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新论文 · v1arXiv:2611.17162

时间中的对称性:线性循环记忆的表示理论

Symmetry in Time: A Representation Theory of Linear Recurrent Memory

Anif N. Shikder, Ramit Dey, Jan Minac, Lyle E. Muller

AI 速读 基于摘要

作者用表示理论刻画线性循环状态空间模型的状态追踪能力,并提出引入四元数通道的 HyperSSM 以突破对角实/复 SSM 只能追踪交换群的限制。

cs.LG · cs.NE · math.RT

查看原文摘要

State space models (SSMs) are an emerging alternative to Transformers. SSMs offer linear-time inference and parallel training, but most implementations make the parallel scan efficient by making the recurrence diagonal: each channel of the hidden state is multiplied by an input-dependent real or complex number. These numbers commute, so the state records which inputs occurred but not their order. We formalize this with representation theory, which explains and fixes the state-tracking failures previously reported for SSMs. The state update defines a linear representation of the monoid of input sequences, and we show that an SSM tracks a group at every sequence length exactly when that group is a quotient of the group generated by its transition matrices. Two consequences follow. Diagonal real- and complex-valued SSMs can track only commutative groups, while the transition matrices of any SSM that can track a group must split into independent blocks over the real, complex, and quaternion numbers. We then introduce HyperSSM, which adds quaternion channels while keeping linear-time inference and parallel training. Trained only on final answers, HyperSSM solves the group tasks of recent state-tracking benchmarks exactly with at most five state numbers. This includes $S_5$ with 32 generators, where previous SSMs are at chance, and HyperSSM generalizes to sequences 25 times longer than those seen in training. Because the theory says what the transitions must encode, the learned weights of the linear recurrence can be interpreted directly. We demonstrate this by recovering the calibration of a real gyroscope, the rotations of imperfect qubit gates and the geometry of protein backbones.

版本更新 · v2arXiv:2610.12421

Beyond Spatio-Temporal Priors: A Generalizable Approach for Dense Correspondence Matching

Luping Liu, Bingyi Kang, Yifan Wang, Dong Xu

原文摘要

Dense correspondence matching has historically been bounded by simplifying spatio-temporal priors, such as smooth motion and rigid geometry. While effective for classical tasks, these assumptions break down in image editing and reference-guided generation (IEG), where transformations can preserve visual identity while breaking physical continuity. To establish identity-preserving correspondence across such transformations, we introduce FreeMatching, a generalizable framework combining generative and semantic foundation representations with heterogeneous supervision from classical datasets, tracked videos, and synthetic scenes. Teacher-guided iterative refinement further improves correspondence in IEG without dense correspondence annotations. Experimentally, a single FreeMatching model substantially improves correspondence quality on challenging IEG image pairs while retaining competitive performance on classical benchmarks. Furthermore, we demonstrate its utility as a quantitative metric for evaluating identity preservation, with scores that correlate with human judgment. The code is available at https://github.com/luping-liu/FreeMatching.

cs.CV · cs.LG

版本更新 · v2arXiv:2604.10009

Towards Multi-Source Domain Generalization for Sleep Staging with Noisy Labels

Kening Wang, Di Wen, Yufan Chen, Ruiping Liu, Junwei Zheng, Jiale Wei, Kailun Yang, Rainer Stiefelhagen 等 9 位作者

原文摘要

Automatic sleep staging is a multimodal learning problem involving heterogeneous physiological signals such as EEG and EOG, which often suffer from domain shifts across institutions, devices, and populations. In practice, these data are also affected by noisy annotations, yet label-noise-robust multi-source domain generalization remains underexplored. We present the first benchmark for Noisy Labels in Multi-Source Domain-Generalized Sleep Staging (NL-DGSS) and show that existing noisy-label learning methods degrade substantially when domain shifts and label noise coexist. To address this challenge, we propose FF-TRUST, a domain-invariant multimodal sleep staging framework with Joint Time-Frequency Early Learning Regularization (JTF-ELR). By jointly exploiting temporal and spectral consistency together with confidence-diversity regularization, FF-TRUST improves robustness under noisy supervision. Experiments on five public datasets demonstrate consistent state-of-the-art performance under diverse symmetric and asymmetric noise settings.

