arXiv:2605.18648v1 Announce Type: new
Abstract: Central to human-aligned AI is understanding the benefits of human-elicited labels over synthetic alternatives. While human soft-labels improve calibration by capturing uncertainty, prior studies conflate these benefits with the implicit correction of mislabeled data (mode shifts), obscuring true effects of soft-labels. We present a controlled audit of soft-label learning across MNIST and a synthetic variant, re-annotating subsets to extract human uncertainty. By decoupling soft-label supervision from underlying label mode shifts, we show that while human soft-labels do provide accuracy gains, their larger value lies in acting as a regularizer that improves model calibration on difficult samples and promotes stable convergence across training runs. Dataset cartography reveals models trained on human soft-labels mirror human uncertainty, whereas those trained on synthetic labels fail to align with humans. Broadly, this work provides a diagnostic testbed for human-AI uncertainty alignment.
Science Journals
arXiv:2605.08567v2 Announce Type: replace
Abstract: Action-conditioned world models (ACWMs) have shown strong promise for video prediction and decision-making. However, existing benchmarks are largely restricted to egocentric navigation or narrow, task-specific robotics datasets, offering only limited coverage of the rich physical interactions required for generalized world understanding. We introduce ACWM-Phys, a new benchmark for evaluating action-conditioned prediction under diverse physical dynamics in a clean, controllable simulation environment with a carefully designed action space. ACWM-Phys contains training and evaluation data spanning rigid-body dynamics, kinematics, deformable-object interactions, and particle dynamics. To evaluate both interpolation and generalization, we design in-distribution and out-of-distribution protocols with controlled shifts in interaction patterns or scene configurations. By building the benchmark in a fully controllable simulator, ACWM-Phys enables precise data collection, reproducible evaluation, and systematic analysis of model capabilities for physically grounded world modeling. Through systematic experiments on ACWM-DiT, we find that OoD generalization depends not only on the physical regime but also on effective task complexity: models generalize well on visually simple, low-dimensional interactions with clear geometric structure, but suffer larger drops on deformable contacts, high-dimensional control, and complex articulated motion. This suggests that the model still relies heavily on visual appearance patterns instead of fully learning the underlying physics. Ablations show that cross-attention improves high-dimensional action conditioning, causal VAEs outperform frame-wise encoders, and larger action spaces are harder to model but can improve generalization by providing richer control signals. These findings guide the design of physically grounded world models.
Toward an Origin of Human Randomness: Interaction-Driven Enhancement in the Rock-Paper-Scissors Game
arXiv:2605.18616v1 Announce Type: new
Abstract: Human-generated randomness is constrained by cognitive, motor, and strategic biases. This study examines how these constraints appear in individual behavior and how they may be modified through interaction with another human. We analyzed repeated rock-paper-scissors data from 9 participants, yielding 108 human-human matches and 216 individual player sequences. Using Lempel-Ziv complexity (LZC), we compared human-human sequences with the RNG-opponent condition. In the RNG-opponent condition, the maximum human LZC value was 84, which we used as an empirical reference. In the human-human condition, most sequences remained below this value, but a small number exceeded it, producing a small high-complexity tail that was not present in the RNG-opponent condition. We introduced a sensitivity measure that captures whether a player responds to the opponent's recent frequency bias by choosing the move that beats the opponent's most frequent recent move. Partial regression showed that focal-player sensitivity positively predicted future entropy in the opponent's move sequence after controlling for the opponent's current entropy. Circular-shift surrogate analyses indicated that this relation was most clearly interaction-specific when the opponent was in a low-entropy state, where the recent move distribution contained a clear frequency bias. These results suggest that human randomness is not only an isolated individual capacity, but can be shaped by interaction in a state-dependent manner. The findings identify a local mechanism by which interaction may destabilize biased behavior and increase entropy, providing a concrete basis for future causal experiments and generative models of high-complexity human behavior.
arXiv:2605.07005v2 Announce Type: replace
Abstract: Recent work on provably efficient algorithms for learning with distribution shift has focused on two models: PQ learning (Goldwasser et al. (2020)) and TDS learning (Klivans et al. (2024)). Algorithms for TDS learning are allowed to reject a test set entirely if distribution shift is detected. In contrast, PQ learners may only reject points that are deemed out-of-distribution on an individual basis. Our main result is a surprising equivalence between these two models in the distribution-free setting. In particular, we give an efficient black-box reduction from PQ learning to TDS learning for any Boolean concept class. This equivalence implies the first hardness results for distribution-free TDS learning of basic classes such as halfspaces. The main technical contribution underlying our equivalence is a method for boosting, via branching programs, the weak distinguishing power of TDS learners that have rejected the target domain.
