Haoyi Zhou

Tianyu Chen, Hangbo Bao, Shaohan Huang et al. · microsoft-research

As more and more pre-trained language models adopt on-cloud deployment, the privacy issues grow quickly, mainly for the exposure of plain-text user data (e.g., search history, medical record, bank account). Privacy-preserving inference of transformer models is on the demand of cloud service users. To protect privacy, it is an attractive choice to compute only with ciphertext in homomorphic encryption (HE). However, enabling pre-trained models inference on ciphertext data is difficult due to the complex computations in transformer blocks, which are not supported by current HE tools yet. In this work, we introduce $\textit{THE-X}$, an approximation approach for transformers, which enables privacy-preserving inference of pre-trained models developed by popular frameworks. $\textit{THE-X}$ proposes a workflow to deal with complex computation in transformer networks, including all the non-polynomial functions like GELU, softmax, and LayerNorm. Experiments reveal our proposed $\textit{THE-X}$ can enable transformer inference on encrypted data for different downstream tasks, all with negligible performance drop but enjoying the theory-guaranteed privacy-preserving advantage.

Tianyu Chen, Shaohan Huang, Yuan Xie et al. · microsoft-research

The sparse Mixture-of-Experts (MoE) model is powerful for large-scale pre-training and has achieved promising results due to its model capacity. However, with trillions of parameters, MoE is hard to be deployed on cloud or mobile environment. The inference of MoE requires expert parallelism, which is not hardware-friendly and communication expensive. Especially for resource-limited downstream tasks, such sparse structure has to sacrifice a lot of computing efficiency for limited performance gains. In this work, we observe most experts contribute scarcely little to the MoE fine-tuning and inference. We further propose a general method to progressively drop the non-professional experts for the target downstream task, which preserves the benefits of MoE while reducing the MoE model into one single-expert dense model. Our experiments reveal that the fine-tuned single-expert model could preserve 99.3% benefits from MoE across six different types of tasks while enjoying 2x inference speed with free communication cost.

Jinze Yu, Jiaming Liu, Xiaobao Wei et al.

Recently, DEtection TRansformer (DETR), an end-to-end object detection pipeline, has achieved promising performance. However, it requires large-scale labeled data and suffers from domain shift, especially when no labeled data is available in the target domain. To solve this problem, we propose an end-to-end cross-domain detection Transformer based on the mean teacher framework, MTTrans, which can fully exploit unlabeled target domain data in object detection training and transfer knowledge between domains via pseudo labels. We further propose the comprehensive multi-level feature alignment to improve the pseudo labels generated by the mean teacher framework taking advantage of the cross-scale self-attention mechanism in Deformable DETR. Image and object features are aligned at the local, global, and instance levels with domain query-based feature alignment (DQFA), bi-level graph-based prototype alignment (BGPA), and token-wise image feature alignment (TIFA). On the other hand, the unlabeled target domain data pseudo-labeled and available for the object detection training by the mean teacher framework can lead to better feature extraction and alignment. Thus, the mean teacher framework and the comprehensive multi-level feature alignment can be optimized iteratively and mutually based on the architecture of Transformers. Extensive experiments demonstrate that our proposed method achieves state-of-the-art performance in three domain adaptation scenarios, especially the result of Sim10k to Cityscapes scenario is remarkably improved from 52.6 mAP to 57.9 mAP. Code will be released.

Qi Song, Honglin Li, Yingchen Yu et al.

Recent releases such as o3 highlight human-like "thinking with images" reasoning that combines structured tool use with stepwise verification, yet most open-source approaches still rely on text-only chains, rigid visual schemas, or single-step pipelines, limiting flexibility, interpretability, and transferability on complex tasks. We introduce CodeDance, which explores executable code as a general solver for visual reasoning. Unlike fixed-schema calls (e.g., only predicting bounding-box coordinates), CodeDance defines, composes, and executes code to orchestrate multiple tools, compute intermediate results, and render visual artifacts (e.g., boxes, lines, plots) that support transparent, self-checkable reasoning. To guide this process, we introduce a reward for balanced and adaptive tool-call, which balances exploration with efficiency and mitigates tool overuse. Interestingly, beyond the expected capabilities taught by atomic supervision, we empirically observe novel emergent behaviors during RL training: CodeDance demonstrates novel tool invocations, unseen compositions, and cross-task transfer. These behaviors arise without task-specific fine-tuning, suggesting a general and scalable mechanism of executable visual reasoning. Extensive experiments across reasoning benchmarks (e.g., visual search, math, chart QA) show that CodeDance not only consistently outperforms schema-driven and text-only baselines, but also surpasses advanced closed models such as GPT-4o and larger open-source models.

