Daily Papers

In many robotics and VR/AR applications, 3D-videos are readily-available sources of input (a continuous sequence of depth images, or LIDAR scans). However, those 3D-videos are processed frame-by-frame either through 2D convnets or 3D perception algorithms. In this work, we propose 4-dimensional convolutional neural networks for spatio-temporal perception that can directly process such 3D-videos using high-dimensional convolutions. For this, we adopt sparse tensors and propose the generalized sparse convolution that encompasses all discrete convolutions. To implement the generalized sparse convolution, we create an open-source auto-differentiation library for sparse tensors that provides extensive functions for high-dimensional convolutional neural networks. We create 4D spatio-temporal convolutional neural networks using the library and validate them on various 3D semantic segmentation benchmarks and proposed 4D datasets for 3D-video perception. To overcome challenges in the 4D space, we propose the hybrid kernel, a special case of the generalized sparse convolution, and the trilateral-stationary conditional random field that enforces spatio-temporal consistency in the 7D space-time-chroma space. Experimentally, we show that convolutional neural networks with only generalized 3D sparse convolutions can outperform 2D or 2D-3D hybrid methods by a large margin. Also, we show that on 3D-videos, 4D spatio-temporal convolutional neural networks are robust to noise, outperform 3D convolutional neural networks and are faster than the 3D counterpart in some cases.

The adaptation of large-scale Vision-Language Models (VLMs) like CLIP to downstream tasks with extremely limited data -- specifically in the one-shot regime -- is often hindered by a significant "Stability-Plasticity" dilemma. While efficient caching mechanisms have been introduced by training-free methods such as Tip-Adapter, these approaches often function as local Nadaraya-Watson estimators. Such estimators are characterized by inherent boundary bias and a lack of global structural regularization. In this paper, ReHARK (Refined Hybrid Adaptive RBF Kernels) is proposed as a synergistic training-free framework that reinterprets few-shot adaptation through global proximal regularization in a Reproducing Kernel Hilbert Space (RKHS). A multistage refinement pipeline is introduced, consisting of: (1) Hybrid Prior Construction, where zero-shot textual knowledge from CLIP and GPT-3 is fused with visual class prototypes to form a robust semantic-visual anchor; (2) Support Set Augmentation (Bridging), where intermediate samples are generated to smooth the transition between visual and textual modalities; (3) Adaptive Distribution Rectification, where test feature statistics are aligned with the augmented support set to mitigate domain shifts; and (4) Multi-Scale RBF Kernels, where an ensemble of kernels is employed to capture complex feature geometries across diverse scales. Superior stability and accuracy are demonstrated through extensive experiments on 11 diverse benchmarks. A new state-of-the-art for one-shot adaptation is established by ReHARK, which achieves an average accuracy of 65.83%, significantly outperforming existing baselines. Code is available at https://github.com/Jahid12012021/ReHARK.

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the defined regions of interest. Special instantiations of HRFs lead to well-known methods such as trigonometric (Rahimi and Recht, 2007) or (recently introduced in the context of linear-attention Transformers) positive random features (Choromanski et al., 2021). By generalizing Bochner's Theorem for softmax/Gaussian kernels and leveraging random features for compositional kernels, the HRF-mechanism provides strong theoretical guarantees - unbiased approximation and strictly smaller worst-case relative errors than its counterparts. We conduct exhaustive empirical evaluation of HRF ranging from pointwise kernel estimation experiments, through tests on data admitting clustering structure to benchmarking implicit-attention Transformers (also for downstream Robotics applications), demonstrating its quality in a wide spectrum of machine learning problems.

We introduce Motif-2-12.7B-Reasoning, a 12.7B parameter language model designed to bridge the gap between open-weight systems and proprietary frontier models in complex reasoning and long-context understanding. Addressing the common challenges of model collapse and training instability in reasoning adaptation, we propose a comprehensive, reproducible training recipe spanning system, data, and algorithmic optimizations. Our approach combines memory-efficient infrastructure for 64K-token contexts using hybrid parallelism and kernel-level optimizations with a two-stage Supervised Fine-Tuning (SFT) curriculum that mitigates distribution mismatch through verified, aligned synthetic data. Furthermore, we detail a robust Reinforcement Learning Fine-Tuning (RLFT) pipeline that stabilizes training via difficulty-aware data filtering and mixed-policy trajectory reuse. Empirical results demonstrate that Motif-2-12.7B-Reasoning achieves performance comparable to models with significantly larger parameter counts across mathematics, coding, and agentic benchmarks, offering the community a competitive open model and a practical blueprint for scaling reasoning capabilities under realistic compute constraints.

A natural question arising in Music Source Separation (MSS) is whether long range contextual information is useful, or whether local acoustic features are sufficient. In other fields, attention based Transformers have shown their ability to integrate information over long sequences. In this work, we introduce Hybrid Transformer Demucs (HT Demucs), an hybrid temporal/spectral bi-U-Net based on Hybrid Demucs, where the innermost layers are replaced by a cross-domain Transformer Encoder, using self-attention within one domain, and cross-attention across domains. While it performs poorly when trained only on MUSDB, we show that it outperforms Hybrid Demucs (trained on the same data) by 0.45 dB of SDR when using 800 extra training songs. Using sparse attention kernels to extend its receptive field, and per source fine-tuning, we achieve state-of-the-art results on MUSDB with extra training data, with 9.20 dB of SDR.

Financial services is a prospect industry where unlocked near-term quantum utility could yield profitable potential, and, in particular, quantum machine learning algorithms could potentially benefit businesses by improving the quality of predictive models. Quantum kernel methods have demonstrated success in financial, binary classification tasks, like fraud detection, and avoid issues found in variational quantum machine learning approaches. However, choosing a suitable quantum kernel for a classical dataset remains a challenge. We propose a hybrid, quantum multiple kernel learning (QMKL) methodology that can improve classification quality over a single kernel approach. We test the robustness of QMKL on several financially relevant datasets using both fidelity and projected quantum kernel approaches. We further demonstrate QMKL on quantum hardware using an error mitigation pipeline and show the benefits of QMKL in the large qubit regime.

Linear-attention models that compress the entire input sequence into a fixed-size recurrent state offer an efficient alternative to Transformers, but their finite memory induces forgetfulness that harms retrieval-intensive tasks. To mitigate the issue, we explore a series of hybrid models that restore direct access to past tokens. We interleave token mixers with intermediate time and space complexity between linear and full attention, including sparse attention with token eviction, and the query-aware native sparse attention. Particularly, we propose a novel learnable token eviction approach. Combined with sliding-window attention, an end-to-end trainable lightweight CNN aggregates information from both past and future adjacent tokens to adaptively retain a limited set of critical KV-pairs per head, maintaining linear attention's constant time and space complexity. Efficient Triton kernels for the sparse attention mechanisms are provided. Empirical evaluations on retrieval-intensive benchmarks support the effectiveness of our approaches.

Alignment is crucial for text-to-image (T2I) models to ensure that generated images faithfully capture user intent while maintaining safety and fairness. Direct Preference Optimization (DPO), prominent in large language models (LLMs), is extending its influence to T2I systems. This paper introduces DPO-Kernels for T2I models, a novel extension enhancing alignment across three dimensions: (i) Hybrid Loss, integrating embedding-based objectives with traditional probability-based loss for improved optimization; (ii) Kernelized Representations, employing Radial Basis Function (RBF), Polynomial, and Wavelet kernels for richer feature transformations and better separation between safe and unsafe inputs; and (iii) Divergence Selection, expanding beyond DPO's default Kullback-Leibler (KL) regularizer by incorporating Wasserstein and R'enyi divergences for enhanced stability and robustness. We introduce DETONATE, the first large-scale benchmark of its kind, comprising approximately 100K curated image pairs categorized as chosen and rejected. DETONATE encapsulates three axes of social bias and discrimination: Race, Gender, and Disability. Prompts are sourced from hate speech datasets, with images generated by leading T2I models including Stable Diffusion 3.5 Large, Stable Diffusion XL, and Midjourney. Additionally, we propose the Alignment Quality Index (AQI), a novel geometric measure quantifying latent-space separability of safe/unsafe image activations, revealing hidden vulnerabilities. Empirically, we demonstrate that DPO-Kernels maintain strong generalization bounds via Heavy-Tailed Self-Regularization (HT-SR). DETONATE and complete code are publicly released.

Advancing the frontier of subquadratic architectures for Language Models (LMs) is crucial in the rapidly evolving field of natural language processing. Current innovations, including State Space Models, were initially celebrated for surpassing Transformer performance on language modeling tasks. However, these models have revealed deficiencies in essential In-Context Learning capabilities - a domain where the Transformer traditionally shines. The Based model emerged as a hybrid solution, blending a Linear Transformer with a kernel inspired by the Taylor expansion of exponential functions, augmented by convolutional networks. Mirroring the Transformer's in-context adeptness, it became a strong contender in the field. In our work, we present a singular, elegant alteration to the Based kernel that amplifies its In-Context Learning abilities evaluated with the Multi-Query Associative Recall task and overall language modeling process, as demonstrated on the Pile dataset.

The recent amalgamation of transformer and convolutional designs has led to steady improvements in accuracy and efficiency of the models. In this work, we introduce FastViT, a hybrid vision transformer architecture that obtains the state-of-the-art latency-accuracy trade-off. To this end, we introduce a novel token mixing operator, RepMixer, a building block of FastViT, that uses structural reparameterization to lower the memory access cost by removing skip-connections in the network. We further apply train-time overparametrization and large kernel convolutions to boost accuracy and empirically show that these choices have minimal effect on latency. We show that - our model is 3.5x faster than CMT, a recent state-of-the-art hybrid transformer architecture, 4.9x faster than EfficientNet, and 1.9x faster than ConvNeXt on a mobile device for the same accuracy on the ImageNet dataset. At similar latency, our model obtains 4.2% better Top-1 accuracy on ImageNet than MobileOne. Our model consistently outperforms competing architectures across several tasks -- image classification, detection, segmentation and 3D mesh regression with significant improvement in latency on both a mobile device and a desktop GPU. Furthermore, our model is highly robust to out-of-distribution samples and corruptions, improving over competing robust models.

We propose a hybrid machine learning architecture that simultaneously employs multiple deep learning models analyzing contextual and behavioral characteristics of Windows portable executable, producing a final prediction based on a decision from the meta-model. The detection heuristic in contemporary machine learning Windows malware classifiers is typically based on the static properties of the sample since dynamic analysis through virtualization is challenging for vast quantities of samples. To surpass this limitation, we employ a Windows kernel emulation that allows the acquisition of behavioral patterns across large corpora with minimal temporal and computational costs. We partner with a security vendor for a collection of more than 100k int-the-wild samples that resemble the contemporary threat landscape, containing raw PE files and filepaths of applications at the moment of execution. The acquired dataset is at least ten folds larger than reported in related works on behavioral malware analysis. Files in the training dataset are labeled by a professional threat intelligence team, utilizing manual and automated reverse engineering tools. We estimate the hybrid classifier's operational utility by collecting an out-of-sample test set three months later from the acquisition of the training set. We report an improved detection rate, above the capabilities of the current state-of-the-art model, especially under low false-positive requirements. Additionally, we uncover a meta-model's ability to identify malicious activity in validation and test sets even if none of the individual models express enough confidence to mark the sample as malevolent. We conclude that the meta-model can learn patterns typical to malicious samples from representation combinations produced by different analysis techniques. We publicly release pre-trained models and anonymized dataset of emulation reports.

Transformers have shown great potential in various computer vision tasks. By borrowing design concepts from transformers, many studies revolutionized CNNs and showed remarkable results. This paper falls in this line of studies. Specifically, we propose a new convolutional neural network, ParCNetV2, that extends position-aware circular convolution (ParCNet) with oversized convolutions and bifurcate gate units to enhance attention. The oversized convolution employs a kernel with twice the input size to model long-range dependencies through a global receptive field. Simultaneously, it achieves implicit positional encoding by removing the shift-invariant property from convolution kernels, i.e., the effective kernels at different spatial locations are different when the kernel size is twice as large as the input size. The bifurcate gate unit implements an attention mechanism similar to self-attention in transformers. It is applied through element-wise multiplication of the two branches, one serves as feature transformation while the other serves as attention weights. Additionally, we introduce a uniform local-global convolution block to unify the design of the early and late stage convolution blocks. Extensive experiments demonstrate the superiority of our method over other convolutional neural networks and hybrid models that combine CNNs and transformers. Code will be released.

Optical flow estimation is a classical yet challenging task in computer vision. One of the essential factors in accurately predicting optical flow is to alleviate occlusions between frames. However, it is still a thorny problem for current top-performing optical flow estimation methods due to insufficient local evidence to model occluded areas. In this paper, we propose the Super Kernel Flow Network (SKFlow), a CNN architecture to ameliorate the impacts of occlusions on optical flow estimation. SKFlow benefits from the super kernels which bring enlarged receptive fields to complement the absent matching information and recover the occluded motions. We present efficient super kernel designs by utilizing conical connections and hybrid depth-wise convolutions. Extensive experiments demonstrate the effectiveness of SKFlow on multiple benchmarks, especially in the occluded areas. Without pre-trained backbones on ImageNet and with a modest increase in computation, SKFlow achieves compelling performance and ranks 1st among currently published methods on the Sintel benchmark. On the challenging Sintel clean and final passes (test), SKFlow surpasses the best-published result in the unmatched areas (7.96 and 12.50) by 9.09% and 7.92%. The code is available at https://github.com/littlespray/SKFlow{https://github.com/littlespray/SKFlow}.

