Daily Papers

Large Language Models (LLMs) have become the central paradigm in artificial intelligence, yet the core computational primitive of attention has remained structurally unchanged. Local Linear Attention (LLA) is an attention mechanism derived from nonparametric statistics in the test-time regression framework. In contrast to prior research on efficient attention variants, LLA upgrades the local constant estimate in softmax attention to a local linear estimate, yielding provably superior bias-variance tradeoffs for associative memory. However, LLA has not been scaled in LLM pretraining due to computational and numerical stability concerns. We introduce Parallax, a parameterized Local Linear Attention that is scalable for LLMs. Parallax eliminates the numerical solver in LLA and learns an extra query-like projector that probes the KV covariance. We place Parallax within a family of attention mechanisms connected by the bandwidth, the probe construction and the affine structure. We propose a hardware-aware algorithm that increases the arithmetic intensity over FlashAttention, shifting attention into a more compute bound regime. Our prototype decode kernel matches or outperforms FlashAttention 2/3 across diverse batch sizes and context lengths. We pretrain Parallax at 0.6B and 1.7B scales and find consistent perplexity improvements throughout pretraining with gains that transfer to downstream benchmarks. The advantage persists under both parameter-matched and compute-matched controls, demonstrating a Pareto improvement. We perform careful pretraining ablations and identify a novel phenomenon whereby Muon unlocks the capacity of Parallax. To our knowledge, this is the first empirical demonstration of strong architecture-optimizer codesign for attention mechanisms in the architecture research literature.

The rapid scaling of Protein Language Models (PLMs) has unlocked unprecedented accuracy in protein structure prediction and design, but the quadratic memory growth of the Key-Value (KV) cache during inference remains a prohibitive barrier for single-GPU deployment and high-throughput generation. While 8-bit quantization is now standard, 3-bit quantization remains elusive due to severe numerical outliers in activations. This paper presents TurboESM, an adaptation of Google's TurboQuant to the PLM domain. We solve the fundamental incompatibility between Rotary Position Embeddings (RoPE) and orthogonal transformations by deriving a RoPE-first rotation pipeline. We introduce a head-wise SVD calibration method tailored to the amino acid activation manifold, a dual look-up table (LUT) strategy for asymmetric K/V distributions, and a 1-bit Quantized Johnson-Lindenstrauss (QJL) residual correction. All experiments are conducted on ESM-2 650M, where our implementation achieves a 7.1x memory reduction (330 MB to 47 MB) while maintaining cosine similarity > 0.96 in autoregressive decoding across diverse protein families, including short peptides, transmembrane helices, enzyme active site fragments, and intrinsically disordered regions. We further implement a Triton-based fused decode attention kernel that eliminates intermediate dequantization memory allocations, achieving a 1.96x speedup over the PyTorch two-step path for the KV fetch operation alone; however, TurboESM incurs a prefill overhead of 21-27 ms relative to the original model due to KV quantization and packing, making it most suitable for memory-bound scenarios rather than latency-critical short-sequence workloads. Analysis reveals that PLMs exhibit sharper outlier profiles than large language models (LLMs) due to amino acid vocabulary sparsity, and our method effectively addresses these distributions.

Sampling from a categorical distribution is mathematically simple, but in large-vocabulary decoding, it often triggers extra memory traffic and extra kernels after the LM head. We present FlashSampling, an exact sampling primitive that fuses sampling into the LM-head matmul and never materializes the logits tensor in HBM. The method is simple: compute logits tile-by-tile on chip, add Gumbel noise, keep only one maximizer per row and per vocabulary tile, and finish with a small reduction over tiles. The fused tiled kernel is exact because argmax decomposes over a partition; grouped variants for online and tensor-parallel settings are exact by hierarchical factorization of the categorical distribution. Across H100, H200, B200, and B300 GPUs, FlashSampling speeds up kernel-level decode workloads, and in end-to-end vLLM experiments, it reduces time per output token by up to 19% on the models we test. These results show that exact sampling, with no approximation, can be integrated into the matmul itself, turning a bandwidth-bound postprocessing step into a lightweight epilogue. Project Page: https://github.com/FlashSampling/FlashSampling.

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.

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.