Chengwei Wu, Jiapu Wang, Mingyang Gao et al.

Large Language Models (LLMs) have achieved remarkable success across a wide range of natural language processing tasks. However, Chinese LLMs face unique challenges, primarily due to the dominance of unstructured free text and the lack of structured representations in Chinese corpora. While existing benchmarks for LLMs partially assess Chinese LLMs, they are still predominantly English-centric and fail to address the unique linguistic characteristics of Chinese, lacking structured datasets essential for robust evaluation. To address these challenges, we present a Comprehensive Benchmark for Evaluating Chinese Large Language Models (CB-ECLLM) based on the newly constructed Chinese Data-Text Pair (CDTP) dataset. Specifically, CDTP comprises over 7 million aligned text pairs, each consisting of unstructured text coupled with one or more corresponding triples, alongside a total of 15 million triples spanning four critical domains. The core contributions of CDTP are threefold: (i) enriching Chinese corpora with high-quality structured information; (ii) enabling fine-grained evaluation tailored to knowledge-driven tasks; and (iii) supporting multi-task fine-tuning to assess generalization and robustness across scenarios, including Knowledge Graph Completion, Triple-to-Text generation, and Question Answering. Furthermore, we conduct rigorous evaluations through extensive experiments and ablation studies to assess the effectiveness, Supervised Fine-Tuning (SFT), and robustness of the benchmark. To support reproducible research, we offer an open-source codebase and outline potential directions for future investigations based on our insights.

Ishika Singh, Haoyi Zhou, Kunlin Yang et al.

Neural architecture search, which aims to automatically search for architectures (e.g., convolution, max pooling) of neural networks that maximize validation performance, has achieved remarkable progress recently. In many application scenarios, several parties would like to collaboratively search for a shared neural architecture by leveraging data from all parties. However, due to privacy concerns, no party wants its data to be seen by other parties. To address this problem, we propose federated neural architecture search (FNAS), where different parties collectively search for a differentiable architecture by exchanging gradients of architecture variables without exposing their data to other parties. To further preserve privacy, we study differentially-private FNAS (DP-FNAS), which adds random noise to the gradients of architecture variables. We provide theoretical guarantees of DP-FNAS in achieving differential privacy. Experiments show that DP-FNAS can search highly-performant neural architectures while protecting the privacy of individual parties. The code is available at https://github.com/UCSD-AI4H/DP-FNAS

Haoyi Zhou, Shuo Li, Tianyu Chen et al.

While large vision-language models (VLMs) demonstrate strong long-context understanding, their prevalent small branches fail on linguistics-photography alignment for a limited window size. We discover that knowledge distillation improves students' capability as a complement to Rotary Position Embeddings (RoPE) on window sizes (anchored from large models). Building on this insight, we propose LAid, which directly aims at the transfer of long-range attention mechanisms through two complementary components: (1) a progressive distance-weighted attention matching that dynamically emphasizes longer position differences during training, and (2) a learnable RoPE response gain modulation that selectively amplifies position sensitivity where needed. Extensive experiments across multiple model families demonstrate that LAid-distilled models achieve up to 3.2 times longer effective context windows compared to baseline small models, while maintaining or improving performance on standard VL benchmarks. Spectral analysis also suggests that LAid successfully preserves crucial low-frequency attention components that conventional methods fail to transfer. Our work not only provides practical techniques for building more efficient long-context VLMs but also offers theoretical insights into how positional understanding emerges and transfers during distillation.

Guoan Wan, Tianyu Chen, Fangzheng Feng et al.

