlier-Centric Probing for structured pruning), a principled framework that prioritizes capturing outlier-triggering tokens rather than reconstructing full hidden distributions. Specifically, OCP includes three key components: (1) sensitivity-weighted probing for FFN layers that identifies outlier patterns via precomputed weight aggregations, (2) attention-accumulated probing that leverages preceding attention matrices to identify salient tokens, and (3) online adaptive sparsity allocation that dynamically adjusts layer-wise pruning based on history-guided outlier statistics. Extensive experiments on LLaMA2, LLaMA3, and OPT demonstrate that OCP consistently outperforms state-of-the-art methods across benchmarks, achieving up to 25% perplexity reduction at 1.6\times speedup.
Towards Order Fairness: Mitigating LLMs Order Sensitivity through Dual Group Advantage Optimization
PDF ↗Large Language Models (LLMs) suffer from order bias, where their performance is affected by the arrangement order of input elements. This unfairness limits the model’s applications in scenarios such as in-context learning and Retrieval-Augmented Generation (RAG). Recent studies attempt to obtain optimal or suboptimal arrangements based on statistical results or using dataset-based search, but these methods increase inference overhead while leaving the model’s inherent order bias unresolved. Other studies mitigate order sensitivity through supervised fine-tuning using augmented training sets with multiple order variants, but often at the cost of accuracy, trapping the model in consistent yet incorrect hallucinations. In this paper, we propose Dual Group Advantage Optimization (DGAO), which aims to improve model accuracy and order stability simultaneously. DGAO calculates and balances intra-group relative accuracy advantage and inter-group relative stability advantage, rewarding the policy model for generating order-stable and correct outputs while penalizing order-sensitive or incorrect responses. This marks the first time reinforcement learning has been used to mitigate LLMs’ order sensitivity. We also propose two new metrics, Consistency Rate and Overconfidence Rate, to reveal the pseudo-stability of previous methods and guide more comprehensive evaluation. Extensive experiments demonstrate that DGAO achieves superior order fairness while improving performance on RAG, mathematical reasoning, and classification tasks. Our code is available at: https://anonymous.4open.science/r/DGAO-A481/
Scaling large language models (LLMs) improves performance but significantly increases inference costs, with feed-forward networks (FFNs) consuming the majority of computational resources. While Mixture-of-Experts (MoE) architectures can reduce this cost through sparse activation, restructuring existing dense models into MoEs typically requires extensive retraining on hundreds of billions of tokens.We propose an analytical post-training framework that rapidly restructures FFNs into sparse MoE architectures using only a small calibration dataset. The method analyzes neuron activation patterns to partition neurons into always-active shared experts and conditionally activated routed experts, then constructs a router analytically from representative neuron statistics, enabling immediate deployment or optional lightweight fine-tuning. This approach applies both to dense models and recursively to existing MoE models for hierarchical sparsity.Experiments demonstrate up to 1.17\times speedup in compute-bound scenarios with only minutes of processing and 2k-sample fine-tuning, outperforming methods requiring orders of magnitude more resources.
Traditional tabular data synthesis methods often overlook the cross-modal heterogeneity of real-world tables, where structured continuous and discrete attributes coexist with unstructured long-text columns. Existing synthesis approaches struggle to simultaneously achieve accurate statistical fidelity for non-textual attributes and consistent semantic constraints between textual and non-textual attributes. In this work, we establish the first benchmark for long-text tabular data synthesis and introduce a novel metric, termed Textual Column Correlation Fidelity (TCCF), to quantify cross-modal semantic alignment. We propose AFT-Tab, an adversarial fine-tuning framework that synergistically trains an LLM-based text generator and a deep-learning-based non-textual generator. Through a dual-feedback mechanism guided by an LLM discriminator, AFT-Tab ensures both precise statistical distributions and rigorous semantic constraints. Experimental results show that AFT-Tab significantly outperforms state-of-the-art baselines in statistical fidelity, TCCF, diversity, and downstream task utility.