cs.LG · cs.CV · cs.RO

新论文 · v1arXiv:2611.11914

CRAFT-GBM: Selecting Best Features for Gradient-Boosted Machine Learning

Basil Kuok, Yi Zhou, Yao Xuan, Shuping Li, Ke-Wei Huang

原文摘要

Feature subsampling is used to accelerate gradient-boosted trees, yet standard approaches fix the feature count in advance and largely ignore the split-gain evidence accumulated during training. We introduce CRAFT-GBM (Confidence-Ranked Adaptive Feature Tracking), a native LightGBM extension that uses this evidence to adapt which---and, by default, how many---features are searched each boosting round. CRAFT-GBM transforms root-split gains into bounded observations and constructs joint time-uniform bounds valid under adaptive, non-stationary training histories. In its default endogenous mode, after initialization, CRAFT-GBM retains exactly the features that cannot yet be ruled out as best, letting the selected feature-set size $K_t$ emerge from training history rather than a pre-specified fraction. With probability at least $1-δ$, every feature with the largest expected gain is retained jointly across all rounds after initialization. When a feature fraction $f$ is specified instead, CRAFT-GBM ranks features by their interval point estimates and provides an approximate top-$K$ guarantee for feature budget $K_f$. We implement CRAFT-GBM within LightGBM while preserving its native feature-bundling representation, and evaluate it across 14 public and synthetic dataset families and four noise-augmented settings. In the fully endogenous setting, CRAFT-GBM reduces per-fit training time by 39.74\% with 1.04\% lower test loss in the geometric mean across all 18 RQ1 experiments. Under pre-specified feature fraction $f$, Exogenous CRAFT-GBM also yields aggregate training-time reductions up to 13.52 percentage points larger than random feature subsampling, with no increase in aggregate test loss relative to full-feature LightGBM. Accumulated training evidence can thus support adaptive feature search with statistical guarantees while retaining the practical advantages of native gradient boosting.

cs.LG · math.ST

新论文 · v1arXiv:2611.11371

D3Tree: Learning to Prune Block-Diffusion Draft Trees for Efficient Verification

Hong Nie, Zhangchi Gao, Jun Yu, Bo Wang, Jianqing Sun, Shengping Liu

原文摘要

Block-diffusion drafters propose a whole block of tokens in one forward pass, and draft trees built from their position-wise marginals increase the expected accepted length of speculative decoding. Every tree node occupies a query row in target verification, so under concurrent serving low-yield branches compete with other requests for verification capacity. Existing tree methods select verified nodes by draft probability under a fixed or cost-selected per-request budget, and thus always retain a prefix of the drafter's ranking. We present D3Tree, which learns which nodes of a block-diffusion draft tree are worth verifying. A tree-size head with 2H+2 parameters predicts each candidate's conditional survival from the draft state, the candidate embedding, and its draft log-probability. Thresholding the product of these scores along parent chains yields an ancestor-closed subtree whose size adapts to each request and decoding round. The head is trained on a frozen drafter with conditional labels on the full candidate tree; an optional joint mode also steers the drafter toward the retained reference path. At serving time, D3Tree verifies whole trees under light load and, under heavy load, allocates one batch-wide node budget by predicted survival, sized to the target's matrix-multiplication tiles. Retained trees share one ancestor-masked target pass, while construction, pruning, and scheduling run on the GPU and overlap with the host. Across six vision-language verifiers and 17 text and multimodal benchmarks, D3Tree is fastest in 70 of 72 load settings, with 3.2-4.0x speedup over autoregressive decoding for one request and 1.3-1.8x at 64 concurrent requests, where fixed-budget trees fall below autoregressive speed. Under a time-varying arrival trace, it has the lowest mean end-to-end latency in every arrival phase.

