Yicheng Li

Haobo Zhang, Yicheng Li, Qian Lin

In the misspecified spectral algorithms problem, researchers usually assume the underground true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\|f_ρ^{*}\|_{L^{\infty}}<\infty$ which implicitly requires $s > α_{0}$ where $α_{0}\in (0,1)$ is the embedding index, a constant depending on $\mathcal{H}$. Whether the spectral algorithms are optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that spectral algorithms are minimax optimal for any $α_{0}-\frac{1}β < s < 1$, where $β$ is the eigenvalue decay rate of $\mathcal{H}$. We also give several classes of RKHSs whose embedding index satisfies $ α_0 = \frac{1}β $. Thus, the spectral algorithms are minimax optimal for all $s\in (0,1)$ on these RKHSs.

Yicheng Li, Haobo Zhang, Qian Lin

The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theory. Since the generalization ability of the 'lazy trained' over-parametrized neural network can be well approximated by that of the neural tangent kernel regression, the curve of the excess risk (namely, the learning curve) of kernel ridge regression attracts increasing attention recently. However, most recent arguments on the learning curve are heuristic and are based on the 'Gaussian design' assumption. In this paper, under mild and more realistic assumptions, we rigorously provide a full characterization of the learning curve: elaborating the effect and the interplay of the choice of the regularization parameter, the source condition and the noise. In particular, our results suggest that the 'benign overfitting phenomenon' exists in very wide neural networks only when the noise level is small.

Weihao Lu, Haobo Zhang, Yicheng Li et al.

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^γ$ for some $γ>0$ ). We first build a general tool to characterize the upper bound and the minimax lower bound of kernel regression for large dimensional data through the Mendelson complexity $\varepsilon_{n}^{2}$ and the metric entropy $\bar{\varepsilon}_{n}^{2}$ respectively. When the target function falls into the RKHS associated with a (general) inner product model defined on $\mathbb{S}^{d}$, we utilize the new tool to show that the minimax rate of the excess risk of kernel regression is $n^{-1/2}$ when $n\asymp d^γ$ for $γ=2, 4, 6, 8, \cdots$. We then further determine the optimal rate of the excess risk of kernel regression for all the $γ>0$ and find that the curve of optimal rate varying along $γ$ exhibits several new phenomena including the multiple descent behavior and the periodic plateau behavior. As an application, For the neural tangent kernel (NTK), we also provide a similar explicit description of the curve of optimal rate. As a direct corollary, we know these claims hold for wide neural networks as well.

Yu Wang, Shaohua Wang, Yicheng Li et al.

In recent years, 3D object perception has become a crucial component in the development of autonomous driving systems, providing essential environmental awareness. However, as perception tasks in autonomous driving evolve, their variants have increased, leading to diverse insights from industry and academia. Currently, there is a lack of comprehensive surveys that collect and summarize these perception tasks and their developments from a broader perspective. This review extensively summarizes traditional 3D object detection methods, focusing on camera-based, LiDAR-based, and fusion detection techniques. We provide a comprehensive analysis of the strengths and limitations of each approach, highlighting advancements in accuracy and robustness. Furthermore, we discuss future directions, including methods to improve accuracy such as temporal perception, occupancy grids, and end-to-end learning frameworks. We also explore cooperative perception methods that extend the perception range through collaborative communication. By providing a holistic view of the current state and future developments in 3D object perception, we aim to offer a more comprehensive understanding of perception tasks for autonomous driving. Additionally, we have established an active repository to provide continuous updates on the latest advancements in this field, accessible at: https://github.com/Fishsoup0/Autonomous-Driving-Perception.

Yicheng Li, Haobo Zhang, Qian Lin

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in the literature on deep networks. In this paper, under mild conditions, we show that for any $\varepsilon>0$, the generalization error of kernel interpolation is lower bounded by $Ω(n^{-\varepsilon})$. In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on the sphere generalize poorly.