Large Language Models (LLMs) have achieved strong performance across natural language and multimodal tasks, yet their practical deployment remains constrained by inference latency and kernel launch overhead, particularly in interactive, short-sequence settings. This paper presents a hybrid runtime framework that combines Just-In-Time (JIT) compilation with CUDA Graph execution to reduce launch overhead while preserving runtime flexibility during autoregressive decoding. The framework partitions transformer inference into static components executed via CUDA Graph replay and dynamic components handled through JIT-compiled kernels, enabling asynchronous graph capture and reuse across decoding steps. We evaluate the proposed approach on LLaMA-2 7B using single-GPU, batch-size-one inference across prompt lengths from 10 to 500 tokens. Experimental results show that the hybrid runtime reduces Time-to-First-Token (TTFT) by up to 66.0% and achieves lower P99 latency compared with TensorRT-LLM in this regime. These results indicate that hybrid JIT-CUDA Graph execution can effectively reduce inference latency and variance for short-sequence LLM workloads, making it a practical optimization strategy for latency-sensitive AI applications.

The rapid rise of large language models (LLMs) has unlocked many applications but also underscores the challenge of aligning them with diverse values and preferences. Direct Preference Optimization (DPO) is central to alignment but constrained by fixed divergences and limited feature transformations. We propose DPO-Kernels, which integrates kernel methods to address these issues through four key contributions: (i) Kernelized Representations with polynomial, RBF, Mahalanobis, and spectral kernels for richer transformations, plus a hybrid loss combining embedding-based and probability-based objectives; (ii) Divergence Alternatives (Jensen-Shannon, Hellinger, Renyi, Bhattacharyya, Wasserstein, and f-divergences) for greater stability; (iii) Data-Driven Selection metrics that automatically choose the best kernel-divergence pair; and (iv) a Hierarchical Mixture of Kernels for both local precision and global modeling. Evaluations on 12 datasets demonstrate state-of-the-art performance in factuality, safety, reasoning, and instruction following. Grounded in Heavy-Tailed Self-Regularization, DPO-Kernels maintains robust generalization for LLMs, offering a comprehensive resource for further alignment research.

Real-time streaming video-to-video editing (V2V) is critical for interactive applications such as live broadcasting and gaming, yet it remains a formidable challenge due to the stringent requirements for temporal consistency and inference throughput. In this paper, we present SANA-Streaming, a system-algorithm co-designed framework for high-resolution, real-time streaming video editing on consumer GPUs, with the following three core designs: (1) Hybrid Diffusion Transformer architecture introduces softmax attention in part of the blocks to improve local modeling capabilities while preserving the efficiency of linear layers. (2) Cycle-Reverse Regularization is a novel training strategy that enforces semantic consistency by predicting source frames from generated content via flow matching, improving temporal consistency without requiring paired long edited videos. (3) Efficient System Co-design combines fused GDN kernels and Mixed-Precision Quantization (MPQ) optimized for the NVIDIA Blackwell (RTX 5090) architecture. By profiling real-world throughput, our MPQ maximizes Tensor Core utilization while maintaining generation quality. The resulting system achieves real-time 1280 x 704 resolution editing at 24 end-to-end FPS on a single RTX 5090 GPU, with the DiT core running at 58 FPS. Experimental results demonstrate that our co-design approach significantly outperforms existing SOTA methods in both temporal coherence and system throughput.

Hybrid State-Space models combine Attention with recurrent State-Space Model (SSM) layers, balancing eidetic memory from Attention with compressed fading memory from SSMs. This yields smaller Key-Value caches and faster decoding than Transformers, along with a richer architectural design space. Exploring that design space at scale has so far required training from scratch, a barrier that has kept most large-model Hybrid research within a narrow range of architectures. We introduce Priming, a method that turns Hybrid architecture design from a pre-training problem into a knowledge transfer one. Priming initializes a Hybrid model from a pre-trained Transformer and, through short alignment and post-training phases, recovers downstream quality using less than 0.5% of the source model's pre-training token budget. Priming is agnostic to the source Transformer family (e.g., Qwen, Llama, Mistral), model class (dense or Mixture-of-Experts), and model scale. Priming enables us to run the first controlled comparison of SSM layer types at scale under identical conditions. We evaluate, Gated KalmaNet (GKA), Gated DeltaNet (GDN), and Mamba-2, and show that their expressiveness hierarchy, GKA>GDN>Mamba-2, directly predicts downstream performance on long-context reasoning tasks. We scale Priming to 8B/32B reasoning models with native 128K contexts. Our Hybrid GKA 32B improves over its source Qwen3-32B by +3.8 average reasoning points, while staying within 1% of a Transformer post-trained on the same data and enabling up to 2.3x higher decode throughput. To foster research on Hybrid architectures, we release a model zoo of primed Hybrid models for long-context reasoning and instruction following, together with the Priming training and inference code (Sequence Parallelism algorithms for long-context training, optimized GKA kernels, and vLLM serving plugin), all under Apache~2.0 License.

RGB-thermal salient object detection (RGB-T SOD) aims to identify prominent objects by integrating complementary information from RGB and thermal modalities. However, learning the precise boundaries and complete objects remains challenging due to the intrinsic insufficient feature fusion and the extrinsic limitations of data scarcity. In this paper, we propose a novel hybrid prompt-driven segment anything model (HyPSAM), which leverages the zero-shot generalization capabilities of the segment anything model (SAM) for RGB-T SOD. Specifically, we first propose a dynamic fusion network (DFNet) that generates high-quality initial saliency maps as visual prompts. DFNet employs dynamic convolution and multi-branch decoding to facilitate adaptive cross-modality interaction, overcoming the limitations of fixed-parameter kernels and enhancing multi-modal feature representation. Moreover, we propose a plug-and-play refinement network (P2RNet), which serves as a general optimization strategy to guide SAM in refining saliency maps by using hybrid prompts. The text prompt ensures reliable modality input, while the mask and box prompts enable precise salient object localization. Extensive experiments on three public datasets demonstrate that our method achieves state-of-the-art performance. Notably, HyPSAM has remarkable versatility, seamlessly integrating with different RGB-T SOD methods to achieve significant performance gains, thereby highlighting the potential of prompt engineering in this field. The code and results of our method are available at: https://github.com/milotic233/HyPSAM.

In this paper, we introduce a mesh-free two-level hybrid Tucker tensor format for approximation of multivariate functions, which combines the product Chebyshev interpolation with the ALS-based Tucker decomposition of the tensor of Chebyshev coefficients. It allows to avoid the expenses of the rank-structured approximation of function-related tensors defined on large spacial grids, while benefiting from the Tucker decomposition of the rather small core tensor of Chebyshev coefficients. This leads to nearly optimal Tucker rank parameters which are close to the results for well established Tucker-ALS algorithm applied to the large grid-based tensors. These rank parameters inherited from the Tucker-ALS decomposition of the coefficient tensor can be much less than the polynomial degrees of the initial Chebyshev interpolant via function independent basis set. Furthermore, the tensor product Chebyshev polynomials discretized on a tensor grid leads to a low-rank two-level orthogonal algebraic Tucker tensor that approximates the initial function with controllable accuracy. It is shown that our techniques could be gainfully applied to the long-range part of the electrostatic potential of multi-particle systems approximated in the range-separated tensor format. Error and complexity estimates of the proposed methods are presented. We demonstrate the efficiency of the suggested method numerically on examples of the long-range components of multi-particle interaction potentials generated by 3D Newton kernel for large bio-molecule systems and lattice-type compounds.

Brain stroke remains one of the principal causes of death and disability worldwide, yet most tabular-data prediction models still hover below the 95% accuracy threshold, limiting real-world utility. Addressing this gap, the present work develops and validates a completely data-driven and interpretable machine-learning framework designed to predict strokes using ten routinely gathered demographic, lifestyle, and clinical variables sourced from a public cohort of 4,981 records. We employ a detailed exploratory data analysis (EDA) to understand the dataset's structure and distribution, followed by rigorous data preprocessing, including handling missing values, outlier removal, and class imbalance correction using Synthetic Minority Over-sampling Technique (SMOTE). To streamline feature selection, point-biserial correlation and random-forest Gini importance were utilized, and ten varied algorithms-encompassing tree ensembles, boosting, kernel methods, and a multilayer neural network-were optimized using stratified five-fold cross-validation. Their predictions based on probabilities helped us build the proposed model, which included Random Forest, XGBoost, LightGBM, and a support-vector classifier, with logistic regression acting as a meta-learner. The proposed model achieved an accuracy rate of 97.2% and an F1-score of 97.15%, indicating a significant enhancement compared to the leading individual model, LightGBM, which had an accuracy of 91.4%. Our study's findings indicate that rigorous preprocessing, coupled with a diverse hybrid model, can convert low-cost tabular data into a nearly clinical-grade stroke-risk assessment tool.

The demand for machine intelligence capable of processing continuous, long-context inputs on local devices is growing rapidly. However, the quadratic complexity and memory requirements of traditional Transformer architectures make them inefficient and often unusable for these tasks. This has spurred a paradigm shift towards new architectures like State Space Models (SSMs) and hybrids, which promise near-linear scaling. While most current research focuses on the accuracy and theoretical throughput of these models, a systematic performance characterization on practical consumer hardware is critically needed to guide system-level optimization and unlock new applications. To address this gap, we present a comprehensive, comparative benchmarking of carefully selected Transformer, SSM, and hybrid models specifically for long-context inference on consumer and embedded GPUs. Our analysis reveals that SSMs are not only viable but superior for this domain, capable of processing sequences up to 220K tokens on a 24GB consumer GPU-approximately 4x longer than comparable Transformers. While Transformers may be up to 1.8x faster at short sequences, SSMs demonstrate a dramatic performance inversion, becoming up to 4x faster at very long contexts (~57K tokens). Our operator-level analysis reveals that custom, hardware-aware SSM kernels dominate the inference runtime, accounting for over 55% of latency on edge platforms, identifying them as a primary target for future hardware acceleration. We also provide detailed, device-specific characterization results to guide system co-design for the edge. To foster further research, we will open-source our characterization framework.

Compared to traditional Vision Transformers (ViT), Mixture-of-Experts Vision Transformers (MoE-ViT) are introduced to scale model size without a proportional increase in computational complexity, making them a new research focus. Given the high performance and reconfigurability, FPGA-based accelerators for MoE-ViT emerge, delivering substantial gains over general-purpose processors. However, existing accelerators often fall short of fully exploring the design space, leading to suboptimal trade-offs between resource utilization and performance. To overcome this problem, we introduce UbiMoE, a novel end-to-end FPGA accelerator tailored for MoE-ViT. Leveraging the unique computational and memory access patterns of MoE-ViTs, we develop a latency-optimized streaming attention kernel and a resource-efficient reusable linear kernel, effectively balancing performance and resource consumption. To further enhance design efficiency, we propose a two-stage heuristic search algorithm that optimally tunes hardware parameters for various FPGA resource constraints. Compared to state-of-the-art (SOTA) FPGA designs, UbiMoE achieves 1.34x and 3.35x throughput improvements for MoE-ViT on Xilinx ZCU102 and Alveo U280 platforms, respectively, while enhancing energy efficiency by 1.75x and 1.54x. Our implementation is available at https://github.com/DJ000011/UbiMoE.

As agentic AI systems become increasingly capable of generating and optimizing GPU kernels, progress is constrained by benchmarks that reward speedup over software baselines rather than proximity to hardware-efficient execution. We present SOL-ExecBench, a benchmark of 235 CUDA kernel optimization problems extracted from 124 production and emerging AI models spanning language, diffusion, vision, audio, video, and hybrid architectures, targeting NVIDIA Blackwell GPUs. The benchmark covers forward and backward workloads across BF16, FP8, and NVFP4, including kernels whose best performance is expected to rely on Blackwell-specific capabilities. Unlike prior benchmarks that evaluate kernels primarily relative to software implementations, SOL-ExecBench measures performance against analytically derived Speed-of-Light (SOL) bounds computed by SOLAR, our pipeline for deriving hardware-grounded SOL bounds, yielding a fixed target for hardware-efficient optimization. We report a SOL Score that quantifies how much of the gap between a release-defined scoring baseline and the hardware SOL bound a candidate kernel closes. To support robust evaluation of agentic optimizers, we additionally provide a sandboxed harness with GPU clock locking, L2 cache clearing, isolated subprocess execution, and static analysis based checks against common reward-hacking strategies. SOL-ExecBench reframes GPU kernel benchmarking from beating a mutable software baseline to closing the remaining gap to hardware Speed-of-Light.

Shape-from-Focus (SFF) is a passive depth estimation technique that infers scene depth by analyzing focus variations in a focal stack. Most recent deep learning-based SFF methods typically operate in two stages: first, they extract focus volumes (a per pixel representation of focus likelihood across the focal stack) using heavy feature encoders; then, they estimate depth via a simple one-step aggregation technique that often introduces artifacts and amplifies noise in the depth map. To address these issues, we propose a hybrid framework. Our method computes multi-scale focus volumes traditionally using handcrafted Directional Dilated Laplacian (DDL) kernels, which capture long-range and directional focus variations to form robust focus volumes. These focus volumes are then fed into a lightweight, multi-scale GRU-based depth extraction module that iteratively refines an initial depth estimate at a lower resolution for computational efficiency. Finally, a learned convex upsampling module within our recurrent network reconstructs high-resolution depth maps while preserving fine scene details and sharp boundaries. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach outperforms state-of-the-art deep learning and traditional methods, achieving superior accuracy and generalization across diverse focal conditions.

