arXiv subjects

Mingyue Xu

Publications and source records attributed to Mingyue Xu.

14 recordsLinked to original sources

arXiv2026

Towards a theory of inference-time alignment with unknown rewards

Generative model alignment has received broad interest, and significant progress has been made in supervised fine-tuning and inference-time computation. Yet, alignment has remained poorly understood from a statistical learning perspective. We formulate inference-time alignment as a weak-to-strong learning problem, where a reference policy (weak model) is assumed to be fairly good and the goal is to produce a strong model that predicts a good response at test time with arbitrarily high probability. Our problem is formulated as learning from scratch --- everything is learned from data rather than assuming access to a good reward estimate, and thus differs from the existing inference-time alignment theory. Our framework shares similarity to the recent work of Joshi et al., (arXiv:2510.15464), where for each prompt, there could be multiple good responses. Our definition of the alignment learnability follows the standard PAC learning principle. We introduce a novel combinatorial dimension of the reward class which we call the alignment dimension, and show that it completely characterizes the alignment learnability --- a reward class is alignment learnable if and only if its alignment dimension is finite. The core of our learning procedure works by learning a pairwise comparator and then running a tournament over candidate responses. We believe that our results might shed light toward establishing a complete theoretical understanding of alignment.

cs.LG↗

arXiv2026

Optimal Learning Under Tsybakov Noise

Probably Approximately Correct (PAC) learning [Val84] is a fundamental learning model that has been extensively investigated. In this model, $\mathcal{H} \subseteq \{0,1\}^{\mathcal{X}}$ is a concept class, and $h^*\in\mathcal{H}$ is the target concept to be learned. Having access to i.i.d. labeled examples from a distribution $\mathcal{D}$ over $\mathcal{X}\times\{0,1\}$, which admits $h^*$ as the best concept in $\mathcal{H}$, the goal is to design a learning algorithm that outputs a hypothesis having low error competitive to $h^{*}$ with high probability. This model was initially studied under the realizable setting, which assumes that $h^*$ has no error. A natural relaxation is to allow label noise, that is, the true label can be flipped with probability $\eta\in(0,1/2)$. In reality, certain labels might be extremely noisy, especially for those points near the decision boundary. Hence, it is natural to allow very noisy points, though only rarely. This is quantified by a noise model introduced by [MT99] and [Tsy04], now known as Tsybakov noise. For learning general concept classes, [MN06] gave the general upper and lower bounds for error guarantees under Tsybakov noise. However, their upper and lower bounds differ by a logarithmic factor. Resolving this gap has remained a well-known open question for the past twenty years. In this work, we resolve this open question by improving the upper bound to match the best known lower bound, thus establishing the optimal error guarantee for learning under Tsybakov noise. Our learning algorithm operates by adaptively partitioning the instance space into regions, roughly corresponding to different noise levels, and returning a hypothesis in the concept class satisfying a specific error constraint for each region. Our technique shares a conceptual foundation with several recent advances in non-realizable learning, such as [HLZ24] and [Han25].

cs.LG↗

arXiv2026

Attention-based representations for multi-task computation

Multi-head attention layers produce vector representations that support multiple downstream tasks. We establish bounds on the number of heads required in two simple and concrete multi-task scenarios. In the first scenario, a vector representation is sought so that linear predictors can compute both the smallest and largest numbers in a given list. In this case, it is known two attention heads with small embedding dimension and bit precision level suffice. We prove that a single attention head requires exponentially higher embedding dimension or precision level. In the second scenario, a vector representation is sought so that a polynomial threshold function can compute the XOR of a given string of $n$ bits. This scenario is analogous to the first one for $n=2$, since XOR is readily computed by a linear function using a vector representation that encodes both the AND and the OR of the two bits. We observe that $n$-bit XOR requires the product of the number of heads and the polynomial degree to be at least $n$, and we construct multi-head attention layers that match this lower bound. These results generalize to arbitrary (symmetric) Boolean functions, where the bound is given in terms of the threshold degree.