We also show that giving a learner access to membership queries sidesteps these hardness results and allows for efficient, distribution-free PQ learnability of halfspaces. Our algorithm iteratively recovers large-margin separators obtained by applying successive Forster transforms on the training data.
arXiv:2605.18593v1 Announce Type: new
Abstract: Open-vocabulary embodied AI agents increasingly rely on vision-language models such as CLIP for object perception and task grounding. However, the shared embedding space that enables this flexibility introduces a structural vulnerability to typographic attacks, where printed text in a physical scene semantically overrides visual judgment. While prior work has quantified this threat in static 2D benchmarks and 3D navigation tasks, its impact on the full Sense-Plan-Act pipeline of household robot manipulation remains unexplored.
This work evaluates typographic attacks in a Habitat-based simulation using the HomeRobot benchmark. We introduce a decoupled perception architecture that exposes a frozen CLIP encoder to adversarial stickers while maintaining geometric grounding via DETIC. In a controlled evaluation pool of 59 attributable episodes, the attack achieves an overall Attack Success Rate (ASR) of 67.8%, rising to 70.0% among fully successful episodes, under uncontrolled viewing angles and occlusion with no perceptual optimization.
Critically, we find that perceptual errors propagate through the persistent 3D semantic map to produce kinetic failures, defined here as physically executed grasping and transport of the wrong object driven by an adversarially poisoned semantic state. In these cases, the robot physically grasps and delivers the wrong object to a target receptacle. These results establish typographic misclassification as a real, measurable, and physically consequential threat to the safety of modular manipulation pipelines that prior typographic attack research has left unexamined.
arXiv:2605.06506v2 Announce Type: replace
Abstract: Language-model (LM) surprisal is widely used as a proxy for contextual predictability and has been reported to correlate with metaphor novelty judgments. However, surprisal is tightly intertwined with lexical frequency. We explore this interaction on metaphor novelty ratings using two different word frequency measures. We analyse surprisal estimates from eight Pythia model sizes and 154 training checkpoints. Across settings, word frequency is a stronger predictor of metaphor novelty than surprisal. Across training stages, the surprisal--novelty association peaks at an early stage and then falls again, mirroring a similarly timed increase in the surprisal--frequency association. These results suggest that the often-reported optimal LM surprisal settings may incorrectly associate contextual predictability with metaphor novelty and processing difficulty, whereas lexical frequency may be the major underlying factor.
arXiv:2605.18583v1 Announce Type: new
Abstract: Coding agents now run autonomously with shell, file, and network privileges. When a user issues a benign request, the agent sometimes does more than asked: it deletes unrelated files, wipes a stale credentials backup, or rewrites configuration the user never mentioned. We call these scope expansions overeager actions, an authorization problem distinct from capability failures, prompt injection, or sandbox escapes.
We present OverEager-Gen, a benchmark dedicated to overeager behavior on benign tasks. Building it surfaces a measurement-validity issue: if a benchmark spells out the authorized scope inside the prompt, the agent stops inferring boundaries and starts pattern-matching declaration text. On Claude Code, stripping the consent declaration alone raises the overeager rate from 0.0% to 17.1% on paired scenarios (McNemar exact p = 2.4 x 10^-4). OverEager-Gen therefore certifies each scenario's discriminative power before admission via a behavioral-gradient validator, audits internal tool calls through a dual-channel stack (PATH-injected shim plus per-agent event streams), and ships byte-identical consent_kept and consent_stripped variants.
