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Applications · Chemistry, Physics, and Earth Sciences

Mohammad Rashed, Duarte Filipe Valoroso Madeira, Babak Gholami, Caglar Guerbuez, Yunjia Yang, Nils Thuerey

Surrogate models for topology optimization (TO) exhibit highly variable out-of-distribution (OOD) generalization under distribution shifts such as changing loads or boundary conditions, yet the source of this variability remains unclear. We hypothesize that OOD performance is governed by how much information the conditioning signal preserves about the adjoint sensitivity (reduced gradient) that drives classical TO. Modeling the TO pipeline as a causal Markov chain, the Data Processing Inequality establishes that, under this abstraction, the sensitivity field is an information-theoretically optimal conditioning signal for topology prediction. However, computing exact adjoint sensitivities can be expensive or unavailable in practice; we observe that certain physical fields can approximate sensitivities through monotone transformations. To formalize this, we introduce \textbf{pseudo-sensitivities} to characterize which fields enable generalization versus those that are information-poor. We then show that a sensitivity-conditioned Bernoulli flow-matching generator empirically confirms these predictions: conditioning on sensitivities yields state-of-the-art OOD performance, while increasingly distant physical fields degrade toward raw parameter conditioning. We further benchmark against competitive baselines, and find the same ordering of conditioning signals and the same OOD trends. Results hold across structural TO benchmarks under load shifts and our new CFD-TO dataset under boundary-condition shifts such as multi-outlet configurations.

Deep Learning · Large Language Models

Frédéric Berdoz, Luca Lanzendörfer, Fabian Farestam, Roger Wattenhofer

Large reasoning models (LRMs) are often evaluated using metrics such as final-answer accuracy or token count. However, identical scores on these metrics can hide fundamentally different reasoning structures. To address this limitation, we introduce a scalable LRM benchmark of logic puzzles and a pipeline that converts unstructured traces into verifiable reasoning graphs of claims and dependencies. This turns reasoning into a structured, measurable object whose topology can be quantitatively analyzed. Building on this, we define a reasoning efficiency metric that quantifies how concentrated the model's logical flow is. Our analysis on open-source reasoning models shows that structural measurements separate behaviors that token count and accuracy conflate, providing a practical tool for diagnosing failure modes and comparing how reasoning scales with puzzle difficulty.

Sejun Park, Yeachan Park, Geonho Hwang

Research on the expressive power of neural networks has identified the minimum depth and width of neural networks that enable universal approximation and memorization. However, existing results are derived under exact arithmetic and cannot be directly applied to real implementations on computers, which can only use a finite set of numbers and inexact machine operations with round-off errors. In this work, we study floating-point ReLU networks that have floating-point parameters and use floating-point operations. Specifically, we investigate their minimum depth and width to represent all functions from the set of floating-point vectors $\mathbb F^d$ to the set of floating-point numbers $\mathbb F$. We first show that the minimum depth for representing all functions from $\mathbb F^d$ to $\mathbb F$ is exactly three, where two layers can be sufficient if we consider a smaller domain and/or codomain. We further show that the minimum width for representing all functions from $\mathbb F^d$ to $\mathbb F$ lies between $2d$ and $2d+4$. In addition, if we restrict the domain to non-negative floats, it lies between $d$ and $d+4$, where it can be smaller for a smaller domain, even beyond $d$. Our results show that the existing results analyzed under exact arithmetic do not extend to the floating-point setup.

Social Aspects · Privacy

Huikang Liu, Aras Selvi, Wolfram Wiesemann

We design a class of additive noise mechanisms that satisfy $(\varepsilon, \delta)$-differential privacy (DP) for scalar, real-valued query functions with known sensitivities, with a particular focus on moderate and low-privacy regimes. These mechanisms, which we call *mixture mechanisms*, are constructed by mixing multiple Gaussian distributions that share the same variance but differ in their means and mixture weights. The resulting distributions can be interpreted as convex combinations of a zero-mean Gaussian (as used in the analytic Gaussian mechanism) and additional Gaussians whose means depend on the sensitivity of the query function. We derive tight conditions on the variances required for $(\varepsilon, \delta)$-DP and provide efficient algorithms to compute them. Compared to the analytic Gaussian mechanism, our mechanisms yield substantially lower expected noise amplitudes ($l_1$-loss) and variances ($l_2$-loss for zero-mean distributions). In the low-privacy regime that motivates our design, our mechanisms approach optimality, mitigating nearly all of the optimality gap of the analytic Gaussian mechanism.