cs.LG↗

arXiv2026

To Grok Grokking: Provable Grokking in Ridge Regression

We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting. We prove end-to-end grokking results for learning over-parameterized linear regression models using gradient descent with weight decay. Specifically, we prove that the following stages occur: (i) the model overfits the training data early during training; (ii) poor generalization persists long after overfitting has manifested; and (iii) the generalization error eventually becomes arbitrarily small. Moreover, we show, both theoretically and empirically, that grokking can be amplified or eliminated in a principled manner through proper hyperparameter tuning. To the best of our knowledge, these are the first rigorous quantitative bounds on the generalization delay (which we refer to as the "grokking time") in terms of training hyperparameters. Lastly, going beyond the linear setting, we empirically demonstrate that our quantitative bounds also capture the behavior of grokking on non-linear neural networks. Our results suggest that grokking is not an inherent failure mode of deep learning, but rather a consequence of specific training conditions, and thus does not require fundamental changes to the model architecture or learning algorithm to avoid.

cs.LG↗

arXiv2026

When More Data Doesn't Help: Limits of Adaptation in Multitask Learning

Multitask learning and related frameworks have achieved tremendous success in modern applications. In multitask learning problem, we are given a set of heterogeneous datasets collected from related source tasks and hope to enhance the performance above what we could hope to achieve by solving each of them individually. The recent work of arXiv:2006.15785 has showed that, without access to distributional information, no algorithm based on aggregating samples alone can guarantee optimal risk as long as the sample size per task is bounded. In this paper, we focus on understanding the statistical limits of multitask learning. We go beyond the no-free-lunch theorem in arXiv:2006.15785 by establishing a stronger impossibility result of adaptation that holds for arbitrarily large sample size per task. This improvement conveys an important message that the hardness of multitask learning cannot be overcame by having abundant data per task. We also discuss the notion of optimal adaptivity that may be of future interests.

cs.LG↗

arXiv2026

Rethinking Gradient-based Adversarial Attacks on Point Cloud Classification

Gradient-based adversarial attacks are widely used to evaluate the robustness of 3D point cloud classifiers, yet they often rely on uniform update rules that neglect point-wise heterogeneity, leading to perceptible perturbations. We propose two complementary strategies to improve both the effectiveness and imperceptibility of the attack. \textbf{WAAttack} employs weighted gradients to dynamically adjust per-point perturbation magnitudes and uses an adaptive step size strategy to regulate the global perturbation scale. \textbf{SubAttack} partitions the point cloud into subsets and, at each iteration, perturbs only those combinations with high adversarial efficacy and low perceptual saliency. Together, these methods offer a principled refinement of gradient-based attacks for 3D point clouds. Extensive experiments show that our approach consistently outperforms state-of-the-art methods in generating highly imperceptible adversarial examples. The code is available at https://github.com/chenjun0326/WA_SubAttack.

cs.CV↗

arXiv2026

DSKC: Domain Style Modeling with Adaptive Knowledge Consolidation for Exemplar-free Lifelong Person Re-Identification

Lifelong Person Re-identification (LReID) aims to continuously match individuals across camera views from sequential data streams. Existing LReID methods often ignore domain-specific style awareness and unified knowledge consolidation, which are crucial for mitigating forgetting when adapting to new information. We propose DSKC, a novel rehearsal-free and distillation-free framework for LReID. DSKC designs a domain-style encoder (DSE) to dynamically model domain-specific styles, and a unified knowledge consolidation (UKC) mechanism to adaptively integrate instance-level representations with domain-specific style into a cross-domain unified representation. By leveraging unified representation as a bridge, DSKC explicitly models inter-domain associations at both instance and domain levels to enhance anti-forgetting and generalization. Experimental results demonstrate that our DSKC outperforms state-of-the-art methods in two training orders and enhances the model's strong performance. Our code is available at https://github.com/LiuShiBen/DKUA.