OverEager-Bench contains 500 validated scenarios and ~7,500 runs across four agent products (Claude Code, OpenHands, Codex CLI, Gemini CLI) and six base models; a 50-sample re-annotation gives Cohen's kappa = 0.73 and rule-judge recall = 1.00. Stripping consent multiplies the overeager rate on every shared base model (Delta in [11.9, 17.2] pp). The framework axis dominates effect size: a permissive cluster (Claude Code, Codex CLI, Gemini CLI) runs at 5.4-27.7% while the ask-to-continue framework (OpenHands) sits at 0.2-4.5% (Fisher p <= 10^-5). Within-framework base-model variance reaches 15.9 pp, indicating that model-layer alignment does not fully propagate through permissive permission gating.
arXiv:2605.18582v1 Announce Type: new
Abstract: Long-duration energy storage (LDES) faces significant revenue volatility that impedes investment. This paper evaluates four contract-based support mechanisms using an equilibrium model with risk-averse investors and incomplete risk markets. Applied to a stylized 2035 Great Britain case, we find that all mechanisms can achieve the targeted LDES capacity but differ substantially in cost-effectiveness and risk-aversion sensitivity. Contracts that eliminate revenue volatility achieve the lowest costs but may weaken operational incentives, while contracts that preserve market exposure maintain incentives at higher costs.
arXiv:2605.06017v2 Announce Type: replace
Abstract: Sequence-level evaluations in autoregressive Large Language Models (LLMs) rely on highly dependent token generation. Establishing tight concentration bounds for these processes remains a challenge due to two fundamental bottlenecks in existing frameworks: (i) classical inequalities typically separate dependency structures from target sensitivities, leading to a scalar collapse that inflates the variance proxy to a suboptimal $\mathcal{O}(N)$ for sparse terminal rewards; (ii) conversely, while certain spatial methods achieve tighter bounds, they lack the strictly causal filtration required by sequential generation, rendering them inapplicable to the autoregressive setting. To resolve both bottlenecks, we establish a sharp McDiarmid-type inequality for dependent sequences, governed strictly by the exact matrix-vector multiplication of the causal dependency resolvent and the target sensitivity vector. This Matrix-Decoupled Concentration (MDC) framework natively recovers optimal constants for Markov chains and exploits directed $d$-separation to yield order-optimal bounds for causal trees. Crucially, by exactly preserving the coordinate-wise sparsity of rewards within a strictly causal framework, MDC mathematically prevents scalar collapse, guaranteeing a dimension-free $\mathcal{O}(1)$ variance proxy and providing a rigorous mathematical justification for the stability of long-context reasoning.
arXiv:2605.18563v1 Announce Type: new
Abstract: A key question in psycholinguistics is how inferences about the meaning of linguistic input unfold incrementally a comprehender's mind. In this work, we study reading dynamics for ``noisy-channel garden-path'' sentences, which temporarily appear well-formed but feature late-appearing violations of expectation that can be resolved not by inferring an alternative syntactic structure, but by inferring the presence of an error. We find evidence for targeted regressions -- eye movements towards regions that are promising loci of possible errors in light of later-arriving information, showing patterns consistent with the posterior inferences of a model of noisy-channel processing with reanalysis. We discuss the implications of these findings for theories of noisy-channel language comprehension and information-theoretic explanations of reading dynamics.
arXiv:2605.18542v1 Announce Type: new
Abstract: We extend the recently-developed explicit, energy-conserving particle-in-cell (PIC) scheme of [1] to the relativistic Vlasov-Maxwell system. As in the non-relativistic case, the method is built on an optimization problem that is analytically solvable, local to each particle, and designed to enforce exact energy conservation. Although the solution to this optimization problem is not guaranteed to be real, we show that such instances are rare enough for practical simulation parameters to permit dramatic improvements in energy conservation over traditional explicit PIC schemes. We show that, as in the non-relativistic case, the scheme is compatible with popular field-solvers for electromagnetic PIC schemes, including the Yee/FDTD and pseudo-spectral analytic time-domain (PSATD) methods. The scheme is verified on standard relativistic test problems, where its conservation properties are confirmed.