Recent advancements in anomaly detection have seen the efficacy of CNN- and transformer-based approaches. However, CNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Mamba-based models, with their superior long-range modeling and linear efficiency, have garnered substantial attention. This study pioneers the application of Mamba to multi-class unsupervised anomaly detection, presenting MambaAD, which consists of a pre-trained encoder and a Mamba decoder featuring (Locality-Enhanced State Space) LSS modules at multi-scales. The proposed LSS module, integrating parallel cascaded (Hybrid State Space) HSS blocks and multi-kernel convolutions operations, effectively captures both long-range and local information. The HSS block, utilizing (Hybrid Scanning) HS encoders, encodes feature maps into five scanning methods and eight directions, thereby strengthening global connections through the (State Space Model) SSM. The use of Hilbert scanning and eight directions significantly improves feature sequence modeling. Comprehensive experiments on six diverse anomaly detection datasets and seven metrics demonstrate state-of-the-art performance, substantiating the method's effectiveness. The code and models are available at https://lewandofskee.github.io/projects/MambaAD.

Large language models incur high inference latency due to sequential autoregressive decoding. Speculative decoding alleviates this bottleneck by using a lightweight draft model to propose multiple tokens for batched verification. However, its adoption has been limited by the lack of high-quality draft models and scalable training infrastructure. We introduce SpecForge, an open-source, production-oriented framework for training speculative decoding models with full support for EAGLE-3. SpecForge incorporates target-draft decoupling, hybrid parallelism, optimized training kernels, and integration with production-grade inference engines, enabling up to 9.9x faster EAGLE-3 training for Qwen3-235B-A22B. In addition, we release SpecBundle, a suite of production-grade EAGLE-3 draft models trained with SpecForge for mainstream open-source LLMs. Through a systematic study of speculative decoding training recipes, SpecBundle addresses the scarcity of high-quality drafts in the community, and our draft models achieve up to 4.48x end-to-end inference speedup on SGLang, establishing SpecForge as a practical foundation for real-world speculative decoding deployment.

Deploying massive diffusion models for real-time, infinite-duration, audio-driven avatar generation presents a significant engineering challenge, primarily due to the conflict between computational load and strict latency constraints. Existing approaches often compromise visual fidelity by enforcing strictly unidirectional attention mechanisms or reducing model capacity. To address this problem, we introduce SoulX-FlashTalk, a 14B-parameter framework optimized for high-fidelity real-time streaming. Diverging from conventional unidirectional paradigms, we use a Self-correcting Bidirectional Distillation strategy that retains bidirectional attention within video chunks. This design preserves critical spatiotemporal correlations, significantly enhancing motion coherence and visual detail. To ensure stability during infinite generation, we incorporate a Multi-step Retrospective Self-Correction Mechanism, enabling the model to autonomously recover from accumulated errors and preventing collapse. Furthermore, we engineered a full-stack inference acceleration suite incorporating hybrid sequence parallelism, Parallel VAE, and kernel-level optimizations. Extensive evaluations confirm that SoulX-FlashTalk is the first 14B-scale system to achieve a sub-second start-up latency (0.87s) while reaching a real-time throughput of 32 FPS, setting a new standard for high-fidelity interactive digital human synthesis.

Standard transformers apply self-attention uniformly at every layer and token, regardless of whether the input requires dynamic cross-token interaction. We propose CHIAR-Former (Chiaroscuro Attention), a 4-layer hybrid transformer that routes each token to one of three operators - DCT spectral mixing, RBF kernel mixing, or full self-attention - based on per-token spectral entropy, a theoretically justified complexity signal. Through systematic ablation on WikiText-103, we discover routing collapse: the router consistently rejects RBF in favour of DCT and attention, revealing that spectral mixing and dynamic attention are complementary and sufficient. A purpose-designed DCT+Attention-only variant achieves Val PPL 36.54 on WikiText-103 - a 45% improvement over a full-attention baseline (PPL 66.62) at 62.5% fewer attention FLOPs. We extend evaluation to WikiText-2, IMDB sentiment classification, and synthetic ListOps operations, establishing a clear operating regime: CHIAR-Former excels on large-scale naturalistic text where token diversity supports spectral specialisation, while full attention retains an edge on small datasets and synthetic pattern-matching tasks. These findings - both the wins and the losses - together define when and why spectral routing earns its keep.

Longitudinal health agents must reason across multi-source trajectories that combine continuous device streams, sparse clinical exams, and episodic life events - yet evaluating them is hard: real-world data cannot be released at scale, and temporally grounded attribution questions seldom admit definitive answers without structured ground truth. We present ESL-Bench, an event-driven synthesis framework and benchmark providing 100 synthetic users, each with a 1-5 year trajectory comprising a health profile, a multi-phase narrative plan, daily device measurements, periodic exam records, and an event log with explicit per-indicator impact parameters. Each indicator follows a baseline stochastic process driven by discrete events with sigmoid-onset, exponential-decay kernels under saturation and projection constraints; a hybrid pipeline delegates sparse semantic artifacts to LLM-based planning and dense indicator dynamics to algorithmic simulation with hard physiological bounds. Users are each paired with 100 evaluation queries across five dimensions - Lookup, Trend, Comparison, Anomaly, Explanation - stratified into Easy, Medium, and Hard tiers, with all ground-truth answers programmatically computable from the recorded event-indicator relationships. Evaluating 13 methods spanning LLMs with tools, DB-native agents, and memory-augmented RAG, we find that DB agents (48-58%) substantially outperform memory RAG baselines (30-38%), with the gap concentrated on Comparison and Explanation queries where multi-hop reasoning and evidence attribution are required.

Deploying deep learning models on mobile devices draws more and more attention recently. However, designing an efficient inference engine on devices is under the great challenges of model compatibility, device diversity, and resource limitation. To deal with these challenges, we propose Mobile Neural Network (MNN), a universal and efficient inference engine tailored to mobile applications. In this paper, the contributions of MNN include: (1) presenting a mechanism called pre-inference that manages to conduct runtime optimization; (2)deliveringthorough kernel optimization on operators to achieve optimal computation performance; (3) introducing backend abstraction module which enables hybrid scheduling and keeps the engine lightweight. Extensive benchmark experiments demonstrate that MNN performs favorably against other popular lightweight deep learning frameworks. MNN is available to public at: https://github.com/alibaba/MNN.

This technical report introduces AngelSlim, a comprehensive and versatile toolkit for large model compression developed by the Tencent Hunyuan team. By consolidating cutting-edge algorithms, including quantization, speculative decoding, token pruning, and distillation. AngelSlim provides a unified pipeline that streamlines the transition from model compression to industrial-scale deployment. To facilitate efficient acceleration, we integrate state-of-the-art FP8 and INT8 Post-Training Quantization (PTQ) algorithms alongside pioneering research in ultra-low-bit regimes, featuring HY-1.8B-int2 as the first industrially viable 2-bit large model. Beyond quantization, we propose a training-aligned speculative decoding framework compatible with multimodal architectures and modern inference engines, achieving 1.8x to 2.0x throughput gains without compromising output correctness. Furthermore, we develop a training-free sparse attention framework that reduces Time-to-First-Token (TTFT) in long-context scenarios by decoupling sparse kernels from model architectures through a hybrid of static patterns and dynamic token selection. For multimodal models, AngelSlim incorporates specialized pruning strategies, namely IDPruner for optimizing vision tokens via Maximal Marginal Relevance and Samp for adaptive audio token merging and pruning. By integrating these compression strategies from low-level implementations, AngelSlim enables algorithm-focused research and tool-assisted deployment.

In this report, we introduce INTELLECT-1, the first 10 billion parameter language model collaboratively trained across the globe, demonstrating that large-scale model training is no longer confined to large corporations but can be achieved through a distributed, community-driven approach. INTELLECT-1 was trained on 1 trillion tokens using up to 14 concurrent nodes distributed across 3 continents, with contributions from 30 independent compute providers dynamically joining and leaving the training process, while maintaining 83-96% compute utilization and 36.2-41.4% model FLOPS utilization. We leverage PRIME, our scalable distributed training framework designed for fault-tolerant, high-performance training on unreliable, globally distributed nodes. Key innovations in PRIME include the ElasticDeviceMesh, which manages dynamic global process groups for fault-tolerant communication across the internet and local process groups for communication within a node, live checkpoint recovery kernels, and a hybrid DiLoCo-FSDP2 implementation. Using PRIME with DiLoCo and our custom int8 all-reduce, we achieve a 400x reduction in communication bandwidth compared to traditional data-parallel training settings while delivering comparable performance. These results demonstrate the feasibility and promise of training frontier foundation models in a decentralized network of global GPU resources.

We present VoxelKP, a novel fully sparse network architecture tailored for human keypoint estimation in LiDAR data. The key challenge is that objects are distributed sparsely in 3D space, while human keypoint detection requires detailed local information wherever humans are present. We propose four novel ideas in this paper. First, we propose sparse selective kernels to capture multi-scale context. Second, we introduce sparse box-attention to focus on learning spatial correlations between keypoints within each human instance. Third, we incorporate a spatial encoding to leverage absolute 3D coordinates when projecting 3D voxels to a 2D grid encoding a bird's eye view. Finally, we propose hybrid feature learning to combine the processing of per-voxel features with sparse convolution. We evaluate our method on the Waymo dataset and achieve an improvement of 27% on the MPJPE metric compared to the state-of-the-art, HUM3DIL, trained on the same data, and 12% against the state-of-the-art, GC-KPL, pretrained on a 25times larger dataset. To the best of our knowledge, VoxelKP is the first single-staged, fully sparse network that is specifically designed for addressing the challenging task of 3D keypoint estimation from LiDAR data, achieving state-of-the-art performances. Our code is available at https://github.com/shijianjian/VoxelKP.

Skin lesion segmentation is a critical task in computer-aided diagnosis systems for dermatological diseases. Accurate segmentation of skin lesions from medical images is essential for early detection, diagnosis, and treatment planning. In this paper, we propose a new model for skin lesion segmentation namely AC-MambaSeg, an enhanced model that has the hybrid CNN-Mamba backbone, and integrates advanced components such as Convolutional Block Attention Module (CBAM), Attention Gate, and Selective Kernel Bottleneck. AC-MambaSeg leverages the Vision Mamba framework for efficient feature extraction, while CBAM and Selective Kernel Bottleneck enhance its ability to focus on informative regions and suppress background noise. We evaluate the performance of AC-MambaSeg on diverse datasets of skin lesion images including ISIC-2018 and PH2; then compare it against existing segmentation methods. Our model shows promising potential for improving computer-aided diagnosis systems and facilitating early detection and treatment of dermatological diseases. Our source code will be made available at: https://github.com/vietthanh2710/AC-MambaSeg.

Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of their equivalence to wide neural networks in certain regimes. However, a key feature of DNNs is their ability to scale the model size and training data size independently, whereas in traditional kernel machines model size is tied to data size. Because of this coupling, scaling kernel machines to large data has been computationally challenging. In this paper, we provide a way forward for constructing large-scale general kernel models, which are a generalization of kernel machines that decouples the model and data, allowing training on large datasets. Specifically, we introduce EigenPro 3.0, an algorithm based on projected dual preconditioned SGD and show scaling to model and data sizes which have not been possible with existing kernel methods.

Making deep learning recommendation model (DLRM) training and inference fast and efficient is important. However, this presents three key system challenges - model architecture diversity, kernel primitive diversity, and hardware generation and architecture heterogeneity. This paper presents KernelEvolve-an agentic kernel coding framework-to tackle heterogeneity at-scale for DLRM. KernelEvolve is designed to take kernel specifications as input and automate the process of kernel generation and optimization for recommendation model across heterogeneous hardware architectures. KernelEvolve does so by operating at multiple programming abstractions, from Triton and CuTe DSL to low-level hardware agnostic languages, spanning the full hardware-software optimization stack. The kernel optimization process is described as graph-based search with selection policy, universal operator, fitness function, and termination rule, dynamically adapts to runtime execution context through retrieval-augmented prompt synthesis. We designed, implemented, and deployed KernelEvolve to optimize a wide variety of production recommendation models across generations of NVIDIA and AMD GPUs, as well as Meta's AI accelerators. We validate KernelEvolve on the publicly-available KernelBench suite, achieving 100% pass rate on all 250 problems across three difficulty levels, and 160 PyTorch ATen operators across three heterogeneous hardware platforms, demonstrating 100% correctness. KernelEvolve reduces development time from weeks to hours and achieves substantial performance improvements over PyTorch baselines across diverse production use cases and for heterogeneous AI systems at-scale. Beyond performance efficiency improvements, KernelEvolve significantly mitigates the programmability barrier for new AI hardware by enabling automated kernel generation for in-house developed AI hardware.

Training Large Language Models (LLMs) efficiently at scale presents a formidable challenge, driven by their ever-increasing computational demands and the need for enhanced performance. In this work, we introduce Liger-Kernel, an open-sourced set of Triton kernels developed specifically for LLM training. With kernel optimization techniques like kernel operation fusing and input chunking, our kernels achieve on average a 20% increase in training throughput and a 60% reduction in GPU memory usage for popular LLMs compared to HuggingFace implementations. In addition, Liger-Kernel is designed with modularity, accessibility, and adaptability in mind, catering to both casual and expert users. Comprehensive benchmarks and integration tests are built in to ensure compatibility, performance, correctness, and convergence across diverse computing environments and model architectures. The source code is available under a permissive license at: github.com/linkedin/Liger-Kernel.

