Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off between synthetic and real data. Our approach leverages algorithmic stability to derive generalization error bounds, characterizing the optimal synthetic-to-real data ratio that minimizes expected test error as a function of the Wasserstein distance between the real and synthetic distributions. We motivate our framework in the setting of kernel ridge regression with mixed data, offering a detailed analysis that may be of independent interest. Our theory predicts the existence of an optimal ratio, leading to a U-shaped behavior of test error with respect to the proportion of synthetic data. Empirically, we validate this prediction on CIFAR-10 and a clinical brain MRI dataset. Our theory extends to the important scenario of domain adaptation, showing that carefully blending synthetic target data with limited source data can mitigate domain shift and enhance generalization. We conclude with practical guidance for applying our results to both in-domain and out-of-domain scenarios.

Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model performance on the test set, and averages the model performance across different data splits. A well-known criticism is that such cross-validation procedure does not directly estimate the performance of the particular model recommended for future use. In this paper, we propose a new method to estimate the performance of a model trained on a specific (random) training set. A naive estimator can be obtained by applying the model to a disjoint testing set. Surprisingly, cross-validation estimators computed from other random splits can be used to improve this naive estimator within a random-effects model framework. We develop two estimators -- a hierarchical Bayesian estimator and an empirical Bayes estimator -- that perform similarly to or better than both the conventional cross-validation estimator and the naive single-split estimator. Simulations and a real-data example demonstrate the superior performance of the proposed method.

Large Language Models (LLMs) show promise in medicine but are prone to factual and logical errors, which is unacceptable in this high-stakes field. To address this, we introduce the "Haibu Mathematical-Medical Intelligent Agent" (MMIA), an LLM-driven architecture that ensures reliability through a formally verifiable reasoning process. MMIA recursively breaks down complex medical tasks into atomic, evidence-based steps. This entire reasoning chain is then automatically audited for logical coherence and evidence traceability, similar to theorem proving. A key innovation is MMIA's "bootstrapping" mode, which stores validated reasoning chains as "theorems." Subsequent tasks can then be efficiently solved using Retrieval-Augmented Generation (RAG), shifting from costly first-principles reasoning to a low-cost verification model. We validated MMIA across four healthcare administration domains, including DRG/DIP audits and medical insurance adjudication, using expert-validated benchmarks. Results showed MMIA achieved an error detection rate exceeding 98% with a false positive rate below 1%, significantly outperforming baseline LLMs. Furthermore, the RAG matching mode is projected to reduce average processing costs by approximately 85% as the knowledge base matures. In conclusion, MMIA's verifiable reasoning framework is a significant step toward creating trustworthy, transparent, and cost-effective AI systems, making LLM technology viable for critical applications in medicine.

The integration of large language models (LLMs) into conversational robots has made human-robot conversations more dynamic. Yet, LLM-powered conversational robots remain prone to errors, e.g., misunderstanding user intent, prematurely interrupting users, or failing to respond altogether. Detecting and addressing these failures is critical for preventing conversational breakdowns, avoiding task disruptions, and sustaining user trust. To tackle this problem, the ERR@HRI 2.0 Challenge provides a multimodal dataset of LLM-powered conversational robot failures during human-robot conversations and encourages researchers to benchmark machine learning models designed to detect robot failures. The dataset includes 16 hours of dyadic human-robot interactions, incorporating facial, speech, and head movement features. Each interaction is annotated with the presence or absence of robot errors from the system perspective, and perceived user intention to correct for a mismatch between robot behavior and user expectation. Participants are invited to form teams and develop machine learning models that detect these failures using multimodal data. Submissions will be evaluated using various performance metrics, including detection accuracy and false positive rate. This challenge represents another key step toward improving failure detection in human-robot interaction through social signal analysis.

Logical reasoning is a core capability for large language models (LLMs), yet existing benchmarks that rely solely on final-answer accuracy fail to capture the quality of the reasoning process. To address this, we introduce FineLogic, a fine-grained evaluation framework that assesses logical reasoning across three dimensions: overall accuracy, stepwise soundness, and representation-level probing. Leveraging this framework, we conduct a comprehensive study on how different supervision formats in fine-tuning shape reasoning abilities. We fine-tune LLMs on four supervision styles: one in natural language and three symbolic variants. We find a key trade-off: natural language supervision excels at generalization to out-of-distribution and long-chain problems, whereas symbolic supervision is superior at instilling structurally sound, atomic reasoning steps. Furthermore, our probing analysis indicates that fine-tuning primarily refines the model's step-by-step generation process, rather than improving its ability to converge on an answer early. Together, our framework and analysis provide a more rigorous lens for evaluating and improving logical reasoning in LLMs. The code is available at https://github.com/YujunZhou/FineLogic.