Yicheng Li

We prove a general lower bound for differentially private federated learning protocols with arbitrary public-transcript interactions. The protocol may use any number of adaptive rounds, and each client's local samples may be reused across rounds. For parameter estimation under squared \(\ell_2\) loss, we establish a federated van Trees lower bound for every estimator satisfying a total clientwise sample-level zero-concentrated differential privacy (zCDP) constraint. The main technical ingredient is a privacy-information contraction inequality for complete public transcripts. We illustrate the bound through applications to mean estimation, linear regression, and nonparametric regression.

Yicheng Li, Qian Lin

It is well known that eigenfunctions of a kernel play a crucial role in kernel regression. Through several examples, we demonstrate that even with the same set of eigenfunctions, the order of these functions significantly impacts regression outcomes. Simplifying the model by diagonalizing the kernel, we introduce an over-parameterized gradient descent in the realm of sequence model to capture the effects of various orders of a fixed set of eigen-functions. This method is designed to explore the impact of varying eigenfunction orders. Our theoretical results show that the over-parameterization gradient flow can adapt to the underlying structure of the signal and significantly outperform the vanilla gradient flow method. Moreover, we also demonstrate that deeper over-parameterization can further enhance the generalization capability of the model. These results not only provide a new perspective on the benefits of over-parameterization and but also offer insights into the adaptivity and generalization potential of neural networks beyond the kernel regime.

Yang Zhou, Yicheng Li, Yuqian Cheng et al.

Recent studies have reported $\textit{saturation effects}$ and $\textit{multiple descent behavior}$ in large dimensional kernel ridge regression (KRR). However, these findings are predominantly derived under restrictive settings, such as inner product kernels on sphere or strong eigenfunction assumptions like hypercontractivity. Whether such behaviors hold for other kernels remains an open question. In this paper, we establish a broad, new family of large dimensional kernels and derive the corresponding convergence rates of the generalization error. As a result, we recover key phenomena previously associated with inner product kernels on sphere, including: $i)$ the $\textit{minimax optimality}$ when the source condition $s\le 1$; $ii)$ the $\textit{saturation effect}$ when $s>1$; $iii)$ a $\textit{periodic plateau phenomenon}$ in the convergence rate and a $\textit {multiple-descent behavior}$ with respect to the sample size $n$.

Quanhao Ren, Yicheng Li, Nan Song

Motion forecasting is a core task in autonomous driving systems, aiming to accurately predict the future trajectories of surrounding agents to ensure driving safety. Existing methods typically process discrete driving scenes independently, neglecting the temporal continuity and historical context correlations inherent in real-world driving environments. This paper proposes PanguMotion, a motion forecasting framework for continuous driving scenarios that integrates Transformer blocks from the Pangu-1B large language model as feature enhancement modules into autonomous driving motion prediction architectures. We conduct experiments on the Argoverse 2 datasets processed by the RealMotion data reorganization strategy, transforming each independent scene into a continuous sequence to mimic real-world driving scenarios.

T. Tony Cai, Yicheng Li

The covariance matrix plays a fundamental role in the analysis of high-dimensional data. This paper studies minimax and adaptive estimation of high-dimensional bandable covariance matrices under differential privacy constraints. We propose a novel differentially private blockwise tridiagonal estimator that achieves minimax-optimal convergence rates under both the operator norm and the Frobenius norm. In contrast to the non-private setting, the privacy-induced error exhibits a polynomial dependence on the ambient dimension, revealing a substantial additional cost of privacy. To establish optimality, we develop a new differentially private van Trees inequality and construct carefully designed prior distributions to obtain matching minimax lower bounds. The proposed private van Trees inequality applies more broadly to general private estimation problems and is of independent interest. We further introduce an adaptive estimator that attains the optimal rate up to a logarithmic factor without prior knowledge of the decay parameter, based on a novel hierarchical tridiagonal approach. Numerical experiments corroborate the theoretical results and illustrate the fundamental privacy-accuracy trade-off.