cs.LG · cs.AI

版本更新 · v3arXiv:2604.20568

Amortized Vine Copulas for High-Dimensional Density and Information Estimation

Houman Safaai

原文摘要

Modeling high-dimensional dependencies while keeping likelihoods tractable re- mains challenging. Classical vine copulas provide an explicit dependence structure but require repeated, costly bivariate fitting. We propose Vine Denoising Copula (VDC)1, an amortized estimator for simplified vines on continuous data. VDC trains a single bivariate denoising network on simulated copulas and reuses it across all vine edges. For each edge, the network maps an empirical histogram to a density grid, and iterative proportional fitting approximately enforces uniform grid marginals. The predicted densities and cached conditional transforms support stan- dard vine recursion, likelihood evaluation, sampling, and information estimation. This retains the classical vine factorization while replacing repeated per-edge fitting with reusable neural inference. Across synthetic and real-data benchmarks, VDC combines accurate bivariate density estimation, competitive information estimates, and faster high-dimensional vine fitting after pretraining. Performance varies across datasets; finite grid resolution and conditional prediction remain limitations. The explicit fitted structure supports edge- and tree-level information decomposition, making repeated dependence analysis more practical.

cs.LG · cs.IT · stat.ME

版本更新 · v3arXiv:2602.05214

Disentangled Representation Learning via Flow Matching

Jinjin Chi, Taoping Liu, Mengtao Yin, Ximing Li, Yongcheng Jing, Jialie Shen, Leszek Rutkowski, Dacheng Tao

原文摘要

Disentangled representation learning aims to capture the underlying explanatory factors of observed data, enabling a principled understanding of the data-generating process. Recent advances in generative modeling have introduced new paradigms for learning such representations. However, existing diffusion-based methods encourage factor independence via inductive biases, yet frequently lack strong semantic alignment. In this work, we propose a flow matching-based framework for disentangled representation learning, which casts disentanglement as learning factor-conditioned flows in a compact latent space. To enforce explicit semantic alignment, we introduce a non-overlap (orthogonality) regularizer that suppresses cross-factor interference and reduces information leakage between factors. Extensive experiments across multiple datasets demonstrate consistent improvements over representative baselines, yielding higher disentanglement scores as well as improved controllability and sample fidelity.

cs.LG

新论文 · v1arXiv:2611.07375

When Scores Conflict with Preferences: Pre-Alignment Diagnosis and Adaptive Correction of Constraint Drift in DPO

Ping Liu, Yan Yan

原文摘要

Direct Preference Optimization (DPO) is increasingly used in settings where pairwise preferences coexist with pointwise criteria such as response length, answer correctness, or safety scores. When the two disagree, standard DPO treats pairs whose preferred output scores worse on the pointwise criterion (conflict pairs) in the same way as the remaining (matching) pairs. We characterize a systematic failure mode, constraint drift: for sufficiently small updates, conflict pairs tend to increase constraint cost while matching pairs tend to repair it, and the net change depends on their balance. This balance yields a closed-form pre-alignment diagnostic, $ρ^{*}_{\mathrm{eq}}$, computable from dataset statistics, that indicates whether a dataset is self-correcting or requires intervention. Building on this diagnostic, we propose Conflict-aware DPO (CoDPO), which down-weights conflict pairs with a strength set from $ρ^{*}_{\mathrm{eq}}$ rather than tuned, and adds an adaptive margin shift that addresses residual drift during training. Empirically, drift grows monotonically with conflict exposure on the conflict-dominated domains, and the intervention decision given by $ρ^{*}_{\mathrm{eq}}$ matches the observed drift on every domain, including one that it identifies as self-correcting. On all four domains of the main comparison, CoDPO reduces drift while largely preserving the preference learning of vanilla DPO. Compared with hard filtering and recent constrained and multi-objective baselines, CoDPO also achieves a more favorable drift-preference trade-off.