Yao Zhu, Yunjian Zhang, Yang Li, Wang Lu, Xiu Yan, Rui Sun

Low-rank approximation has emerged as a cornerstone technique for model compression and parameter-efficient fine-tuning, enabling substantial reductions in computation and memory without altering model architectures. However, existing approaches often overlook the shifts in feature distributions induced by the approximation process, which can lead to error amplification and unstable inference. We propose a distribution-aware whitening framework that dynamically whitens layer inputs based on the evolving feature distributions, ensuring second-order isotropy of input features. This allows that the discarded components in the low-rank approximation are those with minimal impact on model outputs, thereby minimizing cumulative approximation errors across layers. We theoretically analyze how distribution misalignment leads to error propagation and demonstrate that our approach achieves tighter control over layerwise distortion. Extensive experiments across various large language models demonstrate the superiority of our method in post-training compression. Moreover, our method can also serve as an effective initialization for LoRA-style parameter-efficient fine-tuning. Our findings highlight the importance of considering feature distributions in low-rank approximations, paving the way for reliable and effective model compression strategies.

Social Aspects · Accountability, Transparency, and Interpretability

Jongwook Han, Jongwon Lim, Injin Kong, Yohan Jo

Large language models can express values in two main ways: (1) $\textit{intrinsic}$ expression, reflecting the model's inherent values learned during training, and (2) $\textit{prompted}$ expression, elicited by explicit prompts. Given their widespread use in value alignment, it is paramount to clearly understand their underlying mechanisms, particularly whether they mostly overlap (as one might expect) or rely on distinct mechanisms, but this remains largely understudied. We analyze this at the mechanistic level using two approaches: (1) $\textit{value vectors}$, feature directions representing value mechanisms extracted from the residual stream, and (2) $\textit{value neurons}$, MLP neurons that contribute to value vectors. We demonstrate that intrinsic and prompted value mechanisms partly share common components crucial for inducing value expression, generalizing across languages and reconstructing theoretical inter-value correlations in the model's internal representations. Yet, as these mechanisms also possess unique elements that fulfill distinct roles, they lead to different degrees of response diversity ($\textit{intrinsic}$ $>$ $\textit{prompted}$) and value steerability ($\textit{prompted}$ $>$ $\textit{intrinsic}$). In particular, components unique to the intrinsic mechanism promote lexical diversity in responses, whereas those specific to the prompted mechanism strengthen instruction following, taking effect even in distant tasks like jailbreaking.

Theory · Deep Learning

Lei Qian, Wu Su, Yanqi Huang, Song Chen

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To efficiently compute the reverse sample likelihood, the equivalence, a quasi-likelihood is considered to approximate each reverse transition density by a Gaussian distribution with matched conditional mean and covariance, respectively. The score and Hessian functions for the diffusion generation are estimated by maximizing the quasi-likelihood, ensuring a consistent matching of both the first two transition moments between every two time points. A stochastic sampler is introduced to facilitate the computation that leverages both the estimated score and Hessian information. We establish consistency of the quasi-maximum likelihood estimation, and provide non-asymptotic convergence guarantees for the proposed sampler, quantifying the rates of the approximation errors due to score and Hessian estimation, dimensionality, and the number of diffusion steps. Empirical and simulation evaluations demonstrate the effectiveness of the proposed Likelihood Matching and validate the theoretical results.

Deep Learning · Large Language Models

Zichong Li, Liming Liu, Chen Liang, Weizhu Chen, Tuo Zhao

The choice of optimizer significantly impacts the training efficiency and computational costs of large language models (LLMs). Recently, the Muon optimizer has demonstrated promising results by orthogonalizing parameter updates, improving optimization geometry through better conditioning. Despite Muon’s emergence as a candidate successor to Adam, the potential for jointly leveraging their strengths—has not been systematically explored. In this work, we bridge this gap by proposing NorMuon (Neuron-wise Normalized Muon), an optimizer that synergistically combines orthogonalization with neuron-level adaptive learning rates. Our analysis reveals that while Muon effectively reduces condition numbers, the resulting updates exhibit highly non-uniform neuron norms, causing certain neurons to dominate the optimization process. NorMuon addresses this imbalance by maintaining second-order momentum statistics for each neuron and applying row-wise normalization after orthogonalization, ensuring balanced parameter utilization while preserving Muon's conditioning benefits. To enable practical deployment at scale, we develop an efficient distributed implementation under the FSDP2 framework that strategically distributes orthogonalization computations across devices. Experiments across multiple model scales demonstrate that NorMuon consistently outperforms both Adam and Muon, achieving 21.74\% better training efficiency than Adam and 11.31\% improvement over Muon on 1.1B pretraining setting, while maintaining a comparable memory footprint to Muon. Our findings suggest that orthogonalization and adaptive learning rates are complementary rather than competing approaches, opening new avenues for optimizer design in large-scale deep learning.