What is a protest anyway? Codebook conceptualization is still a first-order concern in LLM-era classification
PDF ↗Generative large language models (LLMs) are now used extensively for text classification in computational social science (CSS). In this work, we focus on the steps before and after LLM prompting: conceptualization of the categories to classify and using LLM predictions in downstream statistical inference. We argue these steps have been overlooked in much of LLM-era CSS and LLMs can tempt analysts to skip conceptualization altogether. For example, a political scientist classifying "protest" with LLMs may never be forced to craft a definition: unlike human annotators who would ask clarifying questions, an LLM can silently accept an underspecified concept to classify and return plausible-looking labels. Using simulations, we show that conceptualization failures induce downstream inferential bias that cannot be corrected solely by a more accurate LLM or post-hoc bias correction methods. We conclude by reminding CSS analysts that conceptualization is still a first-order concern in the LLM-era and provide concrete advice for pursuing low-cost, unbiased, low-variance downstream estimates.
Social Aspects · Privacy
Federated Learning (FL) faces significant challenges due to domain heterogeneity, where data from different clients exhibit substantial statistical shifts that hinder the generalization of the global model. Although existing methods attempt to mitigate this by exchanging class prototypes, they fall short by representing an entire class's complex distribution with a single point. This oversimplification disregards the rich structural information within the data, especially across diverse domains. To address this limitation, we propose a paradigm shift from point-based representation to structure-based knowledge transfer. We introduce Federated Manifold Learning (FML), a novel framework that leverages perceptual manifolds—the intrinsic geometric structures of classes in the feature space—as rich knowledge carriers. In FML, clients transmit compressed manifolds, which are adaptively fused on the server using an attention-based Manifold Mutual Learning (MML) mechanism. This process enables domain-specific structures to learn from each other, creating a unified yet flexible global convergence target. Manifold-guided local training, enforced by a manifold approximation loss and a separation loss, further aligns local models with this global structure. Extensive experiments on the Digits and Office31 benchmarks demonstrate that FML substantially outperforms state-of-the-art methods, achieving accuracy improvements of up to 6.48%.
General Machine Learning · Transfer, Multitask and Meta-learning
Multi-task learning (MTL) aims to construct a joint model for multiple tasks by sharing a common representation across domains. To achieve this goal, existing optimization-centric methods either balance task gradients or modify the shared architecture. However, as these approaches remain agnostic to the content of the shared representation, they fail to disentangle task-relevant structure from spurious context, leading to negative transfer and poor generalization. To overcome this limitation, we propose Causal Orthogonal Representations for Multi-Task Learning (CORE-MTL) , a representation-centric framework that structurally disentangles the shared representation into semantic and residual streams, concentrating task-relevant structure in the semantic stream while relegating nuisance variation to the residual stream. We instantiate this framework in the visual domain by leveraging physical priors for structured scenes and statistical constraints for attributes. Theoretically, our method enjoys a tighter out-of-distribution generalization bound than optimization-centric methods and reduces task gradient interference without explicit gradient projection or reweighting. Empirically, CORE-MTL consistently outperforms existing methods on visual multi-task benchmarks in both in-distribution and out-of-distribution settings.
Theory · Optimization
Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms underlying these gains through a dynamical analysis of a nonlinear phase retrieval model with anisotropic Gaussian inputs, equivalent to training a two-layer neural network with quadratic activation and fixed second-layer weights. Focusing on a spiked covariance setting where the dominant variance direction is orthogonal to the signal, we show that gradient descent (GD) suffers from a variance-induced misalignment: during the early escape phase, high-variance but uninformative directions are multiplicatively amplified, degrading alignment with the true signal under strong anisotropy. In contrast, spectral gradient descent (SpecGD) removes this anisotropic magnification effect, leading to stable alignment and accelerated noise contraction. Numerical experiments confirm the theory and show that these phenomena persist under more general anisotropic covariances.
Applications · Computer Vision
Test-Time Adaptation (TTA) empowers pre-trained models to adapt online to distribution shifts during inference, but such online updates often become unstable in long-horizon deployments. Prevailing approaches attribute this failure to error accumulation from noisy pseudo-labels, relying on heuristics to gate which samples are used for updates. We argue that this statistical view is insufficient: the problem lies not only in the quality of samples but also in the directionality of their gradients. In this work, we identify a geometric failure mode termed manifold erosion. Through spectral analysis, we find that reliable gradients concentrate in a stable low-rank subspace, while gradients from confident mispredictions are high-rank yet exhibit a persistent directional leakage into this protected subspace. This leakage can accumulate coherently and gradually erode core representations, eventually leading to collapse. To address this, we propose Manifold-Aware Gradient Projection (MGP), a geometric intervention that tracks the dominant subspace online and projects gradients onto its orthogonal complement. By blocking the leakage path, MGP decouples stability from plasticity. Extensive experiments on diverse TTA benchmarks demonstrate the long-horizon stability of our method, whereas prior methods often fail.