Inspired by the long-range modeling ability of ViTs, large-kernel convolutions are widely studied and adopted recently to enlarge the receptive field and improve model performance, like the remarkable work ConvNeXt which employs 7x7 depthwise convolution. Although such depthwise operator only consumes a few FLOPs, it largely harms the model efficiency on powerful computing devices due to the high memory access costs. For example, ConvNeXt-T has similar FLOPs with ResNet-50 but only achieves 60% throughputs when trained on A100 GPUs with full precision. Although reducing the kernel size of ConvNeXt can improve speed, it results in significant performance degradation. It is still unclear how to speed up large-kernel-based CNN models while preserving their performance. To tackle this issue, inspired by Inceptions, we propose to decompose large-kernel depthwise convolution into four parallel branches along channel dimension, i.e. small square kernel, two orthogonal band kernels, and an identity mapping. With this new Inception depthwise convolution, we build a series of networks, namely IncepitonNeXt, which not only enjoy high throughputs but also maintain competitive performance. For instance, InceptionNeXt-T achieves 1.6x higher training throughputs than ConvNeX-T, as well as attains 0.2% top-1 accuracy improvement on ImageNet-1K. We anticipate InceptionNeXt can serve as an economical baseline for future architecture design to reduce carbon footprint. Code is available at https://github.com/sail-sg/inceptionnext.

The neural tangent kernel is a kernel function defined over the parameter distribution of an infinite width neural network. Despite the impracticality of this limit, the neural tangent kernel has allowed for a more direct study of neural networks and a gaze through the veil of their black box. More recently, it has been shown theoretically that the Laplace kernel and neural tangent kernel share the same reproducing kernel Hilbert space in the space of S^{d-1} alluding to their equivalence. In this work, we analyze the practical equivalence of the two kernels. We first do so by matching the kernels exactly and then by matching posteriors of a Gaussian process. Moreover, we analyze the kernels in R^d and experiment with them in the task of regression.

Existing GPU libraries often struggle to fully exploit the parallel resources and on-chip memory (SRAM) of GPUs when chaining multiple GPU functions as individual kernels. While Kernel Fusion (KF) techniques like Horizontal Fusion (HF) and Vertical Fusion (VF) can mitigate this, current library implementations often require library developers to manually create fused kernels. Hence, library users rely on limited sets of pre-compiled or template-based fused kernels. This limits the use cases that can benefit from HF and VF and increases development costs. In order to solve these issues, we present a novel methodology for building GPU libraries that enables automatic on-demand HF and VF for arbitrary combinations of GPU library functions. Our methodology defines reusable, fusionable components that users combine via high-level programming interfaces. Leveraging C++17 metaprogramming features available in compilers like nvcc, our methodology generates a single and optimized fused kernel tailored to the user's specific sequence of operations at compile time, without needing a custom compiler or manual development and pre-compilation of kernel combinations. This approach abstracts low-level GPU complexities while maximizing GPU resource utilization and keeping intermediate data in SRAM. We provide an open-source implementation demonstrating significant speedups compared to traditional libraries in various benchmarks, validating the effectiveness of this methodology for improving GPU performance in the range of 2x to more than 1000x, while preserving high-level programmability.

The kernel thinning (KT) algorithm of Dwivedi and Mackey (2021) compresses a probability distribution more effectively than independent sampling by targeting a reproducing kernel Hilbert space (RKHS) and leveraging a less smooth square-root kernel. Here we provide four improvements. First, we show that KT applied directly to the target RKHS yields tighter, dimension-free guarantees for any kernel, any distribution, and any fixed function in the RKHS. Second, we show that, for analytic kernels like Gaussian, inverse multiquadric, and sinc, target KT admits maximum mean discrepancy (MMD) guarantees comparable to or better than those of square-root KT without making explicit use of a square-root kernel. Third, we prove that KT with a fractional power kernel yields better-than-Monte-Carlo MMD guarantees for non-smooth kernels, like Laplace and Mat\'ern, that do not have square-roots. Fourth, we establish that KT applied to a sum of the target and power kernels (a procedure we call KT+) simultaneously inherits the improved MMD guarantees of power KT and the tighter individual function guarantees of target KT. In our experiments with target KT and KT+, we witness significant improvements in integration error even in 100 dimensions and when compressing challenging differential equation posteriors.

We present Flash-GMM, a fused Triton kernel for efficient computation of Gaussian Mixture Models (GMMs) over large-scale data in a single GPU pass. By eliminating the need to materialize the full responsibility matrix in GPU memory, Flash-GMM achieves a 20times speedup over existing implementations and enables training on datasets more than 100times larger than previously feasible on one device. To demonstrate its impact, we integrate Flash-GMM into the IVF coarse quantizer for approximate nearest-neighbor (ANN) search. We show that soft GMM clustering is now a viable drop-in replacement for k-means, and that GMM responsibilities can be leveraged to assign border vectors to multiple clusters. Our approach reaches fixed recall targets with up to 1.7times fewer distance computations, or equivalently, yields +2--12 recall@10 at matched computational cost. We release the kernel as an open-source project.

Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for instance, be used to compare probability distributions with disjoint supports. In this paper, we study a class of statistical Hilbert distances that we term the Schoenberg-Rao distances, a generalization of the MMD that allows one to consider a broader class of kernels, namely the conditionally negative semi-definite kernels. In particular, we introduce a principled way to construct such kernels and derive novel closed-form distances between mixtures of Gaussian distributions. These distances, derived from the concave Rao's quadratic entropy, enjoy nice theoretical properties and possess interpretable hyperparameters which can be tuned for specific applications. Our method constitutes a practical alternative to Wasserstein distances and we illustrate its efficiency on a broad range of machine learning tasks such as density estimation, generative modeling and mixture simplification.

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit, thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of an ANN, the network function f_theta (which maps input vectors to output vectors) follows the kernel gradient of the functional cost (which is convex, in contrast to the parameter cost) w.r.t. a new kernel: the Neural Tangent Kernel (NTK). This kernel is central to describe the generalization features of ANNs. While the NTK is random at initialization and varies during training, in the infinite-width limit it converges to an explicit limiting kernel and it stays constant during training. This makes it possible to study the training of ANNs in function space instead of parameter space. Convergence of the training can then be related to the positive-definiteness of the limiting NTK. We prove the positive-definiteness of the limiting NTK when the data is supported on the sphere and the non-linearity is non-polynomial. We then focus on the setting of least-squares regression and show that in the infinite-width limit, the network function f_theta follows a linear differential equation during training. The convergence is fastest along the largest kernel principal components of the input data with respect to the NTK, hence suggesting a theoretical motivation for early stopping. Finally we study the NTK numerically, observe its behavior for wide networks, and compare it to the infinite-width limit.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real-world data. We introduce a class of quantum kernels that can be used for data with a group structure. The kernel is defined in terms of a unitary representation of the group and a fiducial state that can be optimized using a technique called kernel alignment. We apply this method to a learning problem on a coset-space that embodies the structure of many essential learning problems on groups. We implement the learning algorithm with 27 qubits on a superconducting processor.

We discuss how to define a kernel for Signal Temporal Logic (STL) formulae. Such a kernel allows us to embed the space of formulae into a Hilbert space, and opens up the use of kernel-based machine learning algorithms in the context of STL. We show an application of this idea to a regression problem in formula space for probabilistic models.

A recent trend in explainable AI research has focused on surrogate modeling, where neural networks are approximated as simpler ML algorithms such as kernel machines. A second trend has been to utilize kernel functions in various explain-by-example or data attribution tasks. In this work, we combine these two trends to analyze approximate empirical neural tangent kernels (eNTK) for data attribution. Approximation is critical for eNTK analysis due to the high computational cost to compute the eNTK. We define new approximate eNTK and perform novel analysis on how well the resulting kernel machine surrogate models correlate with the underlying neural network. We introduce two new random projection variants of approximate eNTK which allow users to tune the time and memory complexity of their calculation. We conclude that kernel machines using approximate neural tangent kernel as the kernel function are effective surrogate models, with the introduced trace NTK the most consistent performer. Open source software allowing users to efficiently calculate kernel functions in the PyTorch framework is available (https://github.com/pnnl/projection\_ntk).

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

We present Metal-Sci, a 10-task benchmark of scientific Apple Silicon Metal compute kernels spanning six optimization regimes (stencils, all-pairs in n-body problems, multi-field Boltzmann, neighbor-list molecular dynamics, multi-kernel PDE, FFT). Each task ships a CPU reference, a roofline-anchored fitness function, and a held-out generalization size. We pair the benchmark with a lightweight harness for automatic kernel search that runtime-compiles each candidate, scores it against the roofline across multiple sizes, and feeds structured compile and per-size correctness diagnostics back to a frozen LLM driving a (1{+}1) evolutionary loop. We report matched single-model sweeps of Claude Opus 4.7, Gemini 3.1 Pro, and GPT 5.5 on M1 Pro: in-distribution self-speedups span 1.00times to 10.7times. Beyond raw speedup, our central methodological claim is structural: the held-out gate scoring function Φ_T (evaluated once at end-of-run on a configuration the agent never sees during search) functions as a cheap mechanical oversight primitive on this automatic search loop, catching e.g. an Opus template <uint D> HMC win that returns wrong samples at unseen dimensions, and a GPT FFT3D best that wins in-distribution at 2.95times speedup but collapses to 0.23times on a 256^3 held-out cube, a silent regression that the in-distribution score alone cannot see. Code at https://github.com/vicgalle/metal-sci-kernels

Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite width NTKs. For networks with O output units (e.g. an O-class classifier), however, the eNTK on N inputs is of size NO times NO, taking O((NO)^2) memory and up to O((NO)^3) computation. Most existing applications have therefore used one of a handful of approximations yielding N times N kernel matrices, saving orders of magnitude of computation, but with limited to no justification. We prove that one such approximation, which we call "sum of logits", converges to the true eNTK at initialization for any network with a wide final "readout" layer. Our experiments demonstrate the quality of this approximation for various uses across a range of settings.

This paper proposes the paradigm of large convolutional kernels in designing modern Convolutional Neural Networks (ConvNets). We establish that employing a few large kernels, instead of stacking multiple smaller ones, can be a superior design strategy. Our work introduces a set of architecture design guidelines for large-kernel ConvNets that optimize their efficiency and performance. We propose the UniRepLKNet architecture, which offers systematical architecture design principles specifically crafted for large-kernel ConvNets, emphasizing their unique ability to capture extensive spatial information without deep layer stacking. This results in a model that not only surpasses its predecessors with an ImageNet accuracy of 88.0%, an ADE20K mIoU of 55.6%, and a COCO box AP of 56.4% but also demonstrates impressive scalability and performance on various modalities such as time-series forecasting, audio, point cloud, and video recognition. These results indicate the universal modeling abilities of large-kernel ConvNets with faster inference speed compared with vision transformers. Our findings reveal that large-kernel ConvNets possess larger effective receptive fields and a higher shape bias, moving away from the texture bias typical of smaller-kernel CNNs. All codes and models are publicly available at https://github.com/AILab-CVC/UniRepLKNet promoting further research and development in the community.

A neural architecture with randomly initialized weights, in the infinite width limit, is equivalent to a Gaussian Random Field whose covariance function is the so-called Neural Network Gaussian Process kernel (NNGP). We prove that a reproducing kernel Hilbert space (RKHS) defined by the NNGP contains only functions that can be approximated by the architecture. To achieve a certain approximation error the required number of neurons in each layer is defined by the RKHS norm of the target function. Moreover, the approximation can be constructed from a supervised dataset by a random multi-layer representation of an input vector, together with training of the last layer's weights. For a 2-layer NN and a domain equal to an n-1-dimensional sphere in {mathbb R}^n, we compare the number of neurons required by Barron's theorem and by the multi-layer features construction. We show that if eigenvalues of the integral operator of the NNGP decay slower than k^{-n-2{3}} where k is an order of an eigenvalue, then our theorem guarantees a more succinct neural network approximation than Barron's theorem. We also make some computational experiments to verify our theoretical findings. Our experiments show that realistic neural networks easily learn target functions even when both theorems do not give any guarantees.

AMD GPUs offer state-of-the-art compute and memory bandwidth; however, peak performance AMD kernels are written in raw assembly. To address the difficulty of mapping AI algorithms to hardware, recent work proposes C++ embedded and PyTorch-inspired domain-specific languages like ThunderKittens (TK) to simplify high performance AI kernel development on NVIDIA hardware. We explore the extent to which such primitives -- for explicit tile-based programming with optimized memory accesses and fine-grained asynchronous execution across workers -- are NVIDIA-specific or general. We provide the first detailed study of the programming primitives that lead to performant AMD AI kernels, and we encapsulate these insights in the HipKittens (HK) programming framework. We find that tile-based abstractions used in prior DSLs generalize to AMD GPUs, however we need to rethink the algorithms that instantiate these abstractions for AMD. We validate the HK primitives across CDNA3 and CDNA4 AMD platforms. In evaluations, HK kernels compete with AMD's hand-optimized assembly kernels for GEMMs and attention, and consistently outperform compiler baselines. Moreover, assembly is difficult to scale to the breadth of AI workloads; reflecting this, in some settings HK outperforms all available kernel baselines by 1.2-2.4times (e.g., d=64 attention, GQA backwards, memory-bound kernels). These findings help pave the way for a single, tile-based software layer for high-performance AI kernels that translates across GPU vendors. HipKittens is released at: https://github.com/HazyResearch/HipKittens.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

Optimizing GPU kernels presents a significantly greater challenge for large language models (LLMs) than standard code generation tasks, as it requires understanding hardware architecture, parallel optimization strategies, and performance profiling outputs. Most existing LLM-based approaches to kernel generation rely on simple prompting and feedback loops, incorporating hardware awareness only indirectly through profiling feedback. We introduce KernelFoundry, an evolutionary framework that efficiently explores the GPU kernel design space through three key mechanisms: (1) MAP-Elites quality-diversity search with kernel-specific behavioral dimensions to sustain exploration across diverse optimization strategies; (2) meta-prompt evolution, which co-evolves prompts with kernels to uncover task-specific optimization strategies, and (3) template-based parameter optimization to tune kernels to inputs and hardware. We evaluate this framework on KernelBench, robust-kbench, and custom tasks, generating SYCL kernels as a cross-platform GPU programming model and CUDA kernels for comparison to prior work. Our approach consistently outperforms the baseline methods, achieving an average speedup of 2.3x on KernelBench for SYCL. Moreover, KernelFoundry is implemented as a distributed framework with remote access to diverse hardware, enabling rapid benchmarking and featuring a flexible user input layer that supports kernel generation for a wide range of real-world use cases beyond benchmarking.