Yicheng Li, Qian Lin

Theoretically exploring the advantages of neural networks might be one of the most challenging problems in the AI era. An adaptive feature program has recently been proposed to analyze the feature learning characteristic property of neural networks in a more abstract way. Motivated by the celebrated Le Cam equivalence, we advocate the over-parametrized sequence models to further simplify the analysis of the training dynamics of adaptive feature program and present several supporting evidences for the adaptive feature program. More precisely, after having introduced the feature error measure (FEM) to characterize the quality of the learned feature, we show that the FEM is decreasing during the training process of several concrete adaptive feature models including linear regression, single/multiple index models, etc. We believe that this hints at the potential successes of the adaptive feature program.

Yicheng Li, Haobo Zhang, Qian Lin

The saturation effect refers to the phenomenon that the kernel ridge regression (KRR) fails to achieve the information theoretical lower bound when the smoothness of the underground truth function exceeds certain level. The saturation effect has been widely observed in practices and a saturation lower bound of KRR has been conjectured for decades. In this paper, we provide a proof of this long-standing conjecture.

Chenglin Li, Qianglong Chen, Liangyue Li et al.

While large language models (LLMs) have demonstrated exceptional performance in recent natural language processing (NLP) tasks, their deployment poses substantial challenges due to high computational and memory demands in real-world applications. Recent studies have focused on enhancing smaller models through knowledge distillation from LLMs, yielding promising results. However, these models often struggle to match the performance of LLMs, especially in tasks that require reasoning. In this work, we introduce Mixed Distillation (MD) framework, which capitalizes on the strengths of Program of Thought (PoT) and Chain of Thought (CoT) capabilities within LLMs, combining multiple prompting techniques and distilling these capabilities into smaller models. Our experimental results show that MD significantly enhances the single-path and multi-path reasoning ability of smaller models in various tasks. In terms of accuracy and generality of reasoning tasks, the model generated by it exceeds the comprehensive performance of two individually distilled models. Notably, LLaMA2-7B and CodeLlama-7B using MD achieved remarkable improvements of (84.5%) and (85.5%), respectively, outperforming GPT-3.5-Turbo by (2.5%) and (3.5%), on the SVAMP benchmark.

Linli Yao, Yicheng Li, Yuancheng Wei et al. · pku

The rapid growth of online video platforms, particularly live streaming services, has created an urgent need for real-time video understanding systems. These systems must process continuous video streams and respond to user queries instantaneously, presenting unique challenges for current Video Large Language Models (VideoLLMs). While existing VideoLLMs excel at processing complete videos, they face significant limitations in streaming scenarios due to their inability to handle dense, redundant frames efficiently. We introduce TimeChat-Online, a novel online VideoLLM that revolutionizes real-time video interaction. At its core lies our innovative Differential Token Drop (DTD) module, which addresses the fundamental challenge of visual redundancy in streaming videos. Drawing inspiration from human visual perception's Change Blindness phenomenon, DTD preserves meaningful temporal changes while filtering out static, redundant content between frames. Remarkably, our experiments demonstrate that DTD achieves an 82.8% reduction in video tokens while maintaining 98% performance on StreamingBench, revealing that over 80% of visual content in streaming videos is naturally redundant without requiring language guidance. To enable seamless real-time interaction, we present TimeChat-Online-139K, a comprehensive streaming video dataset featuring diverse interaction patterns including backward-tracing, current-perception, and future-responding scenarios. TimeChat-Online's unique Proactive Response capability, naturally achieved through continuous monitoring of video scene transitions via DTD, sets it apart from conventional approaches. Our extensive evaluation demonstrates TimeChat-Online's superior performance on streaming benchmarks (StreamingBench and OvOBench) and maintaining competitive results on long-form video tasks such as Video-MME and MLVU.

Yicheng Li, Weiye Gan, Zuoqiang Shi et al.