Parameter-efficient fine-tuning (PEFT) methods have emerged as a practical solution for adapting large foundation models to downstream tasks, reducing computational and memory costs by updating only a small subset of parameters. Among them, approaches like LoRA aim to strike a balance between efficiency and expressiveness, but often suffer from slow convergence and limited adaptation capacity due to their inherent low-rank constraints. This trade-off hampers the ability of PEFT methods to capture complex patterns needed for diverse tasks. To address these challenges, we propose FRoD, a novel fine-tuning method that combines hierarchical joint decomposition with rotational degrees of freedom. By extracting a globally shared basis across layers and injecting sparse, learnable perturbations into scaling factors for flexible full-rank updates, FRoD enhances expressiveness and efficiency, leading to faster and more robust convergence. On 20 benchmarks spanning vision, reasoning, and language understanding, FRoD matches full model fine-tuning in accuracy, while using only 1.72% of trainable parameters under identical training budgets.

Yiming Xu, Bin Shi, Teng Ma et al.

The graph with complex annotations is the most potent data type, whose constantly evolving motivates further exploration of the unsupervised dynamic graph representation. One of the representative paradigms is graph contrastive learning. It constructs self-supervised signals by maximizing the mutual information between the statistic graph's augmentation views. However, the semantics and labels may change within the augmentation process, causing a significant performance drop in downstream tasks. This drawback becomes greatly magnified on dynamic graphs. To address this problem, we designed a simple yet effective framework named CLDG. Firstly, we elaborate that dynamic graphs have temporal translation invariance at different levels. Then, we proposed a sampling layer to extract the temporally-persistent signals. It will encourage the node to maintain consistent local and global representations, i.e., temporal translation invariance under the timespan views. The extensive experiments demonstrate the effectiveness and efficiency of the method on seven datasets by outperforming eight unsupervised state-of-the-art baselines and showing competitiveness against four semi-supervised methods. Compared with the existing dynamic graph method, the number of model parameters and training time is reduced by an average of 2,001.86 times and 130.31 times on seven datasets, respectively.

Tianyu Chen, Haoyi Zhou, Ying Li et al.

Foundation models have revolutionized language modeling, while whether this success is replicated in scientific computing remains unexplored. We present OmniArch, the first prototype aiming at solving multi-scale and multi-physics scientific computing problems with physical alignment. We addressed all three challenges with one unified architecture. Its pre-training stage contains a Fourier Encoder-decoder fading out the disharmony across separated dimensions and a Transformer backbone integrating quantities through temporal dynamics, and the novel PDE-Aligner performs physics-informed fine-tuning under flexible conditions. As far as we know, we first conduct 1D-2D-3D united pre-training on the PDEBench, and it sets not only new performance benchmarks for 1D, 2D, and 3D PDEs but also demonstrates exceptional adaptability to new physics via in-context and zero-shot learning approaches, which supports realistic engineering applications and foresight physics discovery.

Tianyu Chen, Xingcheng Fu, Yisen Gao et al.

Modern vision-language models (VLMs) develop patch embedding and convolution backbone within vector space, especially Euclidean ones, at the very founding. When expanding VLMs to a galaxy scale for understanding astronomical phenomena, the integration of spherical space for planetary orbits and hyperbolic spaces for black holes raises two formidable challenges. a) The current pre-training model is confined to Euclidean space rather than a comprehensive geometric embedding. b) The predominant architecture lacks suitable backbones for anisotropic physical geometries. In this paper, we introduced Galaxy-Walker, a geometry-aware VLM, for the universe-level vision understanding tasks. We proposed the geometry prompt that generates geometry tokens by random walks across diverse spaces on a multi-scale physical graph, along with a geometry adapter that compresses and reshapes the space anisotropy in a mixture-of-experts manner. Extensive experiments demonstrate the effectiveness of our approach, with Galaxy-Walker achieving state-of-the-art performance in both galaxy property estimation ($R^2$ scores up to $0.91$) and morphology classification tasks (up to $+0.17$ F1 improvement in challenging features), significantly outperforming both domain-specific models and general-purpose VLMs.