LLM-based Triton kernel generation has attracted significant interest, yet a fundamental empirical question remains unanswered: where does this capability break down, and why? We present KernelBench-X, a benchmark designed to answer this question through category-aware evaluation of correctness and hardware efficiency across 176 tasks in 15 categories. Our systematic comparison of five representative methods yields three main findings. First, task structure determines correctness more than method design. Category explains nearly three times more variance in semantic correctness than method (9.4% vs 3.3% explained deviance), and 72% of Fusion tasks fail across all five methods while Math tasks are solved consistently. Second, iterative refinement improves correctness, but not performance. Across GEAK iterations, compile rate rises from 52.3% to 68.8% while average speedup declines from 1.58times to 1.44times; newly rescued kernels consistently underperform persistently correct ones (1.16times vs 1.58times speedup in round~0to1). Third, correctness does not imply efficiency. 46.6% of correct kernels are slower than the PyTorch eager baseline, and cross-hardware speedup variance reaches 21.4times. Besides, quantization remains completely unsolved (0/30 successes) despite non-trivial compilation rates, revealing systematic misunderstanding of numerical computation contracts rather than surface-level syntax errors. These findings suggest that future progress depends on handling global coordination, explicitly modeling numerical precision, and incorporating hardware efficiency into generation. The code is available at https://github.com/BonnieW05/KernelBenchX

When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible combinations is unfeasible in practice. A more efficient approach is to learn the kernel size during training. However, existing works that learn the kernel size have a limited bandwidth. These approaches scale kernels by dilation, and thus the detail they can describe is limited. In this work, we propose FlexConv, a novel convolutional operation with which high bandwidth convolutional kernels of learnable kernel size can be learned at a fixed parameter cost. FlexNets model long-term dependencies without the use of pooling, achieve state-of-the-art performance on several sequential datasets, outperform recent works with learned kernel sizes, and are competitive with much deeper ResNets on image benchmark datasets. Additionally, FlexNets can be deployed at higher resolutions than those seen during training. To avoid aliasing, we propose a novel kernel parameterization with which the frequency of the kernels can be analytically controlled. Our novel kernel parameterization shows higher descriptive power and faster convergence speed than existing parameterizations. This leads to important improvements in classification accuracy.

The performance of modern AI systems is fundamentally constrained by the quality of their underlying kernels, which translate high-level algorithmic semantics into low-level hardware operations. Achieving near-optimal kernels requires expert-level understanding of hardware architectures and programming models, making kernel engineering a critical but notoriously time-consuming and non-scalable process. Recent advances in large language models (LLMs) and LLM-based agents have opened new possibilities for automating kernel generation and optimization. LLMs are well-suited to compress expert-level kernel knowledge that is difficult to formalize, while agentic systems further enable scalable optimization by casting kernel development as an iterative, feedback-driven loop. Rapid progress has been made in this area. However, the field remains fragmented, lacking a systematic perspective for LLM-driven kernel generation. This survey addresses this gap by providing a structured overview of existing approaches, spanning LLM-based approaches and agentic optimization workflows, and systematically compiling the datasets and benchmarks that underpin learning and evaluation in this domain. Moreover, key open challenges and future research directions are further outlined, aiming to establish a comprehensive reference for the next generation of automated kernel optimization. To keep track of this field, we maintain an open-source GitHub repository at https://github.com/flagos-ai/awesome-LLM-driven-kernel-generation.

Recent advances in large language models (LLMs) demonstrate their effectiveness in scaling test-time compute for software engineering tasks. However, these approaches often focus on high-level solutions, with limited attention to optimizing low-level CUDA kernel implementations. Additionally, existing kernel generation benchmarks suffer from exploitable loopholes and insufficient diversity in testing conditions, hindering true generalization assessment. To address these limitations, we introduce robust-kbench, a new benchmark for rigorous evaluation of kernel performance and correctness across varied scenarios. Furthermore, we present a comprehensive agentic framework that automates CUDA kernel discovery, verification, and optimization. This pipeline enables frontier LLMs to translate torch code to CUDA kernels and iteratively improve their runtime within our robust evaluation setting. Our sequential workflow first translates PyTorch code into equivalent CUDA kernels. It then optimizes their runtime using a novel evolutionary meta-generation procedure tailored to the CUDA ecosystem, guided by LLM-based verifiers for correctness and efficient filtering. Evaluated on robust-kbench, our approach produces CUDA kernels outperforming torch implementations for practical applications, including forward and backward passes. It can fuse operations and deploy various runtime optimization strategies. The verifier workflow accurately classifies incorrect kernels, enhancing hardware verification efficiency.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability eta(x)=P(Y=1mid X=x), we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2eta(x)-1 and apply the method to real datasets.

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

Efficient GPU kernels are crucial for building performant machine learning architectures, but writing them is a time-consuming challenge that requires significant expertise; therefore, we explore using language models (LMs) to automate kernel generation. We introduce KernelBench, an open-source framework for evaluating LMs' ability to write fast and correct kernels on a suite of 250 carefully selected PyTorch ML workloads. KernelBench represents a real-world engineering environment and making progress on the introduced benchmark directly translates to faster practical kernels. We introduce a new evaluation metric fast_p, which measures the percentage of generated kernels that are functionally correct and offer a speedup greater than an adjustable threshold p over baseline. Our experiments across various state-of-the-art models and test-time methods show that frontier reasoning models perform the best out of the box but still fall short overall, matching the PyTorch baseline in less than 20% of the cases. While we show that results can improve by leveraging execution and profiling feedback during iterative refinement, KernelBench remains a challenging benchmark, with its difficulty increasing as we raise speedup threshold p.

We revisit large kernel design in modern convolutional neural networks (CNNs). Inspired by recent advances in vision transformers (ViTs), in this paper, we demonstrate that using a few large convolutional kernels instead of a stack of small kernels could be a more powerful paradigm. We suggested five guidelines, e.g., applying re-parameterized large depth-wise convolutions, to design efficient high-performance large-kernel CNNs. Following the guidelines, we propose RepLKNet, a pure CNN architecture whose kernel size is as large as 31x31, in contrast to commonly used 3x3. RepLKNet greatly closes the performance gap between CNNs and ViTs, e.g., achieving comparable or superior results than Swin Transformer on ImageNet and a few typical downstream tasks, with lower latency. RepLKNet also shows nice scalability to big data and large models, obtaining 87.8% top-1 accuracy on ImageNet and 56.0% mIoU on ADE20K, which is very competitive among the state-of-the-arts with similar model sizes. Our study further reveals that, in contrast to small-kernel CNNs, large-kernel CNNs have much larger effective receptive fields and higher shape bias rather than texture bias. Code & models at https://github.com/megvii-research/RepLKNet.

This paper revisits the problem of computing empirical cumulative distribution functions (ECDF) efficiently on large, multivariate datasets. Computing an ECDF at one evaluation point requires O(N) operations on a dataset composed of N data points. Therefore, a direct evaluation of ECDFs at N evaluation points requires a quadratic O(N^2) operations, which is prohibitive for large-scale problems. Two fast and exact methods are proposed and compared. The first one is based on fast summation in lexicographical order, with a O(N{log}N) complexity and requires the evaluation points to lie on a regular grid. The second one is based on the divide-and-conquer principle, with a O(Nlog(N)^{(d-1){vee}1}) complexity and requires the evaluation points to coincide with the input points. The two fast algorithms are described and detailed in the general d-dimensional case, and numerical experiments validate their speed and accuracy. Secondly, the paper establishes a direct connection between cumulative distribution functions and kernel density estimation (KDE) for a large class of kernels. This connection paves the way for fast exact algorithms for multivariate kernel density estimation and kernel regression. Numerical tests with the Laplacian kernel validate the speed and accuracy of the proposed algorithms. A broad range of large-scale multivariate density estimation, cumulative distribution estimation, survival function estimation and regression problems can benefit from the proposed numerical methods.

Weight-Decomposed Low-Rank Adaptation (DoRA) extends LoRA by decoupling weight magnitude from direction, but its forward pass requires the row-wise norm of W + sBA, a computation that every major framework we surveyed implements by materializing the dense [d_out, d_in] product BA. At d_in = 8192 and rank r = 384, a single module's norm requires about 512 MB of transient working memory in bf16, making high-rank DoRA costly and often infeasible on common single-GPU setups once hundreds of adapted modules and checkpointing are involved. We present two systems contributions. A factored norm decomposes the squared norm into base, cross, and Gram terms computable through O(d_out r + r^2) intermediates, eliminating the dense product. Fused Triton kernels collapse the four-kernel DoRA composition into a single pass, reducing memory traffic by about 4x and using a numerically stable form that avoids catastrophic cancellation in the near-unity rescaling regime where magnitude scales concentrate in practice. Across six 8-32B vision-language models (VLMs) on three NVIDIA GPUs (RTX 6000 PRO, H200, B200) at r = 384 in bf16, the fused implementation is 1.5-2.0x faster than Hugging Face PEFT's DoRA implementation for inference and 1.5-1.9x faster for gradient computation (optimizer step excluded), with up to 7 GB lower peak VRAM. Microbenchmarks on six GPUs spanning four architecture generations (L40S, A100, RTX 6000 PRO, H200, B200, B300) confirm 1.5-2.7x compose-kernel speedup. Final-logit cosine similarity exceeds 0.9999 across all model/GPU pairs, and multi-seed training curves match within 7.1 x 10^-4 mean per-step loss delta over 2000 steps.

Optimizing GPU kernels is critical for efficient modern machine learning systems yet remains challenging due to the complex interplay of design factors and rapid hardware evolution. Existing automated approaches typically treat Large Language Models (LLMs) merely as stochastic code generators within heuristic-guided evolutionary loops. These methods often struggle with complex kernels requiring coordinated, multi-step structural transformations, as they lack explicit planning capabilities and frequently discard promising strategies due to inefficient or incorrect intermediate implementations. To address this, we propose Search via Co-Evolving World Model and build K-Search based on this method. By replacing static search heuristics with a co-evolving world model, our framework leverages LLMs' prior domain knowledge to guide the search, actively exploring the optimization space. This approach explicitly decouples high-level algorithmic planning from low-level program instantiation, enabling the system to navigate non-monotonic optimization paths while remaining resilient to temporary implementation defects. We evaluate K-Search on diverse, complex kernels from FlashInfer, including GQA, MLA, and MoE kernels. Our results show that K-Search significantly outperforms state-of-the-art evolutionary search methods, achieving an average 2.10x improvement and up to a 14.3x gain on complex MoE kernels. On the GPUMode TriMul task, K-Search achieves state-of-the-art performance on H100, reaching 1030us and surpassing both prior evolution and human-designed solutions.

High quality kernels are critical for reducing training and inference costs of Large Language Models (LLMs), yet they traditionally require significant expertise in hardware architecture and software optimization. While recent advances in LLM-based code generation show promise for complex optimization, existing methods struggle with the vast optimization space due to insufficient hardware domain knowledge, failing to effectively balance exploration and exploitation. We present KernelBand, a novel framework that formulates kernel optimization as a hierarchical multi-armed bandit problem, enabling LLM agents to strategically navigate the optimization space by treating kernel selection and optimization strategy application as sequential decision-making processes. Our approach leverages hardware profiling information to identify promising optimization strategies and employs runtime behavior clustering to reduce exploration overhead across kernel candidates. Extensive experiments on TritonBench demonstrate that KernelBand significantly outperforms state-of-the-art methods, achieving superior performance with fewer tokens while exhibiting consistent improvement without saturation as computational resources increase.

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps and learns the kernel by learning the spectral distribution. This not only helps in learning a generic kernel end-to-end, but also reduces the time and space complexity of Transformers from quadratic to linear. We show that KERNELIZED TRANSFORMERS achieve performance comparable to existing efficient Transformer architectures, both in terms of accuracy as well as computational efficiency. Our study also demonstrates that the choice of the kernel has a substantial impact on performance, and kernel learning variants are competitive alternatives to fixed kernel Transformers, both in long as well as short sequence tasks.

The efficiency of Bayesian optimization (BO) relies heavily on the choice of the Gaussian process (GP) kernel, which plays a central role in balancing exploration and exploitation under limited evaluation budgets. Traditional BO methods often rely on fixed or heuristic kernel selection strategies, which can result in slow convergence or suboptimal solutions when the chosen kernel is poorly suited to the underlying objective function. To address this limitation, we propose a freshly-baked Context-Aware Kernel Evolution (CAKE) to enhance BO with large language models (LLMs). Concretely, CAKE leverages LLMs as the crossover and mutation operators to adaptively generate and refine GP kernels based on the observed data throughout the optimization process. To maximize the power of CAKE, we further propose BIC-Acquisition Kernel Ranking (BAKER) to select the most effective kernel through balancing the model fit measured by the Bayesian information criterion (BIC) with the expected improvement at each iteration of BO. Extensive experiments demonstrate that our fresh CAKE-based BO method consistently outperforms established baselines across a range of real-world tasks, including hyperparameter optimization, controller tuning, and photonic chip design. Our code is publicly available at https://github.com/cake4bo/cake.