The generalization error curve of certain kernel regression method aims at determining the exact order of generalization error with various source condition, noise level and choice of the regularization parameter rather than the minimax rate. In this work, under mild assumptions, we rigorously provide a full characterization of the generalization error curves of the kernel gradient descent method (and a large class of analytic spectral algorithms) in kernel regression. Consequently, we could sharpen the near inconsistency of kernel interpolation and clarify the saturation effects of kernel regression algorithms with higher qualification, etc. Thanks to the neural tangent kernel theory, these results greatly improve our understanding of the generalization behavior of training the wide neural networks. A novel technical contribution, the analytic functional argument, might be of independent interest.

Haobo Zhang, Yicheng Li, Weihao Lu et al.

Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^γ$ for some $γ> 0$. Given an RKHS $\mathcal{H}$ associated with an inner product kernel defined on the sphere $\mathbb{S}^{d}$, we suppose that the true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, the interpolation space of $\mathcal{H}$ with source condition $s>0$. We first determined the exact order (both upper and lower bound) of the generalization error of kernel ridge regression for the optimally chosen regularization parameter $λ$. We then further showed that when $0<s\le1$, KRR is minimax optimal; and when $s>1$, KRR is not minimax optimal (a.k.a. he saturation effect). Our results illustrate that the curves of rate varying along $γ$ exhibit the periodic plateau behavior and the multiple descent behavior and show how the curves evolve with $s>0$. Interestingly, our work provides a unified viewpoint of several recent works on kernel regression in the large-dimensional setting, which correspond to $s=0$ and $s=1$ respectively.

Yijun Dong, Yicheng Li, Yunai Li et al.

Weak-to-strong (W2S) generalization is a type of finetuning (FT) where a strong (large) student model is trained on pseudo-labels generated by a weak teacher. Surprisingly, W2S FT often outperforms the weak teacher. We seek to understand this phenomenon through the observation that FT often occurs in intrinsically low-dimensional spaces. Leveraging the low intrinsic dimensionality of FT, we analyze W2S in the ridgeless regression setting from a variance reduction perspective. For a strong student-weak teacher pair with sufficiently expressive low-dimensional feature subspaces $\mathcal{V}_s, \mathcal{V}_w$, we provide an exact characterization of the variance that dominates the generalization error of W2S. This unveils a virtue of discrepancy between the strong and weak models in W2S: the variance of the weak teacher is inherited by the strong student in $\mathcal{V}_s \cap \mathcal{V}_w$, while reduced by a factor of $\mathrm{dim}(\mathcal{V}_s)/N$ in the subspace of discrepancy $\mathcal{V}_w \setminus \mathcal{V}_s$ with $N$ pseudo-labels for W2S. Our analysis further casts light on the sample complexities and the scaling of performance gap recovery in W2S. The analysis is supported by experiments on synthetic regression problems, as well as real vision and NLP tasks.

Yan Gong, Yiren Song, Yicheng Li et al.

Inspired by the in-context learning mechanism of large language models (LLMs), a new paradigm of generalizable visual prompt-based image editing is emerging. Existing single-reference methods typically focus on style or appearance adjustments and struggle with non-rigid transformations. To address these limitations, we propose leveraging source-target image pairs to extract and transfer content-aware editing intent to novel query images. To this end, we introduce RelationAdapter, a lightweight module that enables Diffusion Transformer (DiT) based models to effectively capture and apply visual transformations from minimal examples. We also introduce Relation252K, a comprehensive dataset comprising 218 diverse editing tasks, to evaluate model generalization and adaptability in visual prompt-driven scenarios. Experiments on Relation252K show that RelationAdapter significantly improves the model's ability to understand and transfer editing intent, leading to notable gains in generation quality and overall editing performance.

Weihao Lu, Haobo Zhang, Yicheng Li et al.