cs.LG

版本更新 · v2arXiv:2610.34158

Last-Iterate Stationarity of Muon with Finitely Many Newton-Schulz Iterations

Ping Li, Vincent Y. F. Tan

原文摘要

Muon has demonstrated strong empirical performance in large-scale language-model training, motivating a deeper theoretical understanding of its practical implementation. Unlike the idealized polar-factor update, practical Muon employs a fixed number of quintic Newton-Schulz iterations. Existing analyses primarily establish average- or best-iterate stationarity guarantees, while last-iterate convergence remains less understood. In this work, we investigate last-iterate gradient convergence of practical finite-step Muon on smooth, lower-bounded nonconvex objectives. In the deterministic setting, we show that Muon without input stabilization can exhibit cyclic behavior even on a smooth convex quadratic. In contrast, with positive stabilization, we establish last-iterate gradient convergence and square-summability of gradients for any fixed momentum coefficient below one and a sufficiently small constant learning rate. In the stochastic setting, we first demonstrate that persistent bounded, unbiased noise can prevent convergence under fixed learning rates and momentum, even with positive stabilization. We then establish almost-sure and mean-square last-iterate gradient convergence under bounded-variance stochastic gradients by combining diminishing learning rates with increasing momentum. Finally, we construct a smooth counterexample demonstrating that neither convergence theorem implies a pointwise polynomial convergence rate. Nevertheless, we establish density-one convergence rates, guaranteeing polynomial gradient decay for all but an asymptotically vanishing fraction of iterations.

cs.LG

版本更新 · v2arXiv:2608.01320

Dense Language Generation Made Simple: Deterministic, Randomized, and Multi-Order Algorithms

Ziyi Cai, Shuangping Li, Yiheng Shen, Kangning Wang, Peng Zhang

原文摘要

Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples. In this model, an adversary chooses an unknown language from a countable family and enumerates its elements in an arbitrary order, while the generator must eventually output only elements of the language that have not yet appeared in the enumeration. Reliable generation is thus formalized through two eventual guarantees: validity and novelty relative to the observed data. To further quantify the breadth of the generator's outputs, Kleinberg and Wei (FOCS 2025, STOC 2026) introduced lower density as a measure of output coverage. Given an order representing the importance or relevance of possible outputs, lower density is the asymptotic lower bound, as $n$ grows, on the fraction of the first $n$ elements of the target language that the generator outputs before they appear in the data. Kleinberg and Wei showed that $1/2$ is the optimal lower-density guarantee for deterministic algorithms. We develop a simple and unified framework for obtaining optimal lower-density guarantees. We first give a deterministic algorithm that recovers the optimal guarantee of $1/2$ with a significantly simpler analysis than prior work. We then demonstrate the flexibility of our framework through two extensions. First, against an oblivious adversary, randomization raises the optimal guarantee to $1-1/e$. Second, for any finite collection of orders, the optimal deterministic and randomized guarantees can be achieved simultaneously with respect to every order, so accommodating multiple notions of importance or relevance entails no loss in the optimal guarantee.

cs.DS · cs.AI · cs.CL · cs.DM · cs.LG

新论文 · v1arXiv:2611.04146

RGDM: Robust Graph Diffusion Model

Yancheng Wang, Ping Li, Dongfang Sun, Yingzhen Yang

原文摘要

Diffusion models represent a powerful class of generative models known for their solid theoretical foundations and remarkable performance across diverse tasks and domains. Existing node level diffusion methods synthesize nodes and edges within a graph, but are not designed to learn a robust generator from adversarially corrupted graphs. In this study, we introduce the Robust Graph Diffusion Model (RGDM), designed to generate labeled synthetic graph structures consisting of nodes and edges that integrate seamlessly into a given graph. The RGDM consists of a Robust Graph Autoencoder (RGAE) and a Latent Diffusion Model (LDM). Leveraging an edge selection mechanism and an innovative low-rank regularization on the latent feature, the RGDM produces clean and high-quality synthetic graph structures, even when trained on graphs subject to adversarial attacks. Comprehensive experimental evaluations reveal that Graph Neural Networks (GNNs) trained on the augmented graph, which is formed by merging the original attacked graph with the synthetic graph structures, exhibit significantly improved robustness against various graph adversarial attacks in the context of semi-supervised node classification. The code of the RGDM is available at https://github.com/Statistical-Deep-Learning/RGDM.