Khashayar Gatmiry, Sitan Chen, Adil Salim

Diffusion models have shown remarkable empirical success in sampling from rich multi-modal distributions. Their inference relies on numerically solving a certain differential equation. This differential equation cannot be solved in closed form, and its resolution via discretization typically requires many small iterations to produce \emph{high-quality} samples. More precisely, prior works have shown that the iteration complexity of discretization methods for diffusion models scales polynomially in the ambient dimension and the inverse accuracy $1/\varepsilon$. In this work, we propose a new solver for diffusion models relying on a subtle interplay between low-degree approximation and the collocation method, and we prove that its iteration complexity scales *polylogarithmically* in $1/\varepsilon$, yielding the first "high-accuracy" guarantee for a diffusion-based sampler that only uses (approximate) access to the scores of the data distribution. In addition, our bound does not depend explicitly on the ambient dimension; more precisely, the dimension affects the complexity of our solver only through the *effective radius* of the support of the target distribution.

Deep Learning · Large Language Models

Yizhao Huang, Haoyang Chen, Pohsun Huang, Jiayuan Li, Shiqin Wang, Haoyuan Du, Yandong Shi, Zheng Wang, Zhixiang Wang

This paper argues that a systemic lack of Agency constrains the implicit reasoning capabilities of current Vision-Language Models (VLMs). Implicit reasoning refers to the ability to autonomously discover and utilize hidden visual evidence to bridge information gaps, rather than merely relying on explicitly specified targets. This capacity underlies human visual understanding and everyday reasoning. We argue that this limitation arises from a tendency to equate visual reasoning with passive semantic retrieval, rather than with active, situated reasoning that depends on autonomous visual exploration. As a result, most existing benchmarks primarily assess Passive Capacity, leaving this aspect of reasoning largely unmeasured. To address this gap, we introduce the Visual Implicit Reasoning Benchmark (V-IRD), which targets this missing quadrant by requiring models to derive answers strictly through autonomous visual analysis. Our results show that, despite strong retrieval abilities, prominent VLMs struggle to utilize reference objects and to attend to visual evidence that requires self-directed inquiry. Simply put, strong semantic recognition does not equate to active visual exploration, revealing a critical gap in current VLMs.

Social Aspects · Accountability, Transparency, and Interpretability

Jiadong Lou, Wenxin Rong, Li Chen, Xing Gao, Rui Zhang, Xu Yuan

Concerns over dataset misuse in deep learning have highlighted the need for effective auditing. Unlike existing intrusive methods that require dataset modifications, which risk model performance and security, we present DataGuard, a non-intrusive framework for quantitative dataset auditing. Specifically, DataGuard integrates three key components: 1) a differential comparison between the target dataset and auxiliary non-training datasets, 2) an information-forensic analysis establishing formal inequalities to distinguish training data; and 3) a multivariate statistical test that translates these discrepancies into rigorous auditing scores. Extensive experiments demonstrate that DataGuard can detect both full and partial dataset usage without false positives while remaining robust under diverse training scenarios, offering a principled, information-theoretic solution for transparent AI development.

Applications · Computer Vision

Xiaoyu Zhou, Jianwei Fei, Peipeng Yu, Jingchang Xie, Chong Cheng, Zhihua Xia

The rapid evolution of generative AI, from GANs to modern diffusion models, has resulted in increasingly subtle discriminative clues. These fine-grained signals are often overshadowed by dominant, high-fidelity image content (e.g., the main subject), limiting the reliability of existing detectors that predominantly rely on global representations. To address this challenge, we propose the Peak-Guided Calibration (PGC) framework. PGC introduces a novel strategy that aggregates salient features via a peak-focusing mechanism. Specifically, by employing a peak-sensitive aggregation that accentuates the most discriminative local clues, PGC leverages these critical signals to calibrate the global decision. This approach recovers subtle patterns that would otherwise be submerged in the global context. Furthermore, to better simulate real-world threats, we introduce the CommGen15 dataset, a challenging benchmark comprising samples from 15 commercial models. Extensive experiments demonstrate that PGC achieves state-of-the-art performance, surpassing existing detectors by +12.3% (Accuracy) on CommGen15, while setting new records on standard benchmarks, including GenImage (+2.1%), AIGI (+3.5%), and UniversalFakeDetect (+1.7%).