cs.CV↗

arXiv2025

GMT: Effective Global Framework for Multi-Camera Multi-Target Tracking

Multi-Camera Multi-Target (MCMT) tracking aims to locate and associate the same targets across multiple camera views. Existing methods typically adopt a two-stage framework, involving single-camera tracking followed by inter-camera tracking. However, in this paradigm, multi-view information is used only to recover missed matches in the first stage, providing a limited contribution to overall tracking. To address this issue, we propose GMT, a global MCMT tracking framework that jointly exploits intra-view and inter-view cues for tracking. Specifically, instead of assigning trajectories independently for each view, we integrate the same historical targets across different views as global trajectories, thereby reformulating the two-stage tracking as a unified global-level trajectory-target association process. We introduce a Cross-View Feature Consistency Enhancement (CFCE) module to align visual and spatial features across views, providing a consistent feature space for global trajectory modeling. With these aligned features, the Global Trajectory Association (GTA) module associates new detections with existing global trajectories, enabling direct use of multi-view information. Compared to the two-stage framework, GMT achieves significant improvements on existing datasets, with gains of up to 21.3 percent in CVMA and 17.2 percent in CVIDF1. Furthermore, we introduce VisionTrack, a high-quality, large-scale MCMT dataset providing significantly greater diversity than existing datasets. Our code and dataset will be released.

cs.CV↗

arXiv2025

Universal rates of ERM for agnostic learning

The universal learning framework has been developed to obtain guarantees on the learning rates that hold for any fixed distribution, which can be much faster than the ones uniformly hold over all the distributions. Given that the Empirical Risk Minimization (ERM) principle being fundamental in the PAC theory and ubiquitous in practical machine learning, the recent work of arXiv:2412.02810 studied the universal rates of ERM for binary classification under the realizable setting. However, the assumption of realizability is too restrictive to hold in practice. Indeed, the majority of the literature on universal learning has focused on the realizable case, leaving the non-realizable case barely explored. In this paper, we consider the problem of universal learning by ERM for binary classification under the agnostic setting, where the ''learning curve" reflects the decay of the excess risk as the sample size increases. We explore the possibilities of agnostic universal rates and reveal a compact trichotomy: there are three possible agnostic universal rates of ERM, being either $e^{-n}$, $o(n^{-1/2})$, or arbitrarily slow. We provide a complete characterization of which concept classes fall into each of these categories. Moreover, we also establish complete characterizations for the target-dependent universal rates as well as the Bayes-dependent universal rates.

stat.ML↗

arXiv2025

Legal Mathematical Reasoning with LLMs: Procedural Alignment through Two-Stage Reinforcement Learning

Legal mathematical reasoning is essential for applying large language models (LLMs) in high-stakes legal contexts, where outputs must be both mathematically accurate and procedurally compliant. However, existing legal LLMs lack structured numerical reasoning, and open-domain models, though capable of calculations, often overlook mandatory legal steps. To address this, we present LexNum, the first Chinese legal mathematical reasoning benchmark, covering three representative scenarios where each instance reflects legally grounded procedural flows. We further propose LexPam, a two-stage reinforcement learning framework for efficient legal reasoning training. Leveraging curriculum learning, we use a stronger teacher model to partition data into basic and challenging subsets. A lightweight 1.5B student model is then fine-tuned with Group Relative Policy Optimization, which avoids costly value networks and enables stable training from sparse, end-of-sequence rewards. The first stage improves accuracy and format; the second introduces a novel reward to guide procedural alignment via task-specific legal elements. Experiments show that existing models perform poorly on LexNum, while LexPam enhances both mathematical accuracy and legal coherence, and generalizes effectively across tasks and domains.