Ziming Wang, Zeyu Shi, Haoyi Zhou et al.

Fine-tuned Large Language Models (LLMs) often demonstrate poor calibration, with their confidence scores misaligned with actual performance. While calibration has been extensively studied in models trained from scratch, the impact of LLMs' prior knowledge on calibration during fine-tuning remains understudied. Our research reveals that LLMs' prior knowledge causes potential poor calibration due to the ubiquitous presence of known data in real-world fine-tuning, which appears harmful for calibration. Specifically, data aligned with LLMs' prior knowledge would induce overconfidence, while new knowledge improves calibration. Our findings expose a tension: LLMs' encyclopedic knowledge, while enabling task versatility, undermines calibration through unavoidable knowledge overlaps. To address this, we propose CogCalib, a cognition-aware framework that applies targeted learning strategies according to the model's prior knowledge. Experiments across 7 tasks using 3 LLM families prove that CogCalib significantly improves calibration while maintaining performance, achieving an average 57\% reduction in ECE compared to standard fine-tuning in Llama3-8B. These improvements generalize well to out-of-domain tasks, enhancing the objectivity and reliability of domain-specific LLMs, and making them more trustworthy for critical human-AI interaction applications.

Tianyu Chen, Haoyi Zhou, Ying Li et al.

Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the sparsity of high-frequency signals limits computational efficiency for high-dimensional inputs, and fixed-pattern truncation often causes high-frequency signal loss, reducing performance in scenarios such as high-resolution inputs or long-term predictions. To address these challenges, we propose FreqMoE, an efficient and progressive training framework that exploits the dependency of high-frequency signals on low-frequency components. The model first learns low-frequency weights and then applies a sparse upward-cycling strategy to construct a mixture of experts (MoE) in the frequency domain, effectively extending the learned weights to high-frequency regions. Experiments on both regular and irregular grid PDEs demonstrate that FreqMoE achieves up to 16.6% accuracy improvement while using merely 2.1% parameters (47.32x reduction) compared to dense FNO. Furthermore, the approach demonstrates remarkable stability in long-term predictions and generalizes seamlessly to various FNO variants and grid structures, establishing a new ``Low frequency Pretraining, High frequency Fine-tuning'' paradigm for solving PDEs.

Pusen Dong, Tianchen Zhu, Yue Qiu et al.

Safe reinforcement learning (RL) requires the agent to finish a given task while obeying specific constraints. Giving constraints in natural language form has great potential for practical scenarios due to its flexible transfer capability and accessibility. Previous safe RL methods with natural language constraints typically need to design cost functions manually for each constraint, which requires domain expertise and lacks flexibility. In this paper, we harness the dual role of text in this task, using it not only to provide constraint but also as a training signal. We introduce the Trajectory-level Textual Constraints Translator (TTCT) to replace the manually designed cost function. Our empirical results demonstrate that TTCT effectively comprehends textual constraint and trajectory, and the policies trained by TTCT can achieve a lower violation rate than the standard cost function. Extra studies are conducted to demonstrate that the TTCT has zero-shot transfer capability to adapt to constraint-shift environments.

Huaiyang Wang, Xiaojie Li, Deqing Wang et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central post-training paradigm for improving the reasoning capabilities of large language models. Yet existing methods share a common blind spot: they optimize policies based on instantaneous group-level or batch-level statistics without ever verifying whether the resulting update actually improved the model. This open-loop design -- updating in isolation at each step, guided only by within-group (batch) reward signals -- means optimization can drift or collapse with no mechanism to detect and correct these failures. We argue that the missing ingredient is policy improvement feedback: the ability to measure and optimize inter-iteration progress directly. To this end, we introduce Policy Improvement Reinforcement Learning (PIRL), a framework that replaces surrogate reward maximization with the explicit objective of maximizing cumulative policy improvement across iterations, and prove this temporal objective is perfectly aligned with maximizing final task performance. Building on PIRL, we propose Policy Improvement Policy Optimization (PIPO), which implements closed-loop optimization through retrospective verification. At each iteration, PIPO evaluates whether the previous update yielded genuine improvement against a sliding-window historical baseline, then actively reinforces beneficial updates and suppresses the harmful ones -- transforming an open-loop process into a self-correcting one. We provide theoretical analysis showing that PIPO performs ascent on the PIRL objective in expectation, and experiments on mathematical reasoning benchmarks demonstrate improved stability and performance over GRPO and its variants.