The saturation effects, which originally refer to the fact that kernel ridge regression (KRR) fails to achieve the information-theoretical lower bound when the regression function is over-smooth, have been observed for almost 20 years and were rigorously proved recently for kernel ridge regression and some other spectral algorithms over a fixed dimensional domain. The main focus of this paper is to explore the saturation effects for a large class of spectral algorithms (including the KRR, gradient descent, etc.) in large dimensional settings where $n \asymp d^γ$. More precisely, we first propose an improved minimax lower bound for the kernel regression problem in large dimensional settings and show that the gradient flow with early stopping strategy will result in an estimator achieving this lower bound (up to a logarithmic factor). Similar to the results in KRR, we can further determine the exact convergence rates (both upper and lower bounds) of a large class of (optimal tuned) spectral algorithms with different qualification $τ$'s. In particular, we find that these exact rate curves (varying along $γ$) exhibit the periodic plateau behavior and the polynomial approximation barrier. Consequently, we can fully depict the saturation effects of the spectral algorithms and reveal a new phenomenon in large dimensional settings (i.e., the saturation effect occurs in large dimensional setting as long as the source condition $s>τ$ while it occurs in fixed dimensional setting as long as $s>2τ$).

Xingxi Yin, Jingfeng Zhang, Yue Deng et al.

Text-to-image (T2I) diffusion models are widely used in image editing due to their powerful generative capabilities. However, achieving fine-grained control over specific object attributes, such as color and material, remains a considerable challenge. Existing methods often fail to accurately modify these attributes or compromise structural integrity and overall image consistency. To fill this gap, we introduce Structure Preservation and Attribute Amplification (SPAA), a novel training-free framework that enables precise generation of color and material attributes for the same object by intelligently manipulating self-attention maps and cross-attention values within diffusion models. Building on SPAA, we integrate multi-modal large language models (MLLMs) to automate data curation and instruction generation. Leveraging this object attribute data collection engine, we construct the Attribute Dataset, encompassing a comprehensive range of colors and materials across diverse object categories. Using this generated dataset, we propose InstructAttribute, an instruction-tuned model that enables fine-grained and object-level attribute editing through natural language prompts. This capability holds significant practical implications for diverse fields, from accelerating product design and e-commerce visualization to enhancing virtual try-on experiences. Extensive experiments demonstrate that InstructAttribute outperforms existing instruction-based baselines, achieving a superior balance between attribute modification accuracy and structural preservation.

Yicheng Li, Qian Lin

This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal adaptive kernel model adapts to the structure of the truth function, significantly improving generalization over fixed-kernel methods, especially when the initial kernel is misaligned with the target. Moreover, we show that the adaptivity comes from learning the right eigenvalues during training, showing a feature learning behavior. By extending to deeper parameterization, we further show how extra depth enhances adaptability and generalization. This study combines the insights from feature learning and implicit regularization and provides new perspective into the adaptivity and generalization potential of neural networks beyond the kernel regime.

Chenglin Li, Qianglong Chen, Zhi Li et al.

Instruction tuning is a crucial technique for aligning language models with humans' actual goals in the real world. Extensive research has highlighted the quality of instruction data is essential for the success of this alignment. However, creating high-quality data manually is labor-intensive and time-consuming, which leads researchers to explore using LLMs to synthesize data. Recent studies have focused on using a stronger LLM to iteratively enhance existing instruction data, showing promising results. Nevertheless, previous work often lacks control over the evolution direction, resulting in high uncertainty in the data synthesis process and low-quality instructions. In this paper, we introduce a general and scalable framework, IDEA-MCTS (Instruction Data Enhancement using Monte Carlo Tree Search), a scalable framework for efficiently synthesizing instructions. With tree search and evaluation models, it can efficiently guide each instruction to evolve into a high-quality form, aiding in instruction fine-tuning. Experimental results show that IDEA-MCTS significantly enhances the seed instruction data, raising the average evaluation scores of quality, diversity, and complexity from 2.19 to 3.81. Furthermore, in open-domain benchmarks, experimental results show that IDEA-MCTS improves the accuracy of real-world instruction-following skills in LLMs by an average of 5\% in low-resource settings.

Xingxi Yin, Yicheng Li, Gong Yan et al.