cs.LG

新论文 · v1arXiv:2611.01642

Sharp Generalization for Nonparametric Regression in Interpolation Space by Shallow Over-Parameterized Neural Networks with Channel Attention

Yingzhen Yang, Ping Li

原文摘要

We study nonparametric regression using an over-parameterized two-layer ReLU neural network with fixed covariance-based channel attention, trained by gradient descent with both layers updated simultaneously. The spherical covariates follow an arbitrary fixed non-atomic distribution, and the target function lies in an interpolation space with spectral bias widely studied in the statistical learning literature. We prove that early-stopped training achieves regression risk $\cO(\eps_n^2)$, where $\eps_n$ is the critical population rate of the attention kernel $\Kattn$. Its positive eigenvalues are $λ_j^{s'}$, where $λ_j$ are those of the ReLU feature covariance kernel $K$ and $s'=2s+3$ for $s\ge1$. Under polynomial eigenvalue decay $λ_j\asymp j^{-2α}$ with $α>1/2$, the regression risk bound $\cO(\eps_n^2)$ specializes to the minimax optimal rate $\cO(n^{-2αs'/(2αs'+1)})$. Our analysis is based on two new technical results on the optimization and generalization of the attention network. First, the neural network function after every gradient descent iteration admits a decomposition into a function with bounded Reproducing Kernel Hilbert Space (RKHS) norm and a uniformly small residual. Second, local Rademacher complexity converts this decomposition into a regression risk bound. Kernel gradient descent on the same ball attains the same rate, while our theorem gives explicit sufficient width and auxiliary-sample conditions for simultaneous network training. Our analysis is further extended to covariates supported on $\RR^d$ through a novel normalization method. Under a sub-Gaussian covariate distribution, the attention network achieves a nearly optimal regression risk $\cO((\log n)n^{-s'(d+3)/(s'(d+3)+d)})$ without a density assumption.

stat.ML · cs.LG

版本更新 · v5arXiv:2407.11353

Sharp Generalization for Nonparametric Regression in Interpolation Space by Over-Parameterized Neural Networks Trained with Preconditioned Gradient Descent and Early Stopping

Yingzhen Yang, Ping Li

原文摘要

We study nonparametric regression using an over-parameterized two-layer neural network trained with algorithmic guarantees in this paper. We consider the setting where the training features are drawn uniformly from the unit sphere in $\RR^d$, and the target function lies in an interpolation space commonly studied in statistical learning theory. We demonstrate that training the neural network with a novel Preconditioned Gradient Descent (PGD) algorithm, equipped with early stopping, achieves a sharp regression rate of $\cO(n^{-\frac{2αs'}{2αs'+1}})$, where $α$ parametrizes the polynomial eigenvalue decay of the regular Neural Tangent Kernel (NTK), $λ_j\asymp j^{-2α}$, and $2α=d/(d-1)$ under the spherical uniform design considered here. The target function is assumed to belong to the interpolation space $\bth{\cH_K}^{s'}$ with $s'\ge3$. This rate is even sharper than the currently known nearly-optimal rate of $\cO(n^{-\frac{2αs'}{2αs'+1}})\log^2(1/δ)$~\citep{Li2024-edr-general-domain}, where $n$ is the size of the training data and $δ\in (0,1)$ is a small probability. Our analysis is based on two key technical contributions. First, we present a principled decomposition of the network output at each PGD step into a function in the reproducing kernel Hilbert space (RKHS) of a newly induced integral kernel, and a residual function with small $L^{\infty}$-norm. Second, leveraging this decomposition, we apply local Rademacher complexity theory to tightly control the complexity of the function class comprising all the neural network functions obtained in the PGD iterates. Our results show how PGD changes the effective kernel in the reference training dynamics, inducing an integral kernel with lower complexity than the regular NTK arising from vanilla GD.

stat.ML · cs.LG · math.ST