Zeyu Shi, Ziming Wang, Tianyu Chen et al.

The honesty of Large Language Models (LLMs) is increasingly important for safe deployment in high-stakes domains. However, this crucial trait is severely undermined by supervised fine-tuning (SFT), a common technique for model specialization. Existing recovery methods rely on data-intensive global parameter adjustments, implicitly assuming that SFT deeply corrupts the models' ability to recognize their knowledge boundaries. However, we observe that fine-tuned LLMs still preserve this ability; what is damaged is their capacity to faithfully express that awareness. Building on this, we propose Honesty-Critical Neurons Restoration (HCNR) to surgically repair this suppressed capacity. HCNR identifies and restores key expression-governing neurons to their pre-trained state while harmonizing them with task-oriented neurons via Hessian-guided compensation. Experiments on four QA tasks and five LLM families demonstrate that HCNR effectively recovers 33.25% of the compromised honesty while achieving at least 2.23x speedup with over 10x less data compared to baseline methods, offering a practical solution for trustworthy LLM deployment.

Chengwei Wu, Li Du, Hanyu Zhao et al.

Scaling the amount of data used for supervied fine-tuning(SFT) does not guarantee the proportional gains in model performance, highlighting a critical need to understand what makes training samples effective. This work identifies two fundamental dataset properties that govern SFT scalability: \textbf{semantic coverage}, or the breadth of task domains, and \textbf{information depth}, or the richness of individual examples. We demonstrate that simple proxies for these properties explain the majority of validation loss variance in our experiments. In this work, we further propose the \textbf{Information Landscape Approximation (ILA)}, a model-agnostic data selection framework that jointly optimizes for these two factors. ILA constructs compact subsets that approximate the informational value of large datasets. Empirical results show that models tuned on ILA-selected data achieve faster and more sustained performance improvements across diverse tasks and model sizes compared to existing methods, a phenomenon we term \textbf{accelerated scaling}.

Xin Xue, Haoyi Zhou, Tianyu Chen et al.

Spatial-temporal sequence forecasting (STSF) is a long-standing research problem with widespread real-world applications. Neural architecture search (NAS), which automates the neural network design, has been shown effective in tackling the STSF problem. However, the existing NAS methods for STSF focus on generating architectures in a time-consuming data-driven fashion, which heavily limits their ability to use background knowledge and explore the complicated search trajectory. Large language models (LLMs) have shown remarkable ability in decision-making with comprehensive internal world knowledge, but how it could benefit NAS for STSF remains unexplored. In this paper, we propose a novel NAS method for STSF based on LLM. Instead of directly generate architectures with LLM, We inspire the LLM's capability with a multi-level enhancement mechanism. Specifically, on the step-level, we decompose the generation task into decision steps with powerful prompt engineering and inspire LLM to serve as instructor for architecture search based on its internal knowledge. On the instance-level, we utilize a one-step tuning framework to quickly evaluate the architecture instance and a memory bank to cumulate knowledge to improve LLM's search ability. On the task-level, we propose a two-stage architecture search, balancing the exploration stage and optimization stage, to reduce the possibility of being trapped in local optima. Extensive experimental results demonstrate that our method can achieve competitive effectiveness with superior efficiency against existing NAS methods for STSF.

Ziqi Yuan, Haoyi Zhou, Tianyu Chen et al.