Recent advances in transformer-based foundation models have made them the default choice for many tasks, but their rapidly growing size makes fitting a full model on a single GPU increasingly difficult and their computational cost prohibitive. Block low-rank (BLR) compression techniques address this challenge by learning compact representations of weight matrices. While traditional low-rank (LR) methods often incur sharp accuracy drops, BLR approaches such as Monarch and BLAST can better capture the underlying structure, thus preserving accuracy while reducing computations and memory footprints. In this work, we use roofline analysis to show that, although BLR methods achieve theoretical savings and practical speedups for single-token inference, multi-token inference often becomes memory-bound in practice, increasing latency despite compiler-level optimizations in PyTorch. To address this, we introduce custom Triton kernels with partial fusion and memory layout optimizations for both Monarch and BLAST. On memory-constrained NVIDIA GPUs such as Jetson Orin Nano and A40, our kernels deliver up to 3.76times speedups and 3times model size compression over PyTorch dense baselines using CUDA backend and compiler-level optimizations, while supporting various models including Llama-7/1B, GPT2-S, DiT-XL/2, and ViT-B. Our code is available at https://github.com/pabillam/mem-efficient-blr.

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

Privacy-utility tradeoff remains as one of the fundamental issues of differentially private machine learning. This paper introduces a geometrically inspired kernel-based approach to mitigate the accuracy-loss issue in classification. In this approach, a representation of the affine hull of given data points is learned in Reproducing Kernel Hilbert Spaces (RKHS). This leads to a novel distance measure that hides privacy-sensitive information about individual data points and improves the privacy-utility tradeoff via significantly reducing the risk of membership inference attacks. The effectiveness of the approach is demonstrated through experiments on MNIST dataset, Freiburg groceries dataset, and a real biomedical dataset. It is verified that the approach remains computationally practical. The application of the approach to federated learning is considered and it is observed that the accuracy-loss due to data being distributed is either marginal or not significantly high.

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

Large language model (LLM)-based inference workloads increasingly dominate data center costs and resource utilization. Therefore, understanding the inference workload characteristics on evolving CPU-GPU coupled architectures is crucial for optimization. This paper presents an in-depth analysis of LLM inference behavior on loosely-coupled (PCIe A100/H100) and closely-coupled (GH200) systems. We analyze performance dynamics using fine-grained operator-to-kernel trace analysis, facilitated by our novel profiler SKIP and metrics like Total Kernel Launch and Queuing Time (TKLQT). Results show that closely-coupled (CC) GH200 significantly outperforms loosely-coupled (LC) systems at large batch sizes, achieving 1.9x-2.7x faster prefill latency for Llama 3.2-1B. However, our analysis also reveals that GH200 remains CPU-bound up to 4x larger batch sizes than LC systems. In this extended CPU-bound region, we identify the performance characteristics of the Grace CPU as a key factor contributing to higher inference latency at low batch sizes on GH200. We demonstrate that TKLQT accurately identifies this CPU/GPU-bound transition point. Based on this analysis, we further show that kernel fusion offers significant potential to mitigate GH200's low-batch latency bottleneck by reducing kernel launch overhead. This detailed kernel-level characterization provides critical insights for optimizing diverse CPU-GPU coupling strategies. This work is an initial effort, and we plan to explore other major AI/DL workloads that demand different degrees of CPU-GPU heterogeneous architectures.

Compact convolutional neural networks gain efficiency mainly through depthwise convolutions, expanded channels and complex topologies, which contrarily aggravate the training process. Besides, 3x3 kernels dominate the spatial representation in these models, whereas even-sized kernels (2x2, 4x4) are rarely adopted. In this work, we quantify the shift problem occurs in even-sized kernel convolutions by an information erosion hypothesis, and eliminate it by proposing symmetric padding on four sides of the feature maps (C2sp, C4sp). Symmetric padding releases the generalization capabilities of even-sized kernels at little computational cost, making them outperform 3x3 kernels in image classification and generation tasks. Moreover, C2sp obtains comparable accuracy to emerging compact models with much less memory and time consumption during training. Symmetric padding coupled with even-sized convolutions can be neatly implemented into existing frameworks, providing effective elements for architecture designs, especially on online and continual learning occasions where training efforts are emphasized.

Large kernels make standard convolutional neural networks (CNNs) great again over transformer architectures in various vision tasks. Nonetheless, recent studies meticulously designed around increasing kernel size have shown diminishing returns or stagnation in performance. Thus, the hidden factors of large kernel convolution that affect model performance remain unexplored. In this paper, we reveal that the key hidden factors of large kernels can be summarized as two separate components: extracting features at a certain granularity and fusing features by multiple pathways. To this end, we leverage the multi-path long-distance sparse dependency relationship to enhance feature utilization via the proposed Shiftwise (SW) convolution operator with a pure CNN architecture. In a wide range of vision tasks such as classification, segmentation, and detection, SW surpasses state-of-the-art transformers and CNN architectures, including SLaK and UniRepLKNet. More importantly, our experiments demonstrate that 3 times 3 convolutions can replace large convolutions in existing large kernel CNNs to achieve comparable effects, which may inspire follow-up works. Code and all the models at https://github.com/lidc54/shift-wiseConv.

The size and compute characteristics of modern large language models have led to an increased interest in developing specialized kernels tailored for training and inference. Existing kernels primarily optimize for compute utilization, targeting the large-batch training and inference settings. However, low-batch inference, where memory bandwidth and kernel launch overheads contribute are significant factors, remains important for many applications of interest such as in edge deployment and latency-sensitive applications. This paper describes FlashFormer, a proof-of-concept kernel for accelerating single-batch inference for transformer-based large language models. Across various model sizes and quantizations settings, we observe nontrivial speedups compared to existing state-of-the-art inference kernels.

Control variates are variance reduction tools for Monte Carlo estimators. They can provide significant variance reduction, but usually require a large number of samples, which can be prohibitive when sampling or evaluating the integrand is computationally expensive. Furthermore, there are many scenarios where we need to compute multiple related integrals simultaneously or sequentially, which can further exacerbate computational costs. In this paper, we propose vector-valued control variates, an extension of control variates which can be used to reduce the variance of multiple Monte Carlo estimators jointly. This allows for the transfer of information across integration tasks, and hence reduces the need for a large number of samples. We focus on control variates based on kernel interpolants and our novel construction is obtained through a generalised Stein identity and the development of novel matrix-valued Stein reproducing kernels. We demonstrate our methodology on a range of problems including multifidelity modelling, Bayesian inference for dynamical systems, and model evidence computation through thermodynamic integration.

The challenge of mapping AI architectures to GPU hardware is creating a critical bottleneck in AI progress. Despite substantial efforts, hand-written custom kernels fail to meet their theoretical performance thresholds, even on well-established operations like linear attention. The diverse hardware capabilities of GPUs might suggest that we need a wide variety of techniques to achieve high performance. However, our work explores whether a small number of key abstractions can drastically simplify the process. We present ThunderKittens (TK), a framework for writing performant AI kernels while remaining easy to use and maintain. Our abstractions map to the three levels of the GPU hierarchy: (1) at the warp-level, we provide 16x16 matrix tiles as basic data structures and PyTorch-like parallel compute operations over tiles, (2) at the thread-block level, we provide a template for overlapping asynchronous operations across parallel warps, and (3) at the grid-level, we provide support to help hide the block launch and tear-down, and memory costs. We show the value of TK by providing kernels that match or outperform prior kernels for a range of AI operations. We match CuBLAS and FlashAttention-3 on GEMM and attention inference performance and outperform the strongest baselines by 10-40% on attention backwards, 8times on state space models, and 14times on linear attention.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position embedding for extrapolation by kernelizing positional differences. We achieve this goal using conditionally positive definite (CPD) kernels, a class of functions known for generalizing distance metrics. To maintain the inner product interpretation of self-attention, we show that a CPD kernel can be transformed into a PD kernel by adding a constant offset. This offset is implicitly absorbed in the Softmax normalization during self-attention. The diversity of CPD kernels allows us to derive various RPEs that enable length extrapolation in a principled way. Experiments demonstrate that the logarithmic variant achieves excellent extrapolation performance on three large language modeling datasets. Our implementation and pretrained checkpoints are released at https://github.com/chijames/KERPLE.git.

The automatic generation of deep learning (DL) kernels using large language models (LLMs) has emerged as a promising approach to reduce the manual effort and hardware-specific expertise required for writing high-performance operator implementations. However, existing benchmarks for evaluating LLMs in this domain suffer from limited hardware support, coarse-grained kernel categorization, and imbalanced task coverage. To address these limitations, we introduce MultiKernelBench, the first comprehensive, multi-platform benchmark for LLM-based DL kernel generation. MultiKernelBench spans 285 tasks across 14 well-defined kernel categories and supports three major hardware platforms: Nvidia GPUs, Huawei NPUs, and Google TPUs. To enable future extensibility, we design a modular backend abstraction layer that decouples platform-specific logic from the core benchmarking infrastructure, allowing easy integration of new hardware platforms. We further propose a simple yet effective category-aware one-shot prompting method that improves generation quality by providing in-category exemplars. Through systematic evaluations of seven state-of-the-art LLMs, we reveal significant variation in task difficulty, poor generalization to platforms with less training exposure, and the effectiveness of targeted prompting strategies. MultiKernelBench is publicly available at https://github.com/wzzll123/MultiKernelBench.

We evaluate AI-assisted generative capabilities on fundamental numerical kernels in high-performance computing (HPC), including AXPY, GEMV, GEMM, SpMV, Jacobi Stencil, and CG. We test the generated kernel codes for a variety of language-supported programming models, including (1) C++ (e.g., OpenMP [including offload], OpenACC, Kokkos, SyCL, CUDA, and HIP), (2) Fortran (e.g., OpenMP [including offload] and OpenACC), (3) Python (e.g., numba, Numba, cuPy, and pyCUDA), and (4) Julia (e.g., Threads, CUDA.jl, AMDGPU.jl, and KernelAbstractions.jl). We use the GitHub Copilot capabilities powered by OpenAI Codex available in Visual Studio Code as of April 2023 to generate a vast amount of implementations given simple <kernel> + <programming model> + <optional hints> prompt variants. To quantify and compare the results, we propose a proficiency metric around the initial 10 suggestions given for each prompt. Results suggest that the OpenAI Codex outputs for C++ correlate with the adoption and maturity of programming models. For example, OpenMP and CUDA score really high, whereas HIP is still lacking. We found that prompts from either a targeted language such as Fortran or the more general-purpose Python can benefit from adding code keywords, while Julia prompts perform acceptably well for its mature programming models (e.g., Threads and CUDA.jl). We expect for these benchmarks to provide a point of reference for each programming model's community. Overall, understanding the convergence of large language models, AI, and HPC is crucial due to its rapidly evolving nature and how it is redefining human-computer interactions.

Large-kernel convolutional neural networks (ConvNets) have recently received extensive research attention, but there are two unresolved and critical issues that demand further investigation. 1) The architectures of existing large-kernel ConvNets largely follow the design principles of conventional ConvNets or transformers, while the architectural design for large-kernel ConvNets remains under-addressed. 2) As transformers have dominated multiple modalities, it remains to be investigated whether ConvNets also have a strong universal perception ability in domains beyond vision. In this paper, we contribute from two aspects. 1) We propose four architectural guidelines for designing large-kernel ConvNets, the core of which is to exploit the essential characteristics of large kernels that distinguish them from small kernels - they can see wide without going deep. Following such guidelines, our proposed large-kernel ConvNet shows leading performance in image recognition. For example, our models achieve an ImageNet accuracy of 88.0%, ADE20K mIoU of 55.6%, and COCO box AP of 56.4%, demonstrating better performance and higher speed than a number of recently proposed powerful competitors. 2) We discover that large kernels are the key to unlocking the exceptional performance of ConvNets in domains where they were originally not proficient. With certain modality-related preprocessing approaches, the proposed model achieves state-of-the-art performance on time-series forecasting and audio recognition tasks even without modality-specific customization to the architecture. Code and all the models at https://github.com/AILab-CVC/UniRepLKNet.

Optimizing GPU kernels manually is a challenging and time-consuming task. With the rapid development of LLMs, automated GPU kernel optimization is gradually becoming a tangible reality. However, current LLM-driven automated optimization methods narrowly focus on machine learning applications, such as PyTorch operator optimization, while overlooking broader domains like sparse matrix operations in scientific computing. Extending to these broader applications brings new challenges for the benchmark and algorithm. Therefore, developing a general-purpose automated kernel optimization method becomes our primary focus. In this paper, we address the absence of systematic evaluation for multi-scenario settings by introducing MSKernelBench, which spans multiple scenarios, including fundamental algebraic operations, common LLM kernels, sparse matrix operators, and scientific computing routines, each supporting both FP32 and BF16 precision. Building on this benchmark, we introduce CUDAMaster, a multi-agent, hardware-aware system for kernel optimization that leverages profiling information and automatically constructs the full compilation and execution toolchain. Experimental results demonstrate that CUDAMaster achieves significant speedups across most operators, outperforming Astra by about 35%. In several cases, its performance matches or surpasses that of highly optimized, closed-source libraries such as cuBLAS. A demo showcasing the original and optimized code for each operator is available at https://hanyx2021.github.io/MSKernelBenchDemo/.