arXiv:2605.01235v2 Announce Type: replace
Abstract: Driven by the escalating global burden of mental health conditions, music-based interventions have attracted significant attention as a non-invasive, cost-effective modality for emotion regulation and psychological stress relief. However, current digital music services rely on static preferences and fail to adapt to users' instantaneous psychological states. Furthermore, directly mapping electroencephalography (EEG) to music generation remains challenging due to severe paired-data scarcity and a lack of interpretability. To address these limitations, we propose MindMelody, a fully functional, closed-loop real-time system for EEG-driven personalized music intervention. MindMelody introduces an emotion-mediated semantic bridge. Specifically, a hybrid Transformer-GNN first decodes real-time EEG signals into global Valence-Arousal states and local temporal affect trajectories. These states are then fed into a Retrieval-Augmented Generation (RAG)-equipped Large Language Model (LLM) to formulate structured intervention plans. Subsequently, a novel Hierarchical EEG Controller injects global affect prefixes and local temporal guidance into a pretrained music backbone, enabling fine-grained controllable audio synthesis. Crucially, the system incorporates a continuous feedback loop that updates generation parameters on the fly based on the user's evolving EEG dynamics. Extensive experiments show that MindMelody improves control adherence and emotional alignment, and receives higher perceived helpfulness in a short-term listening setting, suggesting its promise as an adaptive affect-aware music generation framework.
arXiv:2605.18537v1 Announce Type: new
Abstract: This paper introduces the Manifold Probe, a supervised method for discovering representation manifolds in superposition. The method generalizes linear regression probes by learning the space of features of a concept that can be linearly predicted from the representations, and then learning the directions used to encode them. We demonstrate the probe on representations of time and space in Llama 2-7b, finding manifolds which linearly represent an interpretable set of features in each case. In the case of time, we show that by steering along the manifold, we can influence the model's completions about the years in which famous songs, movies and books were released, providing evidence that the Manifold Probe can discover manifolds which are causally involved in model behaviour.
arXiv:2605.18395v1 Announce Type: new
Abstract: Large language models (LLMs) exhibit systematic political biases in voter simulations, but their underlying mechanisms and cross-lingual generalizations remain poorly understood. We introduce Dynamo-K, a census-grounded simulation framework evaluating Korean-language LLM political behavior across four models on six Korean elections (2017-2025). Using this framework, we identify three systematic failure modes: (1) progressive bias in moderate agents, where explicit mitigation reduces Mean Absolute Error (MAE) by 5.2 times; (2) model-dependent third-party salience collapse, distinguishing between salience failure and decision bias; and (3) regional polarization collapse, where models bidirectionally under-predict historical party strongholds.
To address these failures, we demonstrate that scenario reframing recovers 62% of 2017 MAE by restoring third-party visibility. Furthermore, we introduce a learned reweighting adapter that successfully calibrates opposing-valence models without relying on candidate names at train or test time. Validating our diagnostic framework, Dynamo-K accurately predicts 3/3 presidential winners - including a 2.1%p MAE on the highly contested 0.73%p-margin 2022 race - and correctly identifies the dominant party in a held-out local election. The pipeline is open-source and provides a scalable, cost-effective method for diagnosing LLM political behavior.
arXiv:2605.18390v1 Announce Type: new
Abstract: In this work, we explore the largely unexplored direction of building a generalist image tokenizer directly on top of a frozen vision foundation model (VFM). To build this tokenizer, we utilize a frozen VFM as the encoder and introduce two key innovations: (1) a region-adaptive quantization framework to eliminate spatial redundancy in standard 2D grid features, and (2) a semantic reconstruction objective that aligns the decoded outputs with the VFM's representations to preserve semantic fidelity. Grounded in these designs, we propose VFMTok, a generalist visual tokenizer capable of operating seamlessly in both discrete and continuous latent spaces. VFMTok achieves substantial improvements in synthesis quality while drastically enhancing token efficiency. For discrete autoregressive (AR) generation, it accelerates model convergence by \textbf{3 times} and achieves a state-of-the-art gFID of \textbf{1.36} on ImageNet class-conditional synthesis. Similarly, for continuous-space generation, integrating VFMTok with a denoising model yields an exceptional gFID of \textbf{1.25}. Furthermore, because the latent space inherently captures rich spatial semantics, VFMTok enables high-fidelity class-conditional synthesis without classifier-free guidance (\textbf{w/o CFG}) across both generative paradigms, significantly accelerating inference speed. Beyond these remarkable empirical results, we systematically investigate the underlying mechanisms of our approach. We discover that the specific self-supervised learning objectives utilized during VFM pre-training dictate its effectiveness as a tokenizer. Specifically, a VFM jointly optimized with global contrastive learning and latent masked image modeling provides the optimal representations for image tokenization. These insights establish a strong foundation and offer valuable guidance for the design of future image tokenizers.