Sequential identity consistency under precise transient attribute control remains a long-standing challenge in controllable visual storytelling. Existing datasets lack sufficient fidelity and fail to disentangle stable identities from transient attributes, limiting structured control over pose, expression, and scene composition and thus constraining reliable sequential synthesis. To address this gap, we introduce \textbf{2K-Characters-10K-Stories}, a multi-modal stylized narrative dataset of \textbf{2{,}000} uniquely stylized characters appearing across \textbf{10{,}000} illustration stories. It is the first dataset that pairs large-scale unique identities with explicit, decoupled control signals for sequential identity consistency. We introduce a \textbf{Human-in-the-Loop pipeline (HiL)} that leverages expert-verified character templates and LLM-guided narrative planning to generate highly-aligned structured data. A \textbf{decoupled control} scheme separates persistent identity from transient attributes -- pose and expression -- while a \textbf{Quality-Gated loop} integrating MMLM evaluation, Auto-Prompt Tuning, and Local Image Editing enforces pixel-level consistency. Extensive experiments demonstrate that models fine-tuned on our dataset achieves performance comparable to closed-source models in generating visual narratives.

Dongming Huang, Zhifan Li, Yicheng Li et al.

We study spectral algorithms in the setting where kernels are learned from data. We introduce the effective span dimension (ESD), an alignment-sensitive complexity measure that depends jointly on the signal, spectrum, and noise level $σ^2$. The ESD is well-defined for arbitrary kernels and signals without requiring eigen-decay conditions or source conditions. We prove that for sequence models whose ESD is at most $K$, the minimax excess risk scales as $σ^2 K$. Furthermore, we analyze over-parameterized gradient flow and prove that it can reduce the ESD. This finding establishes a connection between adaptive feature learning and provable improvements in generalization of spectral algorithms. We demonstrate the generality of the ESD framework by extending it to linear models and RKHS regression, and we support the theory with numerical experiments. This framework provides a novel perspective on generalization beyond traditional fixed-kernel theories.

Yicheng Li, Xinghua Sun

This paper proposes and analyzes a gradient-type algorithm based on Burer-Monteiro factorization, called the Asymmetric Projected Gradient Descent (APGD), for reconstructing the point set configuration from partial Euclidean distance measurements, known as the Euclidean Distance Matrix Completion (EDMC) problem. By paralleling the incoherence matrix completion framework, we show for the first time that global convergence guarantee with exact recovery of this routine can be established given $\mathcal{O}(μ^2 r^3 κ^2 n \log n)$ Bernoulli random observations without any sample splitting. Unlike leveraging the tangent space Restricted Isometry Property (RIP) and local curvature of the low-rank embedding manifold in some very recent works, our proof provides extra upper bounds that act as analogies of the random graph lemma under EDMC setting. The APGD works surprisingly well and numerical experiments demonstrate exact linear convergence behavior in rich-sample regions yet deteriorates rapidly when compared with the performance obtained by optimizing the s-stress function, i.e., the standard but unexplained non-convex approach for EDMC, if the sample size is limited. While virtually matching our theoretical prediction, this unusual phenomenon might indicate that: (i) the power of implicit regularization is weakened when specified in the APGD case; (ii) the stabilization of such new gradient direction requires substantially more samples than the information-theoretic limit would suggest.

Weiye Gan, Yicheng Li, Qian Lin et al.

Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep neural networks with physics-informed loss, providing insights into the convergence of NTK during initialization and training, and revealing its explicit structure. We find that, in most cases, the differential operators in the loss function do not induce a faster eigenvalue decay rate and stronger spectral bias. Some experimental results are also presented to verify the theory.

Haobo Zhang, Jianfa Lai, Yicheng Li et al.