Most LLM fingerprinting methods teach the model to respond to a few fixed queries with predefined atypical responses (keys). This memorization often does not survive common deployment steps such as finetuning or quantization, and such keys can be easily detected and filtered from LLM responses, ultimately breaking the fingerprint. To overcome these limitations we introduce LLM fingerprinting via semantically conditioned watermarks, replacing fixed query sets with a broad semantic domain, and replacing brittle atypical keys with a statistical watermarking signal diffused throughout each response. After teaching the model to watermark its responses only to prompts from a predetermined domain e.g., French language, the model owner can use queries from that domain to reliably detect the fingerprint and verify ownership. As we confirm in our thorough experimental evaluation, our fingerprint is both stealthy and robust to all common deployment scenarios.

Parallel scaling has emerged as a powerful paradigm to enhance reasoning capabilities in large language models (LLMs) by generating multiple Chain-of-Thought (CoT) traces simultaneously. However, this approach introduces significant computational inefficiency due to inter-trace redundancy -- our analysis reveals that over 80% of parallel reasoning traces yield identical final answers, representing substantial wasted computation. To address this critical efficiency bottleneck, we propose DeepPrune, a novel framework that enables efficient parallel scaling through dynamic pruning. Our method features a specialized judge model trained with focal loss and oversampling techniques to accurately predict answer equivalence from partial reasoning traces which realizes 0.87 AUROC on equivalence prediction, combined with an online greedy clustering algorithm that dynamically prunes redundant paths while preserving answer diversity. Comprehensive evaluations across three challenging benchmarks (AIME 2024, AIME 2025, and GPQA) and multiple reasoning models demonstrate that DeepPrune achieves remarkable token reduction by over 80% compared to conventional consensus sampling on most cases, while maintaining competitive accuracy within 3 percentage points. Our work establishes a new standard for efficient parallel reasoning, making high-performance reasoning more efficient. Our code and data are here: https://deepprune.github.io/

AI-generated videos have achieved near-perfect visual realism (e.g., Sora), urgently necessitating reliable detection mechanisms. However, detecting such videos faces significant challenges in modeling high-dimensional spatiotemporal dynamics and identifying subtle anomalies that violate physical laws. In this paper, we propose a physics-driven AI-generated video detection paradigm based on probability flow conservation principles. Specifically, we propose a statistic called Normalized Spatiotemporal Gradient (NSG), which quantifies the ratio of spatial probability gradients to temporal density changes, explicitly capturing deviations from natural video dynamics. Leveraging pre-trained diffusion models, we develop an NSG estimator through spatial gradients approximation and motion-aware temporal modeling without complex motion decomposition while preserving physical constraints. Building on this, we propose an NSG-based video detection method (NSG-VD) that computes the Maximum Mean Discrepancy (MMD) between NSG features of the test and real videos as a detection metric. Last, we derive an upper bound of NSG feature distances between real and generated videos, proving that generated videos exhibit amplified discrepancies due to distributional shifts. Extensive experiments confirm that NSG-VD outperforms state-of-the-art baselines by 16.00% in Recall and 10.75% in F1-Score, validating the superior performance of NSG-VD. The source code is available at https://github.com/ZSHsh98/NSG-VD.

One paradigm of language model (LM) fine-tuning relies on creating large training datasets, under the assumption that high quantity and diversity will enable models to generalize to novel tasks after post-training. In practice, gathering large sets of data is inefficient, and training on them is prohibitively expensive; worse, there is no guarantee that the resulting model will handle complex scenarios or generalize better. Moreover, existing techniques rarely assess whether a training sample provides novel information or is redundant with the knowledge already acquired by the model, resulting in unnecessary costs. In this work, we explore a new test-time self-improvement method to create more effective and generalizable agentic LMs on-the-fly. The proposed algorithm can be summarized in three steps: (i) first it identifies the samples that model struggles with (self-awareness), (ii) then generates similar examples from detected uncertain samples (self-data augmentation), and (iii) uses these newly generated samples at test-time fine-tuning (self-improvement). We study two variants of this approach: Test-Time Self-Improvement (TT-SI), where the same model generates additional training examples from its own uncertain cases and then learns from them, and contrast this approach with Test-Time Distillation (TT-D), where a stronger model generates similar examples for uncertain cases, enabling student to adapt using distilled supervision. Empirical evaluations across different agent benchmarks demonstrate that TT-SI improves the performance with +5.48% absolute accuracy gain on average across all benchmarks and surpasses other standard learning methods, yet using 68x less training samples. Our findings highlight the promise of TT-SI, demonstrating the potential of self-improvement algorithms at test-time as a new paradigm for building more capable agents toward self-evolution.

Large language models (LLMs) are transforming cellular biology by enabling the development of "virtual cells"--computational systems that represent, predict, and reason about cellular states and behaviors. This work provides a comprehensive review of LLMs for virtual cell modeling. We propose a unified taxonomy that organizes existing methods into two paradigms: LLMs as Oracles, for direct cellular modeling, and LLMs as Agents, for orchestrating complex scientific tasks. We identify three core tasks--cellular representation, perturbation prediction, and gene regulation inference--and review their associated models, datasets, evaluation benchmarks, as well as the critical challenges in scalability, generalizability, and interpretability.