arXiv:2605.18365v1 Announce Type: new
Abstract: Generating geometrically consistent videos remains an open challenge: text-to-video diffusion models trained on web-scale data treat geometry only implicitly, leading to object deformation, texture drift, and non-rigid backgrounds under camera motion. Existing solutions either improve consistency as a byproduct, apply only to static scenes or realign the latent space of the model completely. We introduce a geometry-consistency reward that directly measures whether motion in a generated video is compatible with a coherent scene. Our key insight is that in physically consistent videos, background motion should be explainable by rigid camera-induced flow, while independently moving objects should preserve appearance identity along motion trajectories. We operationalize this using optical flow, depth--pose predictions, and feature-based correspondence to separate rigid and dynamic regions and evaluate their respective consistency. Integrating this reward with reinforcement fine-tuning transforms geometric consistency from an emergent property into an explicit optimization objective for video generators. The approach is model agnostic and applies to diverse dynamic scenes containing both camera and object motion. Experiments show substantial reductions in temporal geometric artifacts over strong baselines while preserving perceptual quality. Code and model weights are published.
arXiv:2605.18482v1 Announce Type: new
Abstract: The growing adoption of lattice-based structures in soft robotics creates a need for advanced sensing solutions capable of monitoring their global deformation, particularly compression and extension. In this work, we address this challenge by introducing a novel optical sensor based on two patterned waveguides arranged in an ellipsoidal geometry. This Bidirectional Optical sensor for Actuation Tracking (BOAT) is seamlessly co-printed with a lattice structure actuated by an embedded pneumatic artificial muscle (PAM), and its performance is assessed. During PAM elongation or contraction, the bending of the embedded BOAT waveguides induces output signal variations that enable a clear discrimination between compression and extension states.
The designs of both each specific waveguide structure (by surface patterning) and of the sensorized lattice-based unit embedding two BOATs are supported by numerical simulations. Experimental calibration over 100 consecutive pressure cycles ranging from +50 kPa to $-$40 kPa demonstrates a highly repeatable response, allowing a reliable distinction between extension and compression.
Finally, sensor feedback is used to implement a digital shadow, enabling continuous synchronization between the whole sensorized unit and its virtual counterpart. These results establish BOAT as a powerful and reliable approach for deformation monitoring in soft lattice-based robotic systems.
arXiv:2605.18484v1 Announce Type: new
Abstract: The rapid adoption of Web3 infrastructures has led to a growing number of security incidents affecting cryptocurrency exchanges, custody services and blockchain-based platforms. While existing research predominantly focuses on vulnerabilities in smart contracts and blockchain protocols, a substantial portion of real-world losses originates from off-chain systems, organizational processes and human-centered operational workflows.
This paper presents a qualitative, incident-based analysis of publicly documented, high-impact security breaches in the Web3 ecosystem, including the Bybit exchange incident (2025), the Ronin Network bridge compromise (2022), and the DMM Bitcoin exchange breach (2024). The selected cases are systematically analysed and mapped to established Web2 security reference frameworks, including OWASP-based vulnerability categories and organizational security control domains.
The results indicate that dominant failure patterns in Web3 environments are insufficiently addressed by generic security control catalogues, particularly with respect to cryptographic key management, transaction approval governance, signer and validator infrastructure, third-party tooling dependencies, and human-in-the-loop processes.