We study program-learning methods that are efficient in both samples and computation. Classical learning theory suggests that when the target admits a short program description (for example, a short piece of ``Python code''), it can be learned from relatively few examples by performing ERM over the program class. However, this approach relies on enumerating candidate programs, which is typically exponential in the description length. In contrast, gradient-based training avoids explicit search, but for some families of short programs it can require exponentially many samples to succeed. We propose \textsc{LLM-PV}, a propose-and-verify recipe that enables ERM-style selection over a discrete program class without exhaustive enumeration. A pretrained LLM induces a proposal distribution over candidate programs; each proposal is executed, scored on a held-out validation set, and the best program is selected. The method uses no gradient updates and does not use validation feedback to adapt the sampling distribution. Across algorithmic tasks including parity variants, pattern matching, and primality testing, \textsc{LLM-PV} often recovers the exact underlying rule from a small labeled set and generalizes far beyond the training sequence lengths. In the same regimes, SGD-trained transformers and standard adaptation baselines (fine-tuning and in-context learning), as well as classical ML baselines, can fit the training data yet fail to generalize reliably. Together, these results suggest that pretrained LLM priors can serve as effective search biases for ERM, narrowing the gap between statistical and computational efficiency.
Social Aspects · Security
We propose dgMARK, a decoding-guided watermarking method for discrete diffusion language models (dLLMs). Unlike autoregressive models, dLLMs can generate tokens in arbitrary order. While an ideal conditional predictor would be invariant to this order, practical dLLMs exhibit strong sensitivity to the unmasking order, creating a new channel for watermarking. dgMARK steers the unmasking order toward positions whose high-reward candidate tokens satisfy a simple parity constraint induced by a binary hash, without explicitly reweighting the model’s learned probabilities. The method is plug-and-play with common decoding strategies (e.g., confidence, entropy, and margin-based ordering) and can be strengthened with a one-step lookahead variant. Watermarks are detected via elevated parity-matching statistics, and a sliding-window detector ensures robustness under post-editing operations including insertion, deletion, substitution, and paraphrasing.
Social Aspects · Security
Deep Neural Networks (DNNs) remain fundamentally vulnerable to backdoor attacks. Traditional data-free defenses largely operate under the paradigm of internal diagnosis methods like model repairing or input robustness, yet these approaches are often fragile under advanced attacks as they remain entangled with the victim model’s corrupted parameters. We propose a paradigm shift to data-free External Semantic Auditing, using universal Vision-Language Models (VLMs) as independent auditors to decouple defense from the compromised model. We introduce PRISM (Prototype Refinement & Inspection via Statistical Monitoring), which transforms generic VLMs into domain-adaptive gatekeepers purely via online test-time adaptation. PRISM bridges the domain gap through a Hybrid VLM Teacher that refines prototypes from the test stream and an Adaptive Router that calibrates thresholds via statistical monitoring. Evaluation across 17 datasets and 11 attack types confirms PRISM achieves state-of-the-art performance (suppressing Attack Success Rate to < 1% on CIFAR-10), proving that robust defense is achievable without touching the model weights or accessing a single training sample.
General Machine Learning · Online Learning, Active Learning and Bandits
Bagging-based ensembles, most notably Adaptive Random Forests, are among the strongest performers for learning from data streams. A common denominator across these methods is their reliance on Hoeffding Trees as base learners, which grow incrementally by testing whether a candidate split is significantly better than its alternatives using concentration inequalities. Despite their empirical success, existing Hoeffding Trees variants lack valid statistical guarantees. Current analyses rely on fixed-sample concentration bounds, while split decisions are made using data-dependent stopping rules, which invalidates their guarantees and can drive the probabilty of incorrect splits to one. We introduce a principled alternative based on \emph{anytime-valid inference}. Our method provides: (i) anytime-valid control of false splits under arbitrary data streams, including non-stationary settings; (ii) finite commitment time under a predictive advantage; and (iii) under stationary i.i.d.\ data, risk is monotone decreasing and strictly improves at every split. Empirically, we evaluate both standalone trees and their use within Adaptive Random Forests on non-stationary streams. Our method improves performance while producing substantially smaller trees.