Applications · Computer Vision

Hengbo Xu, Shengjie Jin, Yanbiao Ma, Zhiwu Lu

With the rapid advancement of large multimodal models (LMMs), inference-time overhead has become a key bottleneck for real-world deployment. Existing methods typically prune visual tokens at prefill, assuming the required visual evidence remains static during reasoning. However, we empirically show that visual evidence is strongly step-dependent: only a sparse subset of visual tokens is critical at each decoding step, and the critical set evolves across reasoning. Furthermore, we identify a coupled bottleneck where redundant visual context can steer the model toward query-irrelevant regions, lengthening the reasoning trace. Guided by these insights, we propose **VisionPulse**, a step-wise visual token pruning framework during reasoning. VisionPulse computes a lightweight visual attention mass to estimate the step-wise retention budget by exploiting its strong positive correlation with LMMs' effective visual token usage and retain only the most critical tokens under this budget. By enforcing visual sparsity during reasoning, VisionPulse filters redundant visual context while preserving relevant visual evidence, shortening reasoning traces naturally. Extensive experiments show that VisionPulse only retains 5\% of visual tokens per step with reasoning traces shortened by 11.2\%, while keeping accuracy almost unchanged.

Social Aspects · Fairness

Ruyi Chen, Xiaogang Xu, Chiyu Zhang, Jiafei Wu, Liming Fang, Lu Zhou

Text-to-Image (T2I) models have made significant strides in visual realism and semantic consistency, yet they often perpetuate and amplify societal biases. Existing evaluation methods typically address only single-dimensional biases, lacking perspectives to uncover model biases at social-related deeper semantic levels. We introduce HoloFair, a comprehensive benchmark framework for multidimensional demographic bias analysis. Built upon our large-scale fairness-oriented dataset and the SpaFreq (Spatial-Frequency) attribute classifier, this framework proposes the Multi-attribute, Group-wise Bias Index (MGBI) metric, designed to assess both intrinsic diversity and conditional biases. Beyond evaluation, we further introduce Fair-GRPO, a reinforcement-learning-based debiasing method that alters the distribution of generative models through a designed multi-objective reward function. E.g., experiments on the SD3.5-Medium model demonstrate that Fair-GRPO significantly improves multidimensional fairness while maintaining high image quality. We also analyze potential reward hacking phenomena and provide corresponding mitigation strategies.

Deep Learning · Large Language Models

Ling-I Wu, Jian Tong, Yu Sun, Xuan Gao, Xu Guo, Guoqiang Li, Qipeng Guo, Kai Chen

While previous research has documented the sensitivity of Large Language Models (LLMs) to surface-level performance degradation, the underlying impact on internal representations and learning dynamics remains under-explored. In this work, we study this question using a controlled setup with paired reasoning tasks that are logically identical but expressed either in an abstract formal language (FL) or in natural language (NL). We find that converting FL problems into NL consistently degrades reasoning accuracy. More importantly, we show that FL and NL inputs activate largely separate internal representations and exhibit weak learning transfer between them. We refer to this phenomenon as reasoning compartmentalization. To test whether this compartmentalization can be mitigated, we introduce abstraction-based alignment, where models are trained to translate NL inputs into their corresponding FL forms. While this significantly improves reasoning performance, FL and NL representations remain largely distinct, and learning transfer across formulations remains limited. Through activation-level interventions, we further show that performance improvements arise not from representational fusion, but from improved routing. This suggests that abstraction alleviates formulation sensitivity by strengthening connections between formulation-specific reasoning pathways, rather than by aligning their representations.

Deep Learning · Large Language Models

Yoonah Park, Haesung Pyun, Yohan Jo

While large language models (LLMs) perform strongly on diverse tasks, their trustworthiness is limited by erratic behavior that is unfaithful to their internal knowledge. In particular, LLMs often fail on multiple-choice questions (MCQs) even if they encode correct answers in their hidden representations, revealing a misalignment between internal knowledge and output behavior. We investigate and mitigate this knowledge-prediction gap on MCQs through a three-step analysis of hidden representations. First, we quantify the prevalence and magnitude of the gap across models and datasets. Second, we provide a geometric interpretation by identifying distinct knowledge and prediction subspaces in the residual stream. Third, we introduce KAPPA, a lightweight inference-time intervention that aligns the two subspaces within the residual stream to reduce the knowledge-prediction gap. Our results provide a geometric and interpretable explanation of the knowledge-prediction gap in LLMs. Furthermore, KAPPA effectively reduces the gap across diverse MCQ benchmarks and models, and generalizes to free-form settings.