Based on these findings, this paper argues for the adoption of established information security management systems (ISMS) in Web3 organizations and derives a structured set of blockchain-specific cybersecurity control categories to operationalize existing ISMS frameworks for blockchain-based systems. The proposed categories aim to bridge the gap between generic security governance frameworks and domain-specific risks inherent to Web3 infrastructures.
arXiv:2605.18511v1 Announce Type: new
Abstract: A lightweight and reproducible denoising pipeline for high-throughput Raman spectroscopy is presented. The approach relies on a one-dimensional convolutional autoencoder trained using a Noise2Noise strategy, requiring neither external spectral libraries nor high signal-to-noise reference spectra for training. From a reduced training subset composed of repeated short-exposure acquisitions, the model learns to reconstruct Raman spectra while efficiently suppressing stochastic noise. The method is evaluated on a heterogeneous mineral sample, using both quantitative spectral fidelity metrics (RMSE, SNR, SSIM) and task-oriented criteria based on unsupervised K-means classification. Results demonstrate that integration times as short as 5 ms per spectrum, which are typically insufficient for reliable interpretation, yield denoised spectra with high fidelity to the reference data while preserving chemically coherent maps. This work provides a practical trade-off between spectral quality and acquisition speed, enabling fast, adaptable Raman workflows compatible with routine laboratory use. It also offers a transferable framework for other one-dimensional spectroscopic modalities.
arXiv:2605.18531v1 Announce Type: new
Abstract: Understanding ion-transport under molecular confinement is essential for developing next-generation energy technologies, where ionic motion often occurs within nanoscale or angstrom-scale channels. In this study, we use the model system of 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([EMIM]+[TFSI]-) confined within angstrom-scale slit-shaped 2D channels fabricated via van der Waals assembly to exemplify a broader class of confined ionic liquids.This system provides a well-defined platform to unravel generic features of ion transport under extreme confinement. By systematically varying the channel height h, we demonstrate a non-monotonic conductivity dependence on confinement, with a maximum 26.7 S/m at confining height, 1.02 nm, over 30 times of the bulk value for these ionic liquids. The variation of conductivity with confinement arises from structural rearrangements of ionic layers in the slit channel. Enhanced values of conductivity occur under confinements that promote the breakup of ion pairs and larger clusters, thereby increasing the number of free ions. Stronger confinement (h, 0.68 nm) also leads to steric hindrance, lowering conductivity below bulk values. Furthermore, introducing co-solvents with a higher dielectric constant and lower viscosity, such as acetonitrile (ACN), amplifies conductivity to ~145 S/m. Comparative studies using ACN, dimethyl carbonate and diethyl carbonate highlight that both large dielectric constant and low viscosity critically govern ion transport under confinement, as also supported by molecular dynamics simulations. Overall, this work establishes confined [EMIM]+[TFSI]- as a representative system for probing mechanisms of nano- and angstrom-scale ion transport, demonstrating how nanoconfinement and the solvent environment can be systematically tuned to manipulate ionic conductivity at the molecular level.
arXiv:2605.18534v1 Announce Type: new
Abstract: Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.