cs.CL↗

arXiv2025

Universal Rates of Empirical Risk Minimization

The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is its so-called "learning curve", that is, the decay of the expected error as a function of the input sample size. As the PAC model fails to explain the behavior of learning curves, recent research has explored an alternative universal learning model and has ultimately revealed a distinction between optimal universal and uniform learning rates (Bousquet et al., 2021). However, a basic understanding of such differences with a particular focus on the ERM principle has yet to be developed. In this paper, we consider the problem of universal learning by ERM in the realizable case and study the possible universal rates. Our main result is a fundamental tetrachotomy: there are only four possible universal learning rates by ERM, namely, the learning curves of any concept class learnable by ERM decay either at $e^{-n}$, $1/n$, $\log(n)/n$, or arbitrarily slow rates. Moreover, we provide a complete characterization of which concept classes fall into each of these categories, via new complexity structures. We also develop new combinatorial dimensions which supply sharp asymptotically-valid constant factors for these rates, whenever possible.

stat.ML↗

arXiv2024

Efficient Estimation of the Central Mean Subspace via Smoothed Gradient Outer Products

We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional conditions (e.g., the covariate distribution $P_{\mathbf{X}}$ being elliptical symmetric). In this paper, we show that a fast parametric convergence rate of form $C_d \cdot n^{-1/2}$ is achievable via estimating the \emph{expected smoothed gradient outer product}, for a general class of distribution $P_{\mathbf{X}}$ admitting Gaussian or heavier distributions. When the link function is a polynomial with a degree of at most $r$ and $P_{\mathbf{X}}$ is the standard Gaussian, we show that the prefactor depends on the ambient dimension $d$ as $C_d \propto d^r$.

stat.ML↗

arXiv2023

Distributed Semi-Supervised Sparse Statistical Inference

The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant computational costs. This challenge becomes particularly acute in distributed setups, where traditional methods necessitate computing a debiased estimator on every machine. This becomes unwieldy, especially with a large number of machines. In this paper, we delve into semi-supervised sparse statistical inference in a distributed setup. An efficient multi-round distributed debiased estimator, which integrates both labeled and unlabelled data, is developed. We will show that the additional unlabeled data helps to improve the statistical rate of each round of iteration. Our approach offers tailored debiasing methods for $M$-estimation and generalized linear models according to the specific form of the loss function. Our method also applies to a non-smooth loss like absolute deviation loss. Furthermore, our algorithm is computationally efficient since it requires only one estimation of a high-dimensional inverse covariance matrix. We demonstrate the effectiveness of our method by presenting simulation studies and real data applications that highlight the benefits of incorporating unlabeled data.

stat.ML↗

arXiv2021

Establishing a non-hydrostatic global atmospheric modeling system (iAMAS) at 3-km horizontal resolution with online integrated aerosol feedbacks on the Sunway supercomputer of China

During the era of global warming and highly urbanized development, extreme and high impact weather as well as air pollution incidents influence everyday life and might even cause the incalculable loss of life and property. Although with the vast development of numerical simulation of atmosphere, there still exists substantial forecast biases objectively. To predict extreme weather, severe air pollution, and abrupt climate change accurately, the numerical atmospheric model requires not only to simulate meteorology and atmospheric compositions and their impacts simultaneously involving many sophisticated physical and chemical processes but also at high spatiotemporal resolution. Global atmospheric simulation of meteorology and atmospheric compositions simultaneously at spatial resolutions of a few kilometers remains challenging due to its intensive computational and input/output (I/O) requirement. Through multi-dimension-parallelism structuring, aggressive and finer-grained optimizing, manual vectorizing, and parallelized I/O fragmenting, an integrated Atmospheric Model Across Scales (iAMAS) was established on the new Sunway supercomputer platform to significantly increase the computational efficiency and reduce the I/O cost. The global 3-km atmospheric simulation for meteorology with online integrated aerosol feedbacks with iAMAS was scaled to 39,000,000 processor cores and achieved the speed of 0.82 simulation day per hour (SDPH) with routine I/O, which enables us to perform 5-day global weather forecast at 3-km horizontal resolution with online natural aerosol impacts. The results demonstrate the promising future that the increasing of spatial resolution to a few kilometers with online integrated aerosol impacts may significantly improve the global weather forecast.

physics.ao-ph↗