We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic normal distribution, samples undergo sharp, discrete transitions, eventually forming distinct events of a desired distribution while progressively revealing finer structure. As this process is reversible, these transitions also occur in reverse, where intermediate states progressively merge, tracing a path back to the initial distribution. We demonstrate that these transitions can be detected as discontinuities in nth-order cross-fluctuations. For variance-preserving SDEs, we derive a closed-form for these cross-fluctuations that is efficiently computable for the reverse trajectory. We find that detecting these transitions directly boosts sampling efficiency, accelerates class-conditional and rare-class generation, and improves two zero-shot tasks-image classification and style transfer-without expensive grid search or retraining. We also show that this viewpoint unifies classical coupling and mixing from finite Markov chains with continuous dynamics while extending to stochastic SDEs and non Markovian samplers.

Multi-Agent Debate (MAD) has emerged as a promising paradigm for improving the performance of large language models through collaborative reasoning. Despite recent advances, the key factors driving MAD's effectiveness remain unclear. In this work, we disentangle MAD into two key components-Majority Voting and inter-agent Debate-and assess their respective contributions. Through extensive experiments across seven NLP benchmarks, we find that Majority Voting alone accounts for most of the performance gains typically attributed to MAD. To explain this, we propose a theoretical framework that models debate as a stochastic process. We prove that it induces a martingale over agents' belief trajectories, implying that debate alone does not improve expected correctness. Guided by these insights, we demonstrate that targeted interventions, by biasing the belief update toward correction, can meaningfully enhance debate effectiveness. Overall, our findings suggest that while MAD has potential, simple ensembling methods remain strong and more reliable alternatives in many practical settings.

Recent advances in Large Vision-Language Models (LVLMs) have showcased strong reasoning abilities across multiple modalities, achieving significant breakthroughs in various real-world applications. Despite this great success, the safety guardrail of LVLMs may not cover the unforeseen domains introduced by the visual modality. Existing studies primarily focus on eliciting LVLMs to generate harmful responses via carefully crafted image-based jailbreaks designed to bypass alignment defenses. In this study, we reveal that a safe image can be exploited to achieve the same jailbreak consequence when combined with additional safe images and prompts. This stems from two fundamental properties of LVLMs: universal reasoning capabilities and safety snowball effect. Building on these insights, we propose Safety Snowball Agent (SSA), a novel agent-based framework leveraging agents' autonomous and tool-using abilities to jailbreak LVLMs. SSAoperates through two principal stages: (1) initial response generation, where tools generate or retrieve jailbreak images based on potential harmful intents, and (2) harmful snowballing, where refined subsequent prompts induce progressively harmful outputs. Our experiments demonstrate that SSAcan use nearly any image to induce LVLMs to produce unsafe content, achieving high success jailbreaking rates against the latest LVLMs. Unlike prior works that exploit alignment flaws, SSAleverages the inherent properties of LVLMs, presenting a profound challenge for enforcing safety in generative multimodal systems.

Machine learning models have achieved widespread success but often inherit and amplify historical biases, resulting in unfair outcomes. Traditional fairness methods typically impose constraints at the prediction level, without addressing underlying biases in data representations. In this work, we propose a principled framework that adjusts data representations to balance predictive utility and fairness. Using sufficient dimension reduction, we decompose the feature space into target-relevant, sensitive, and shared components, and control the fairness-utility trade-off by selectively removing sensitive information. We provide a theoretical analysis of how prediction error and fairness gaps evolve as shared subspaces are added, and employ influence functions to quantify their effects on the asymptotic behavior of parameter estimates. Experiments on both synthetic and real-world datasets validate our theoretical insights and show that the proposed method effectively improves fairness while preserving predictive performance.

Finetuning provides a scalable and cost-effective means of customizing language models for specific tasks or response styles, with greater reliability than prompting or in-context learning. In contrast, the conventional wisdom is that injecting knowledge via finetuning results in brittle performance and poor generalization. We argue that the dichotomy of "task customization" (e.g., instruction tuning) and "knowledge injection" (e.g., teaching new facts) is a distinction without a difference. We instead identify concrete factors that explain the heterogeneous effectiveness observed with finetuning. To this end, we conduct a large-scale experimental study of finetuning the frontier Gemini v1.5 model family on a spectrum of datasets that are artificially engineered to interpolate between the strengths and failure modes of finetuning. Our findings indicate that question-answer training data formats provide much stronger knowledge generalization than document/articlestyle training data, numerical information can be harder for finetuning to retain than categorical information, and models struggle to apply finetuned knowledge during multi-step reasoning even when trained on similar examples--all factors that render "knowledge injection" to be especially difficult, even after controlling for considerations like data augmentation and information volume. On the other hand, our findings also indicate that it is not fundamentally more difficult to finetune information about a real-world event than information about writing style.

Meritocratic systems, from admissions to hiring, aim to impartially reward skill and effort.

Large Reasoning Models (LRMs) have become powerful tools for complex problem solving, but their structured reasoning pathways can lead to unsafe outputs when exposed to harmful prompts. Existing safety alignment methods reduce harmful outputs but can degrade reasoning depth, leading to significant trade-offs in complex, multi-step tasks, and remain vulnerable to sophisticated jailbreak attacks. To address this, we introduce SAFEPATH, a lightweight alignment method that fine-tunes LRMs to emit a short, 8-token Safety Primer at the start of their reasoning, in response to harmful prompts, while leaving the rest of the reasoning process unsupervised. Empirical results across multiple benchmarks indicate that SAFEPATH effectively reduces harmful outputs while maintaining reasoning performance. Specifically, SAFEPATH reduces harmful responses by up to 90.0% and blocks 83.3% of jailbreak attempts in the DeepSeek-R1-Distill-Llama-8B model, while requiring 295.9x less compute than Direct Refusal and 314.1x less than SafeChain. We further introduce a zero-shot variant that requires no finetuning. In addition, we provide a comprehensive analysis of how existing methods in LLMs generalize, or fail, when applied to reasoning-centric models, revealing critical gaps and new directions for safer AI. We release model and code at https://ai-isl.github.io/safepath.

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This paper presents PartCAD, a novel framework for reconstructing CAD modeling sequences directly from point clouds by projection-guided, part-aware geometry reasoning.

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