arXiv:2512.23178v3 Announce Type: replace-cross
Abstract: Optimization under heavy-tailed noise has become popular recently, since it better fits many modern machine learning tasks, as captured by empirical observations. Concretely, instead of a finite second moment on gradient noise, a bounded ${\frak p}$-th moment where ${\frak p}\in(1,2]$ has been recognized to be more realistic (say being upper bounded by $\sigma_{\frak l}^{\frak p}$ for some $\sigma_{\frak l}\ge0$). A simple yet effective operation, gradient clipping, is known to handle this new challenge successfully. Specifically, Clipped Stochastic Gradient Descent (Clipped SGD) guarantees a high-probability rate ${\cal O}(\sigma_{\frak l}\ln(1/\delta)T^{1/{\frak p}-1})$ (resp. ${\cal O}(\sigma_{\frak l}^2\ln^2(1/\delta)T^{2/{\frak p}-2})$) for nonsmooth convex (resp. strongly convex) problems, where $\delta\in(0,1]$ is the failure probability and $T\in\mathbb{N}$ is the time horizon. In this work, we provide a refined analysis for Clipped SGD and offer two rates, ${\cal O}(\sigma_{\frak l}d_{\rm eff}^{-1/2{\frak p}}\ln^{1-1/{\frak p}}(1/\delta)T^{1/{\frak p}-1})$ and ${\cal O}(\sigma_{\frak l}^2d_{\rm eff}^{-1/{\frak p}}\ln^{2-2/{\frak p}}(1/\delta)T^{2/{\frak p}-2})$, faster than the aforementioned best results, where $d_{\rm eff}\ge1$ is a quantity we call the $\textit{generalized effective dimension}$. Our analysis improves upon the existing approach on two sides: better utilization of Freedman's inequality and finer bounds for clipping error under heavy-tailed noise. In addition, we extend the refined analysis to convergence in expectation and obtain new rates that break the known lower bounds. Lastly, to complement the study, we establish new lower bounds for both high-probability and in-expectation convergence. Notably, the in-expectation lower bounds match our new upper bounds, indicating the optimality of our refined analysis for convergence in expectation.
arXiv:2605.17660v1 Announce Type: cross
Abstract: Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a rigorous mathematical framework for analyzing gradient-based training of transformers in the mean-field regime, where both the depth (number of layers) and width (number of attention heads) tend to infinity. While ResNet training can be understood as controlling a neural ODE, transformer training corresponds to controlling a neural PDE, due to the coupling of multiple token distributions through the attention mechanism. Our mean-field model features two types of measure representations: token distributions evolving through layers and attention parameters at each layer. We establish well-posedness of the forward pass through infinitely deep transformers, characterizing token evolution via flow maps that satisfy ODEs in function spaces. Using adjoint sensitivity analysis, we derive an explicit formula for the conditional Wasserstein gradient of the training risk, involving adjoint variables governed by backward ODEs. We prove the existence and uniqueness of gradient flow curves in the conditional Wasserstein metric space, establishing a rigorous foundation for gradient-based transformer training. A key technical contribution is providing necessary and sufficient conditions for injectivity of the Neural Tangent Kernel (NTK) for attention mechanisms: we show that NTK injectivity is equivalent to linear independence of log-sum-exp functions modulo affine functions, a condition satisfied by diverse token distributions, including discrete distributions, uniform distributions, and Gaussian mixtures. Under this NTK injectivity assumption, we prove that gradient flow converges to global minima when the initial loss is sufficiently small, eliminating spurious local minima from the optimization landscape.
arXiv:2605.08794v2 Announce Type: replace
Abstract: Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field \(b_t\) of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects: \(b_t = u_t + d_t\), where \(u_t\) governs marginal probability transport and \(d_t\) captures an osmotic effect induced by diffusion and determined by the marginal score. Based on this decomposition, we propose Bridge Matching, a flow-based framework for learning decomposed generative dynamics through both marginal and conditional formulations. In generative modeling experiments, we recombine the learned components as \(b_t = u_t + \lambda_d d_t\), showing that the proposed decomposition enables interpretable and controllable sampling by adjusting the osmotic contribution in probability transport.
arXiv:2603.20562v3 Announce Type: replace
Abstract: Large language models (LLMs) are now widely used as judges, yet their decisions can change under presentation choices that should be irrelevant. We study one such source of instability: candidate-order sensitivity in listwise factuality evaluation, where several answers can look similarly polished while differing substantially in hallucination risk. We introduce PCFJudge, an inference-time method that reruns the same factuality-first listwise prompt over multiple orderings of the same candidate set and aggregates the resulting scores, ranks, and uncertainty signals into a single consensus decision. On RewardBench 2 Factuality, the final seven-permutation aggregate (K=7) improves top-1 selection accuracy from 86.00% to 91.33% with GPT-5.4 and from 86.33% to 89.67% with Claude Sonnet 4.6. These results suggest that candidate order can be a meaningful source of factuality-judging error and that marginalizing over this nuisance variation can improve the reliability of LLM evaluation.