A multitude of toxic online behaviors, ranging from network attacks to anonymous traffic and spam, have severely disrupted the smooth operation of networks. Due to the inherent sender-receiver nature of network behaviors, graph-based frameworks are commonly used for detecting anomalous behaviors. However, in real-world scenarios, the boundary between normal and anomalous behaviors tends to be ambiguous. The local heterophily of graphs interferes with the detection, and existing methods based on nodes or edges introduce unwanted noise into representation results, thereby impacting the effectiveness of detection. To address these issues, we propose PhoGAD, a graph-based anomaly detection framework. PhoGAD leverages persistent homology optimization to clarify behavioral boundaries. Building upon this, the weights of adjacent edges are designed to mitigate the effects of local heterophily. Subsequently, to tackle the noise problem, we conduct a formal analysis and propose a disentangled representation-based explicit embedding method, ultimately achieving anomaly behavior detection. Experiments on intrusion, traffic, and spam datasets verify that PhoGAD has surpassed the performance of state-of-the-art (SOTA) frameworks in detection efficacy. Notably, PhoGAD demonstrates robust detection even with diminished anomaly proportions, highlighting its applicability to real-world scenarios. The analysis of persistent homology demonstrates its effectiveness in capturing the topological structure formed by normal edge features. Additionally, ablation experiments validate the effectiveness of the innovative mechanisms integrated within PhoGAD.

Tianyu Chen, Yuan Xie, Shuai Zhang et al.

Music representation learning is notoriously difficult for its complex human-related concepts contained in the sequence of numerical signals. To excavate better MUsic SEquence Representation from labeled audio, we propose a novel text-supervision pre-training method, namely MUSER. MUSER adopts an audio-spectrum-text tri-modal contrastive learning framework, where the text input could be any form of meta-data with the help of text templates while the spectrum is derived from an audio sequence. Our experiments reveal that MUSER could be more flexibly adapted to downstream tasks compared with the current data-hungry pre-training method, and it only requires 0.056% of pre-training data to achieve the state-of-the-art performance.

Xin Guo, Jianlei Yang, Haoyi Zhou et al.

Pre-trained language models achieve outstanding performance in NLP tasks. Various knowledge distillation methods have been proposed to reduce the heavy computation and storage requirements of pre-trained language models. However, from our observations, student models acquired by knowledge distillation suffer from adversarial attacks, which limits their usage in security sensitive scenarios. In order to overcome these security problems, RoSearch is proposed as a comprehensive framework to search the student models with better adversarial robustness when performing knowledge distillation. A directed acyclic graph based search space is built and an evolutionary search strategy is utilized to guide the searching approach. Each searched architecture is trained by knowledge distillation on pre-trained language model and then evaluated under a robustness-, accuracy- and efficiency-aware metric as environmental fitness. Experimental results show that RoSearch can improve robustness of student models from 7%~18% up to 45.8%~47.8% on different datasets with comparable weight compression ratio to existing distillation methods (4.6$\times$~6.5$\times$ improvement from teacher model BERT_BASE) and low accuracy drop. In addition, we summarize the relationship between student architecture and robustness through statistics of searched models.

Haoyi Zhou, Shanghang Zhang, Jieqi Peng et al.

Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, including quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a $ProbSparse$ self-attention mechanism, which achieves $O(L \log L)$ in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.

Shuai Zhang, Jianxin Li, Pengtao Xie et al.

Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by leveraging the kernel trick. Classic kernel methods learn a single layer of nonlinear features, whose representational power may be limited. Motivated by recent success of deep neural networks (DNNs) that learn multi-layer hierarchical representations, we propose a Stacked Kernel Network (SKN) that learns a hierarchy of RKHS-based nonlinear features. SKN interleaves several layers of nonlinear transformations (from a linear space to a RKHS) and linear transformations (from a RKHS to a linear space). Similar to DNNs, a SKN is composed of multiple layers of hidden units, but each parameterized by a RKHS function rather than a finite-dimensional vector. We propose three ways to represent the RKHS functions in SKN: (1)nonparametric representation, (2)parametric representation and (3)random Fourier feature representation. Furthermore, we expand SKN into CNN architecture called Stacked Kernel Convolutional Network (SKCN). SKCN learning a hierarchy of RKHS-based nonlinear features by convolutional operation with each filter also parameterized by a RKHS function rather than a finite-dimensional matrix in CNN, which is suitable for image inputs. Experiments on various datasets demonstrate the effectiveness of SKN and SKCN, which outperform the competitive methods.