A primary advantage of neural networks lies in their feature learning characteristics, which is challenging to theoretically analyze due to the complexity of their training dynamics. We propose a new paradigm for studying feature learning and the resulting benefits in generalizability. After reviewing the neural tangent kernel (NTK) theory and recent results in kernel regression, which address the generalization issue of sufficiently wide neural networks, we examine limitations and implications of the fixed kernel theory (as the NTK theory) and review recent theoretical advancements in feature learning. Moving beyond the fixed kernel/feature theory, we consider neural networks as adaptive feature models. Finally, we propose an over-parameterized Gaussian sequence model as a prototype model to study the feature learning characteristics of neural networks.

Haobo Zhang, Yicheng Li, Weihao Lu et al.

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\|f_ρ^{*}\|_{L^{\infty}}<\infty$ which implicitly requires $s > α_{0}$ where $α_{0}\in (0,1)$ is the embedding index, a constant depending on $\mathcal{H}$. Whether the KRR is optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any $s\in (0,1)$ when the $\mathcal{H}$ is a Sobolev RKHS.

Yicheng Li, Zixiong Yu, Guhan Chen et al.

In this paper, we provide a strategy to determine the eigenvalue decay rate (EDR) of a large class of kernel functions defined on a general domain rather than $\mathbb S^{d}$. This class of kernel functions include but are not limited to the neural tangent kernel associated with neural networks with different depths and various activation functions. After proving that the dynamics of training the wide neural networks uniformly approximated that of the neural tangent kernel regression on general domains, we can further illustrate the minimax optimality of the wide neural network provided that the underground truth function $f\in [\mathcal H_{\mathrm{NTK}}]^{s}$, an interpolation space associated with the RKHS $\mathcal{H}_{\mathrm{NTK}}$ of NTK. We also showed that the overfitted neural network can not generalize well. We believe our approach for determining the EDR of kernels might be also of independent interests.

Feifan Lv, Yinqiang Zheng, Yicheng Li et al.

The current industry practice for 24-hour outdoor imaging is to use a silicon camera supplemented with near-infrared (NIR) illumination. This will result in color images with poor contrast at daytime and absence of chrominance at nighttime. For this dilemma, all existing solutions try to capture RGB and NIR images separately. However, they need additional hardware support and suffer from various drawbacks, including short service life, high price, specific usage scenario, etc. In this paper, we propose a novel and integrated enhancement solution that produces clear color images, whether at abundant sunlight daytime or extremely low-light nighttime. Our key idea is to separate the VIS and NIR information from mixed signals, and enhance the VIS signal adaptively with the NIR signal as assistance. To this end, we build an optical system to collect a new VIS-NIR-MIX dataset and present a physically meaningful image processing algorithm based on CNN. Extensive experiments show outstanding results, which demonstrate the effectiveness of our solution.

Ke Gong, Xiaodan Liang, Yicheng Li et al.

Instance-level human parsing towards real-world human analysis scenarios is still under-explored due to the absence of sufficient data resources and technical difficulty in parsing multiple instances in a single pass. Several related works all follow the "parsing-by-detection" pipeline that heavily relies on separately trained detection models to localize instances and then performs human parsing for each instance sequentially. Nonetheless, two discrepant optimization targets of detection and parsing lead to suboptimal representation learning and error accumulation for final results. In this work, we make the first attempt to explore a detection-free Part Grouping Network (PGN) for efficiently parsing multiple people in an image in a single pass. Our PGN reformulates instance-level human parsing as two twinned sub-tasks that can be jointly learned and mutually refined via a unified network: 1) semantic part segmentation for assigning each pixel as a human part (e.g., face, arms); 2) instance-aware edge detection to group semantic parts into distinct person instances. Thus the shared intermediate representation would be endowed with capabilities in both characterizing fine-grained parts and inferring instance belongings of each part. Finally, a simple instance partition process is employed to get final results during inference. We conducted experiments on PASCAL-Person-Part dataset and our PGN outperforms all state-of-the-art methods. Furthermore, we show its superiority on a newly collected multi-person parsing dataset (CIHP) including 38,280 diverse images, which is the largest dataset so far and can facilitate more advanced human analysis. The CIHP benchmark and our source code are available at http://sysu-hcp.net/lip/.