In recent years, the use of large convolutional kernels has become popular in designing convolutional neural networks due to their ability to capture long-range dependencies and provide large receptive fields. However, the increase in kernel size also leads to a quadratic growth in the number of parameters, resulting in heavy computation and memory requirements. To address this challenge, we propose a neighborhood attention (NA) module that upgrades the standard convolution with a self-attention mechanism. The NA module efficiently extracts long-range dependencies in a sliding window pattern, thereby achieving similar performance to large convolutional kernels but with fewer parameters. Building upon the NA module, we propose a lightweight single image super-resolution (SISR) network named TCSR. Additionally, we introduce an enhanced feed-forward network (EFFN) in TCSR to improve the SISR performance. EFFN employs a parameter-free spatial-shift operation for efficient feature aggregation. Our extensive experiments and ablation studies demonstrate that TCSR outperforms existing lightweight SISR methods and achieves state-of-the-art performance. Our codes are available at https://github.com/Aitical/TCSR.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices Kin R^{ntimes n}. K's columns are indexed by a set of n keys k_1,k_2ldots, k_nin R^d, rows by a set of n queries q_1,q_2,ldots,q_nin R^d , and its i,j entry is K_{ij} = e^{-|q_i-k_j|_2^2/2sigma^2} for some bandwidth parameter sigma>0. Given a vector xin R^n and error parameter epsilon>0, our task is to output a yin R^n such that |Kx-y|_2leq epsilon |x|_2 in time subquadratic in n and linear in d. Our algorithms rely on the following modelling assumption about the matrices K: the sum of the entries of K scales linearly in n, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve good results. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in the low-data regime, enabling flexible non-parametric density estimation in applications with sparse data availability.

Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as physics-informed simulators in which accurate forecasts in real time with a minimal lag are required. The present neural network designs include millions of parameters, which makes it difficult to install such complex models on devices that have limited memory. Compression techniques might be able to resolve these issues by decreasing the size of CNN models that are created by reducing the number of parameters that contribute to the complexity of the models. We propose a compressed tensor format of convolutional layer, a priori, before the training of the neural network. 3-way kernels or 2-way kernels in convolutional layers are replaced by one-way fiters. The overfitting phenomena will be reduced also. The time needed to make predictions or time required for training using the original Convolutional Neural Networks model would be cut significantly if there were fewer parameters to deal with. In this paper we present a method of a priori compressing convolutional neural networks for finite element (FE) predictions of physical data. Afterwards we validate our a priori compressed models on physical data from a FE model solving a 2D wave equation. We show that the proposed convolutinal compression technique achieves equivalent performance as classical convolutional layers with fewer trainable parameters and lower memory footprint.

GPU kernel generation by LLMs has recently experienced rapid development, leveraging test-time scaling and reinforcement learning techniques. However, a key challenge for kernel generation is the scarcity of high-quality data, as most high-quality kernels are proprietary and not open-source. This challenge prevents us from leveraging supervised fine-tuning to align LLMs to the kernel generation task. To address this challenge, we develop a pipeline that generates and curates high-quality CUDA kernels with reasoning traces, motivated by a critical observation that concise yet informative reasoning traces result in robust generation of high-performance kernels. Using this pipeline, we construct our dataset ConCuR and introduce our model KernelCoder, which is the first model trained on a curated dataset consisting of PyTorch, reasoning, and CUDA kernel pairs, to our knowledge. In the KernelBench setup, our model achieves significant improvements over the existing top-performing model, QwQ-32B, and outperforms all open-source models fine-tuned for kernel generation, as well as frontier models such as DeepSeek-V3.1-Think and Claude-4-sonnet. Finally, we show that the average reasoning length can serve as a metric to assess the difficulty of kernel generation tasks. The observations, metrics, and our data collection and curation pipeline can help obtain better data in the kernel generation task in the future.

Conventional neural architectures for sequential data present important limitations. Recurrent networks suffer from exploding and vanishing gradients, small effective memory horizons, and must be trained sequentially. Convolutional networks are unable to handle sequences of unknown size and their memory horizon must be defined a priori. In this work, we show that all these problems can be solved by formulating convolutional kernels in CNNs as continuous functions. The resulting Continuous Kernel Convolution (CKConv) allows us to model arbitrarily long sequences in a parallel manner, within a single operation, and without relying on any form of recurrence. We show that Continuous Kernel Convolutional Networks (CKCNNs) obtain state-of-the-art results in multiple datasets, e.g., permuted MNIST, and, thanks to their continuous nature, are able to handle non-uniformly sampled datasets and irregularly-sampled data natively. CKCNNs match or perform better than neural ODEs designed for these purposes in a faster and simpler manner.

Most kernel-based methods, such as kernel or Gaussian process regression, kernel PCA, ICA, or k-means clustering, do not scale to large datasets, because constructing and storing the kernel matrix K_n requires at least O(n^2) time and space for n samples. Recent works show that sampling points with replacement according to their ridge leverage scores (RLS) generates small dictionaries of relevant points with strong spectral approximation guarantees for K_n. The drawback of RLS-based methods is that computing exact RLS requires constructing and storing the whole kernel matrix. In this paper, we introduce SQUEAK, a new algorithm for kernel approximation based on RLS sampling that sequentially processes the dataset, storing a dictionary which creates accurate kernel matrix approximations with a number of points that only depends on the effective dimension d_{eff}(γ) of the dataset. Moreover since all the RLS estimations are efficiently performed using only the small dictionary, SQUEAK is the first RLS sampling algorithm that never constructs the whole matrix K_n, runs in linear time mathcal{O}(nd_{eff}(γ)^3) w.r.t. n, and requires only a single pass over the dataset. We also propose a parallel and distributed version of SQUEAK that linearly scales across multiple machines, achieving similar accuracy in as little as mathcal{O}(log(n)d_{eff}(γ)^3) time.

Writing high-performance GPU kernels is among the most labor-intensive tasks in machine learning systems engineering. We present AutoKernel, an open-source framework that applies an autonomous agent loop to GPU kernel optimization for arbitrary PyTorch models. Given a model, AutoKernel profiles it to identify computational bottlenecks, ranks them by Amdahl's law impact, and iteratively refines Triton or CUDA C++ kernel implementations through hundreds of experiments without human intervention. A five-stage correctness harness covering smoke tests, shape sweeps, numerical stability, determinism verification, and edge-case coverage ensures every candidate kernel is validated before any speedup is recorded. The system comprises over 9,000 lines of Python, 18 starter kernel implementations across two backends, a six-tier optimization playbook, and integration with the KernelBench benchmark suite. AutoKernel covers nine kernel types spanning the dominant operations in modern transformer architectures. On an NVIDIA H100, our Triton kernels outperform both PyTorch eager and torch.compile (max-autotune) on the majority of tested configurations: 5.29x over eager on RMSNorm, 2.82x on softmax, and 2.21x on cross-entropy, while beating torch.compile by 2.83x, 3.44x, and 2.94x respectively. In community deployment, an AutoKernel-optimized kernel achieved first place on the vectorsum_v2 B200 leaderboard. The full system is available at https://github.com/RightNow-AI/autokernel.

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs), a unified architecture which enconpasses both RNNs and ResNets. We show that in the infinite-width-depth limit and under proper scaling, these architectures converge weakly to Gaussian processes indexed on some spaces of continuous paths and with kernels satisfying certain partial differential equations (PDEs) varying according to the choice of activation function, extending the results of Hayou (2022); Hayou & Yang (2023) to the controlled and homogeneous case. In the special, homogeneous, case where the activation is the identity, we show that the equation reduces to a linear PDE and the limiting kernel agrees with the signature kernel of Salvi et al. (2021a). We name this new family of limiting kernels neural signature kernels. Finally, we show that in the infinite-depth regime, finite-width controlled ResNets converge in distribution to Neural CDEs with random vector fields which, depending on whether the weights are shared across layers, are either time-independent and Gaussian or behave like a matrix-valued Brownian motion.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

Serving Large Language Models (LLMs) is critical for AI-powered applications but demands substantial computational resources, particularly in memory bandwidth and computational throughput. Low-precision computation has emerged as a key technique to improve efficiency while reducing resource consumption. Existing approaches for generating low-precision kernels are limited to weight bit widths that are powers of two and suffer from suboptimal performance due to high-level GPU programming abstractions. These abstractions restrict critical optimizations, such as fine-grained register management and optimized memory access patterns, which are essential for efficient low-precision computations. In this paper, we introduce a virtual machine (VM) designed for General-Purpose GPU (GPGPU) computing, enabling support for low-precision data types with arbitrary bit widths while maintaining GPU programmability. The proposed VM features a thread-block-level programming model, a hierarchical memory space, a novel algebraic layout system, and extensive support for diverse low-precision data types. VM programs are compiled into highly efficient GPU programs with automatic vectorization and instruction selection. Extensive experiments demonstrate that our VM efficiently supports a full spectrum of low-precision data types, and outperforms state-of-the-art low-precision kernels on their supported types. Compared to existing compilers like Triton and Ladder, as well as hand-optimized kernels such as QuantLLM and Marlin, our VM achieves performance improvements of 1.75x, 2.61x, 1.29x and 1.03x, respectively.

High-quality kernel is critical for scalable AI systems, and enabling LLMs to generate such code would advance AI development. However, training LLMs for this task requires sufficient data, a robust environment, and the process is often vulnerable to reward hacking and lazy optimization. In these cases, models may hack training rewards and prioritize trivial correctness over meaningful speedup. In this paper, we systematically study reinforcement learning (RL) for kernel generation. We first design KernelGYM, a robust distributed GPU environment that supports reward hacking check, data collection from multi-turn interactions and long-term RL training. Building on KernelGYM, we investigate effective multi-turn RL methods and identify a biased policy gradient issue caused by self-inclusion in GRPO. To solve this, we propose Turn-level Reinforce-Leave-One-Out (TRLOO) to provide unbiased advantage estimation for multi-turn RL. To alleviate lazy optimization, we incorporate mismatch correction for training stability and introduce Profiling-based Rewards (PR) and Profiling-based Rejection Sampling (PRS) to overcome the issue. The trained model, Dr.Kernel-14B, reaches performance competitive with Claude-4.5-Sonnet in Kernelbench. Finally, we study sequential test-time scaling for Dr.Kernel-14B. On the KernelBench Level-2 subset, 31.6% of the generated kernels achieve at least a 1.2x speedup over the Torch reference, surpassing Claude-4.5-Sonnet (26.7%) and GPT-5 (28.6%). When selecting the best candidate across all turns, this 1.2x speedup rate further increases to 47.8%. All resources, including environment, training code, models, and dataset, are included in https://www.github.com/hkust-nlp/KernelGYM.

Unlabeled data is a key component of modern machine learning. In general, the role of unlabeled data is to impose a form of smoothness, usually from the similarity information encoded in a base kernel, such as the epsilon-neighbor kernel or the adjacency matrix of a graph. This work revisits the classical idea of spectrally transformed kernel regression (STKR), and provides a new class of general and scalable STKR estimators able to leverage unlabeled data. Intuitively, via spectral transformation, STKR exploits the data distribution for which unlabeled data can provide additional information. First, we show that STKR is a principled and general approach, by characterizing a universal type of "target smoothness", and proving that any sufficiently smooth function can be learned by STKR. Second, we provide scalable STKR implementations for the inductive setting and a general transformation function, while prior work is mostly limited to the transductive setting. Third, we derive statistical guarantees for two scenarios: STKR with a known polynomial transformation, and STKR with kernel PCA when the transformation is unknown. Overall, we believe that this work helps deepen our understanding of how to work with unlabeled data, and its generality makes it easier to inspire new methods.

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM kernels has been the pressure placed on DRAM memory. One approach to tackle this problem is to use an inner product method for the SpGEMM kernel implementation. While the inner product produces fewer intermediate results, it can end up saturating the memory bandwidth, given the high number of redundant fetches of the input matrix elements. Using an outer product-based SpGEMM kernel can reduce redundant fetches, but at the cost of increased overhead due to extra computation and memory accesses for producing/managing partial products. In this thesis, we introduce a novel SpGEMM kernel implementation based on the row-wise product approach. We leverage atomic instructions to merge intermediate partial products as they are generated. The use of atomic instructions eliminates the need to create partial product matrices. To evaluate our row-wise product approach, we map an optimized SpGEMM kernel to a custom accelerator designed to accelerate graph-based applications. The targeted accelerator is an experimental system named PIUMA, being developed by Intel. PIUMA provides several attractive features, including fast context switching, user-configurable caches, globally addressable memory, non-coherent caches, and asynchronous pipelines. We tailor our SpGEMM kernel to exploit many of the features of the PIUMA fabric. This thesis compares our SpGEMM implementation against prior solutions, all mapped to the PIUMA framework. We briefly describe some of the PIUMA architecture features and then delve into the details of our optimized SpGEMM kernel. Our SpGEMM kernel can achieve 9.4x speedup as compared to competing approaches.

The self-attention mechanism utilizes large implicit weight matrices, programmed through dot product-based activations with very few trainable parameters, to enable long sequence modeling. In this paper, we investigate the possibility of discarding residual learning by employing large implicit kernels to achieve full context interaction at each layer of the network. To accomplish it, we introduce coordinate-based implicit MLPs as a slow network to generate hyper-kernels for another fast convolutional network. To get context-varying weights for fast dynamic encoding, we propose a HyperZ{cdotZ{cdot}W} operator that connects hyper-kernels (W) and hidden activations (Z) through simple elementwise multiplication, followed by convolution of Z using the context-dependent W. Based on this design, we present a novel Terminator architecture that integrates hyper-kernels of different sizes to produce multi-branch hidden representations for enhancing the feature extraction capability of each layer. Additionally, a bottleneck layer is employed to compress the concatenated channels, allowing only valuable information to propagate to the subsequent layers. Notably, our model incorporates several innovative components and exhibits excellent properties, such as introducing local feedback error for updating the slow network, stable zero-mean features, faster training convergence, and fewer model parameters. Extensive experimental results on pixel-level 1D and 2D image classification benchmarks demonstrate the superior performance of our architecture.