Optimization · Stochastic
Stochastic programming is often challenged by epistemic uncertainty, where critical probability distributions are poorly characterized or unknown due to a lack of data. To address this, we pioneer a novel framework for stochastic programming that minimizes an upper confidence bound (UCB) on the expected random cost, acting as a robustness-seeking strategy. Our central contribution is the Average Percentile Upper Bound (APUB), a new statistical construct that serves as both a statistically rigorous upper bound for population means and an approximate risk metric for sample means. We rigorously prove the asymptotic correctness and consistency of APUB, establishing a reliable foundation for data-driven decision-making. We also develop practical solution methods, including a bootstrap sampling approximation method and an L-shaped method, to solve APUB optimization problems, with a specific focus on two-stage linear stochastic optimization with random recourse. Empirical demonstrations on a two-stage product mix problem reveal the significant benefits of our APUB optimization framework, which fortifies the process against epistemic uncertainty while reinforcing key decision-making attributes like reliability and consistency.
Applications · Neuroscience, Cognitive Science
Clinical brain-to-text interfaces are designed for paralysed patients who cannot provide extensive training recordings. Pre-training improves data-efficient generalisation by learning statistical priors across subjects, but these priors critically depend on context. While natural speech might unfold gradually over minutes, most methods pre-train with only a few seconds of context. Thus, we propose *MEG-XL*, a model pre-trained with 2.5 minutes of MEG context per sample, 5-300× longer than prior work, and equivalent to 191k tokens, capturing extended neural context. Fine-tuning on the task of word decoding from brain data, MEG-XL matches supervised performance with a fraction of the data (e.g. 1hr vs 50hrs) and outperforms brain foundation models. We find that models pre-trained with longer contexts learn representations that transfer better to word decoding. Our results indicate that long-context pre-training helps exploit extended neural context that other methods unnecessarily discard.
Semi‑supervised statistical inference plays a key role in biomedical research, where labeled data often have higher quality but are limited due to costly clinical annotation. Yet, existing semi‑supervised statistical inference methods rely heavily on structured variables and strictly matched covariates between labeled and unlabeled datasets -- limitations ill‑suited for the heterogeneity and unstructured nature of real-world biomedical data. Modern biomedical studies increasingly collect unstructured data (clinical notes, patient audio and video recordings), with inconsistent protocols across datasets causing covariate misalignment (for instance, detailed medication histories may be recorded in one study but not another). Recent advances in pre‑trained multimodal large language models (LLMs), which excel at handling unstructured data, present an attractive potential solution. To transform this potential into rigorous semi-supervised statistical inference methods for biomedical research, two key challenges must be addressed: (1) How can we reliably integrate LLMs to enhance semi-supervised inference efficiency without compromising statistical validity? (2) How can those efficiency gains persist despite mismatched covariates between labeled and unlabeled datasets? In this paper, we tackle these challenges by systematically *calibrating pseudo-labels* provided LLMs with a novel *prediction-invariance identification* strategy. Our resulting semi‑supervised inference framework improves parameter estimation efficiency while maintaining full statistical validity, as demonstrated through our theoretical results and illustrated in a case study for identifying key biomarkers in Alzheimer’s disease detection with speech data.
General Machine Learning · Scalable Algorithms
Heterogeneous federated learning (HtFL) has emerged as a promising approach to address heterogeneity in local computational resources and data distribution. However, existing methods cause performance degradation of model personalization because personalized and generalized knowledge are either intertwined or dominated by one of them. To address this issue, we propose a novel Elastic Mixture of Experts (EMoE) architecture on HtFL, namely FedEMoE, decoupling personalization from generalization. Specially, FedEMoE employs a multi-scale feature extraction mechanism via personalized experts to enrich personalized knowledge. Furthermore, we design an elastic shared expert to break the transferred knowledge bottleneck across heterogeneous client models. The elastic shared expert can adaptively expand or shrink according to the status of each expert by the weight spectrum analysis, respectively. Extensive experiments across statistical and model heterogeneity settings demonstrate that FedEMoE significantly outperforms state-of-the art methods on the accuracy of each heterogeneous model over diverse datasets.