Optimization · Stochastic

Aleksandr Shestakov, Martin Takac, Eduard Gorbunov

Gradient clipping is widely used to stabilize stochastic gradient methods and is often theoretically motivated by heavy-tailed gradient noise, where even second moments may be infinite, seemingly contradicting empirical risk minimization where all moments are finite for a fixed dataset. We resolve this paradox by explicitly separating data sampling from optimization randomness: although moments are finite conditional on the dataset, heavy-tailed data induce dataset-dependent noise whose second moment typically grows with the dataset size $N$. In particular, when $\|\nabla f(x_\star,\xi)\|$ has tail index $\alpha \in (1,2)$, the quantity $\frac{1}{N}\sum_{i=1}^N\|\nabla f(x_\star,\xi_i)\|^2$ scales as $N^{\frac{2}{\alpha}-1}$, leading to deteriorating convergence guarantees for standard SGD as $N$ increases. In contrast, we show that stochastic gradient descent with clipping avoids this growth and admits finite-sum convergence guarantees under heavy-tailed data for broad step-size and clipping schedules. We further derive generalization bounds for strongly convex smooth objectives and show that the tail behavior of gradients at the population minimizer is the key quantity linking optimization and generalization under heavy-tailed data.

Deep Learning · Large Language Models

Zhuo Zuo, Li Yue, Wenhao Zheng, Chenpeng Wang, Xianggen Liu

Despite their strong general capabilities, large language models (LLMs) often remain unreliable when outputs must be numerically precise. A key reason is the training objective: standard cross-entropy treats numeric tokens as unstructured categories and ignores the metric structure of their values. We address this mismatch by proposing **S**mooth **M**aximum **M**ean **D**iscrepancy (**SMMD**), which builds on the classic MMD by incorporating value-distance kernels over numeric tokens and graph-based smoothness. With this kernel defined over a numeric sub-vocabulary, SMMD aligns the predicted numeric distribution to the target via kernel matching and smooths the prediction--target residual over the induced kernel graph to encourage local consistency. We evaluate SMMD on four numeric-target tasks---mathematical reasoning, arithmetic calculation, clock-time recognition, and chart question answering---across multiple open-weight LLM and VLM backbones. SMMD consistently improves accuracy over both cross-entropy and recent numeric-target losses; analyses show complementary effects between MMD and smoothness and underscore the importance of distance-based kernel design.

Rachael Hwee Ling Sim, Jue Fan, Xiao Tian, Xinyi Xu, Patrick Jaillet, Bryan Kian Hsiang Low

Collaborative machine learning involves training high-quality models using datasets from a number of sources. To incentivize sources to share data, existing data valuation methods fairly reward each source based on its data submitted as is. However, as these methods do not verify nor incentivize data truthfulness, the sources can manipulate their data (e.g., by submitting duplicated or noisy data) to artificially increase their valuations and rewards or prevent others from benefiting. This paper presents the first mechanism that provably ensures (**F**) collaborative fairness and incentivizes (**T**) truthfulness at equilibrium for Bayesian models. Our mechanism combines semivalues (e.g., Shapley value), which ensure fairness, and a truthful data valuation function (DVF) based on a validation set that is unknown to the sources. As semivalues are influenced by others' data, we introduce an additional condition to prove that a source can maximize its expected data values in coalitions and semivalues by submitting a dataset that captures its true knowledge. Additionally, we discuss the implications and suitable relaxations of (**F**) and (**T**) when the mediator has a limited budget for rewards or lacks a validation set. Our theoretical findings are validated on synthetic and real-world datasets.

Yanchen Yin, Dongqi Han, Linghui Li

Jailbreak attacks bypass LLM safety alignment, yet their mechanisms remain poorly understood. We provide evidence that attacks do not eliminate safety features but selectively suppress specific attention heads. We identify two functionally differentiated types: **Adversarially Compromised Heads (ACHs)** concentrated in early layers, which are suppressed under attacks; and **Safety-Aligned Heads (SAHs)** in mid-layers, which maintain robust activations even when attacks succeed. Ablation studies support their causal roles: suppressing a small number of ACHs is sufficient to induce jailbreak-like behavior on normally refused inputs, while removing SAHs substantially weakens mid-layer safety activations. Token-level attribution further shows that ACH suppression is driven specifically by attack-template tokens. This provides a mechanistic account of why attacks bypass refusal decisions through ACH suppression, yet may not fully eliminate the internal safety signals sustained by SAHs---a phenomenon we term **Robust Harmful Features**. To validate the practical significance of this robustness, we show that simply reading these persistent activations---without any training---yields a detection signal competitive with dedicated safety models on most benchmarks.