The computing demand of AI is growing at an unprecedented rate, but energy supply is not keeping pace. As a result, energy has become an expensive, contended resource that requires explicit management and optimization. Although recent works have made significant progress in large model training optimization, they focus only on a single aspect of energy consumption: dynamic or static energy. We find that fine-grained kernel scheduling and frequency scaling jointly and interdependently impact both dynamic and static energy consumption. Based on this finding, we design Kareus, a training system that pushes the time--energy tradeoff frontier by optimizing both aspects. Kareus decomposes the intractable joint optimization problem into local, partition-based subproblems. It then uses a multi-pass multi-objective optimization algorithm to find execution schedules that push the time--energy tradeoff frontier. Compared to the state of the art, Kareus reduces training energy by up to 28.3% at the same training time, or reduces training time by up to 27.5% at the same energy consumption.

We here propose a machine learning approach for monitoring particle detectors in real-time. The goal is to assess the compatibility of incoming experimental data with a reference dataset, characterising the data behaviour under normal circumstances, via a likelihood-ratio hypothesis test. The model is based on a modern implementation of kernel methods, nonparametric algorithms that can learn any continuous function given enough data. The resulting approach is efficient and agnostic to the type of anomaly that may be present in the data. Our study demonstrates the effectiveness of this strategy on multivariate data from drift tube chamber muon detectors.

Mixture-of-Experts (MoE) architectures power the majority of frontier large language models, but their inference is bottlenecked by irregular memory access patterns and expert routing overhead. Existing optimized MoE kernels (Megablocks, Tutel, FasterMoE) are implemented in CUDA and locked to NVIDIA hardware. We present TritonMoE, a fused MoE dispatch kernel written entirely in OpenAI Triton that performs the complete forward pass -- router scoring, token permutation, expert GEMMs, and weighted output combination -- using only portable Triton primitives. Our key optimization is a fused gate+up GEMM kernel that computes both SwiGLU projections from shared L2-cached input tiles with in-register SiLU activation, eliminating 35% of global memory traffic. On an NVIDIA A100, TritonMoE achieves 89-131% of the throughput of the CUDA-optimized Megablocks at inference batch sizes (<= 512 tokens) across Mixtral-8x7B, DeepSeek-V3, and Qwen2-MoE configurations. All 162 correctness tests pass on both NVIDIA A100 and AMD MI300X with zero code changes, validating cross-platform portability. We additionally characterize sensitivity to routing imbalance under Zipfian-skewed expert assignments and identify the regime -- 64+ experts under extreme skew -- where our fixed-tile scheduling underperforms Megablocks' block-sparse layout, motivating dynamic block-to-expert assignment as future work. Code is available at https://github.com/bassrehab/triton-kernels.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.

Integral reinforcement learning (IntRL) demands the precise computation of the utility function's integral at its policy evaluation (PEV) stage. This is achieved through quadrature rules, which are weighted sums of utility functions evaluated from state samples obtained in discrete time. Our research reveals a critical yet underexplored phenomenon: the choice of the computational method -- in this case, the quadrature rule -- can significantly impact control performance. This impact is traced back to the fact that computational errors introduced in the PEV stage can affect the policy iteration's convergence behavior, which in turn affects the learned controller. To elucidate how computation impacts control, we draw a parallel between IntRL's policy iteration and Newton's method applied to the Hamilton-Jacobi-Bellman equation. In this light, computational error in PEV manifests as an extra error term in each iteration of Newton's method, with its upper bound proportional to the computational error. Further, we demonstrate that when the utility function resides in a reproducing kernel Hilbert space (RKHS), the optimal quadrature is achievable by employing Bayesian quadrature with the RKHS-inducing kernel function. We prove that the local convergence rates for IntRL using the trapezoidal rule and Bayesian quadrature with a Mat\'ern kernel to be O(N^{-2}) and O(N^{-b}), where N is the number of evenly-spaced samples and b is the Mat\'ern kernel's smoothness parameter. These theoretical findings are finally validated by two canonical control tasks.

Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast ell_2 gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.

State space models (SSMs) have high performance on long sequence modeling but require sophisticated initialization techniques and specialized implementations for high quality and runtime performance. We study whether a simple alternative can match SSMs in performance and efficiency: directly learning long convolutions over the sequence. We find that a key requirement to achieving high performance is keeping the convolution kernels smooth. We find that simple interventions--such as squashing the kernel weights--result in smooth kernels and recover SSM performance on a range of tasks including the long range arena, image classification, language modeling, and brain data modeling. Next, we develop FlashButterfly, an IO-aware algorithm to improve the runtime performance of long convolutions. FlashButterfly appeals to classic Butterfly decompositions of the convolution to reduce GPU memory IO and increase FLOP utilization. FlashButterfly speeds up convolutions by 2.2times, and allows us to train on Path256, a challenging task with sequence length 64K, where we set state-of-the-art by 29.1 points while training 7.2times faster than prior work. Lastly, we introduce an extension to FlashButterfly that learns the coefficients of the Butterfly decomposition, increasing expressivity without increasing runtime. Using this extension, we outperform a Transformer on WikiText103 by 0.2 PPL with 30% fewer parameters.

GPU kernels are the workhorse of modern deep learning, and optimizing them (via evolutionary search or coding agents) usually requires repeated measurement on target hardware. While these measurements provide the ground-truth signal necessary for kernel search, they are costly, because each evaluation of a kernel requires compilation and repeated execution on a GPU. As improvements in LLM inference reduce the cost of writing novel kernels and LLM-driven searches scale to large search budgets, on-device evaluation becomes a bottleneck. To address this, we study how LLMs can serve as selective GPU surrogates for kernel evaluation, by forecasting the performance of proposed kernels. A useful surrogate should be accurate, and it should be selective, by knowing when it could be wrong, and deferring to the GPU. To evaluate surrogates, we measure whether their forecasts are accurate, calibrated, and practically useful for recovering fast kernels under limited GPU-measurement budgets. Next, we study whether reinforcement learning can improve forecast accuracy and confidence calibration. Our experiments demonstrate that LLMs can accurately forecast relative kernel performance, that their utility can be improved through reinforcement learning. Used inside a kernel search, the surrogate lets the search consider several times as many candidates under the same GPU evaluation budget, and that leads to finding faster kernels than an equal-budget baseline. These results suggest that LLMs can play a broader role in kernel optimization, by acting as virtual models of a GPU rather than solely as kernel generators for search.

The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack of a reliable bandwidth selector; practitioners currently rely on iterative optimization methods that are computationally expensive and prone to instability. We derive the ``Beta Reference Rule,'' a fast, closed-form bandwidth selector based on the unweighted Asymptotic Mean Integrated Squared Error (AMISE) of a beta reference distribution. To address boundary integrability issues, we introduce a principled heuristic for U-shaped and J-shaped distributions. By employing a method-of-moments approximation, we reduce the bandwidth selection complexity from iterative optimization to O(1). Extensive Monte Carlo simulations demonstrate that our rule matches the accuracy of numerical optimization while delivering a speedup of over 35,000 times. Real-world validation on socioeconomic data shows that it avoids the ``vanishing boundary'' and ``shoulder'' artifacts common to Gaussian-based methods. We provide a comprehensive, open-source Python package to facilitate the immediate adoption of the Beta kernel as a drop-in replacement for standard density estimation tools.

To meet the ever-increasing demand for computational efficiency, Neural Processing Units (NPUs) have become critical in modern AI infrastructure. However, unlocking their full potential requires developing high-performance compute kernels using vendor-specific Domain-Specific Languages (DSLs), a task that demands deep hardware expertise and is labor-intensive. While Large Language Models (LLMs) have shown promise in general code generation, they struggle with the strict constraints and scarcity of training data in the NPU domain. Our preliminary study reveals that state-of-the-art general-purpose LLMs fail to generate functional complex kernels for Ascend NPUs, yielding a near-zero success rate. To address these challenges, we propose AscendKernelGen, a generation-evaluation integrated framework for NPU kernel development. We introduce Ascend-CoT, a high-quality dataset incorporating chain-of-thought reasoning derived from real-world kernel implementations, and KernelGen-LM, a domain-adaptive model trained via supervised fine-tuning and reinforcement learning with execution feedback. Furthermore, we design NPUKernelBench, a comprehensive benchmark for assessing compilation, correctness, and performance across varying complexity levels. Experimental results demonstrate that our approach significantly bridges the gap between general LLMs and hardware-specific coding. Specifically, the compilation success rate on complex Level-2 kernels improves from 0% to 95.5% (Pass@10), while functional correctness achieves 64.3% compared to the baseline's complete failure. These results highlight the critical role of domain-specific reasoning and rigorous evaluation in automating accelerator-aware code generation.

GPU kernel optimization has long been a central challenge at the intersection of high-performance computing and machine learning. Efficient kernels are crucial for accelerating large language model (LLM) training and serving, yet attaining high performance typically requires extensive manual tuning. Compiler-based systems reduce some of this burden, but still demand substantial manual design and engineering effort. Recently, researchers have explored using LLMs for GPU kernel generation, though prior work has largely focused on translating high-level PyTorch modules into CUDA code. In this work, we introduce Astra, the first LLM-based multi-agent system for GPU kernel optimization. Unlike previous approaches, Astra starts from existing CUDA implementations extracted from SGLang, a widely deployed framework for serving LLMs, rather than treating PyTorch modules as the specification. Within Astra, specialized LLM agents collaborate through iterative code generation, testing, profiling, and planning to produce kernels that are both correct and high-performance. On kernels from SGLang, Astra achieves an average speedup of 1.32x using zero-shot prompting with OpenAI o4-mini. A detailed case study further demonstrates that LLMs can autonomously apply loop transformations, optimize memory access patterns, exploit CUDA intrinsics, and leverage fast math operations to yield substantial performance gains. Our work highlights multi-agent LLM systems as a promising new paradigm for GPU kernel optimization. Our code is publicly available at https://github.com/Anjiang-Wei/Astra.

Although much research has been done on proposing new models or loss functions to improve the generalisation of artificial neural networks (ANNs), less attention has been directed to the impact of the training data on generalisation. In this work, we start from approximating the interaction between samples, i.e. how learning one sample would modify the model's prediction on other samples. Through analysing the terms involved in weight updates in supervised learning, we find that labels influence the interaction between samples. Therefore, we propose the labelled pseudo Neural Tangent Kernel (lpNTK) which takes label information into consideration when measuring the interactions between samples. We first prove that lpNTK asymptotically converges to the empirical neural tangent kernel in terms of the Frobenius norm under certain assumptions. Secondly, we illustrate how lpNTK helps to understand learning phenomena identified in previous work, specifically the learning difficulty of samples and forgetting events during learning. Moreover, we also show that using lpNTK to identify and remove poisoning training samples does not hurt the generalisation performance of ANNs.

In Neural Architecture Search (NAS), reducing the cost of architecture evaluation remains one of the most crucial challenges. Among a plethora of efforts to bypass training of each candidate architecture to convergence for evaluation, the Neural Tangent Kernel (NTK) is emerging as a promising theoretical framework that can be utilized to estimate the performance of a neural architecture at initialization. In this work, we revisit several at-initialization metrics that can be derived from the NTK and reveal their key shortcomings. Then, through the empirical analysis of the time evolution of NTK, we deduce that modern neural architectures exhibit highly non-linear characteristics, making the NTK-based metrics incapable of reliably estimating the performance of an architecture without some amount of training. To take such non-linear characteristics into account, we introduce Label-Gradient Alignment (LGA), a novel NTK-based metric whose inherent formulation allows it to capture the large amount of non-linear advantage present in modern neural architectures. With minimal amount of training, LGA obtains a meaningful level of rank correlation with the post-training test accuracy of an architecture. Lastly, we demonstrate that LGA, complemented with few epochs of training, successfully guides existing search algorithms to achieve competitive search performances with significantly less search cost. The code is available at: https://github.com/nutellamok/DemystifyingNTK.

In standard Convolutional Neural Networks (CNNs), the receptive fields of artificial neurons in each layer are designed to share the same size. It is well-known in the neuroscience community that the receptive field size of visual cortical neurons are modulated by the stimulus, which has been rarely considered in constructing CNNs. We propose a dynamic selection mechanism in CNNs that allows each neuron to adaptively adjust its receptive field size based on multiple scales of input information. A building block called Selective Kernel (SK) unit is designed, in which multiple branches with different kernel sizes are fused using softmax attention that is guided by the information in these branches. Different attentions on these branches yield different sizes of the effective receptive fields of neurons in the fusion layer. Multiple SK units are stacked to a deep network termed Selective Kernel Networks (SKNets). On the ImageNet and CIFAR benchmarks, we empirically show that SKNet outperforms the existing state-of-the-art architectures with lower model complexity. Detailed analyses show that the neurons in SKNet can capture target objects with different scales, which verifies the capability of neurons for adaptively adjusting their receptive field sizes according to the input. The code and models are available at https://github.com/implus/SKNet.

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact representation, as data is only stored where details exist. Convolution kernels and data are Gaussian mixtures with unconstrained weights, positions, and covariance matrices. Similar to discrete convolutional networks, each convolution step produces several feature channels, represented by independent Gaussian mixtures. Since traditional transfer functions like ReLUs do not produce Gaussian mixtures, we propose using a fitting of these functions instead. This fitting step also acts as a pooling layer if the number of Gaussian components is reduced appropriately. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.