It is well-known that if a network aims to learn how to deblur, it should understand the blur process. Blurring is naturally caused by the convolution of the sharp image with the blur kernel. Thus, allowing the network to learn the blur process in the kernel-level can significantly improve the image deblurring performance. But, current deep networks are still at the pixel-level learning stage, either performing end-to-end pixel-level restoration or stage-wise pseudo kernel-level restoration, failing to enable the deblur model to understand the essence of the blur. To this end, we propose Fourier Kernel Estimator (FKE), which considers the activation operation in Fourier space and converts the convolution problem in the spatial domain to a multiplication problem in Fourier space. Our FKE, jointly optimized with the deblur model, enables the network to learn the kernel-level blur process with low complexity and without any additional supervision. Furthermore, we change the convolution object of the kernel from ``image" to network extracted ``feature", whose rich semantic and structural information is more suitable to blur process learning. With the convolution of the feature and the estimated kernel, our model can learn the essence of blur in kernel-level. To further improve the efficiency of feature extraction, we design a decoupled multi-scale architecture with multiple hierarchical sub-unets with a reversible strategy, which allows better multi-scale encoding and decoding in low training memory. Extensive experiments indicate that our method achieves state-of-the-art motion deblurring results and show potential for handling other kernel-related problems. Analysis also shows our kernel estimator is able to learn physically meaningful kernels. The code will be available at https://github.com/DeepMed-Lab-ECNU/Single-Image-Deblur.

Activation sparsity can enable practical inference speedups in large language models (LLMs) by reducing the compute and memory-movement required for matrix multiplications during the forward pass. However, existing methods face limitations that inhibit widespread adoption. Some approaches are tailored towards older models with ReLU-based sparsity, while others require extensive continued pre-training on up to hundreds of billions of tokens. This paper describes TEAL, a simple training-free method that applies magnitude-based activation sparsity to hidden states throughout the entire model. TEAL achieves 40-50% model-wide sparsity with minimal performance degradation across Llama-2, Llama-3, and Mistral families, with sizes varying from 7B to 70B. We improve existing sparse kernels and demonstrate wall-clock decoding speed-ups of up to 1.53times and 1.8times at 40% and 50% model-wide sparsity. TEAL is compatible with weight quantization, enabling further efficiency gains.

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.

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with O(n^3) runtime and O(n^2) space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret O(n^{1+gamma}) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying O(kn^{1+gamma}) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is O(vol({S})log 1/epsilon) locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

We demonstrate that unstructured sparsity significantly improves KV cache compression for LLMs, enabling sparsity levels up to 70% without compromising accuracy or requiring fine-tuning. We conduct a systematic exploration of pruning strategies and find per-token magnitude-based pruning as highly effective for both Key and Value caches under unstructured sparsity, surpassing prior structured pruning schemes. The Key cache benefits from prominent outlier elements, while the Value cache surprisingly benefits from a simple magnitude-based pruning despite its uniform distribution. KV cache size is the major bottleneck in decode performance due to high memory overhead for large context lengths. To address this, we use a bitmap-based sparse format and a custom attention kernel capable of compressing and directly computing over compressed caches pruned to arbitrary sparsity patterns, significantly accelerating memory-bound operations in decode computations and thereby compensating for the overhead of runtime pruning and compression. Our custom attention kernel coupled with the bitmap-based format delivers substantial compression of KV cache upto 45% of dense inference and thereby enables longer context length and increased tokens/sec throughput of upto 2.23x compared to dense inference. Our pruning mechanism and sparse attention kernel is available at https://github.com/dhjoo98/mustafar.

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.

Self-attention dominates the computational and memory cost of long-context LLM inference across both prefill and decode phases. To address this challenge, we introduce Sketch&Walk Attention, a training-free sparse attention method that determines sparsity with lightweight sketches and deterministic walk. Sketch&Walk applies Hadamard sketching to get inexpensive approximations of attention scores, then aggregates these estimates across layers via a walk mechanism that captures attention influence beyond direct interactions between tokens. The accumulated walk scores are used to select top-k attention blocks, enabling dynamic sparsity with a single training-free algorithm that applies uniformly to both the prefill and decode phases, together with custom sparse attention kernels. Across a wide range of models and tasks, Sketch&Walk maintains near-lossless accuracy at 20% attention density and can slightly outperform dense attention in some settings, while achieving up to 6x inference speedup.

Decoding methods play an indispensable role in converting language models from next-token predictors into practical task solvers. Prior research on decoding methods, primarily focusing on task-specific models, may not extend to the current era of general-purpose large language models (LLMs). Moreover, the recent influx of decoding strategies has further complicated this landscape. This paper provides a comprehensive and multifaceted analysis of various decoding methods within the context of LLMs, evaluating their performance, robustness to hyperparameter changes, and decoding speeds across a wide range of tasks, models, and deployment environments. Our findings reveal that decoding method performance is notably task-dependent and influenced by factors such as alignment, model size, and quantization. Intriguingly, sensitivity analysis exposes that certain methods achieve superior performance at the cost of extensive hyperparameter tuning, highlighting the trade-off between attaining optimal results and the practicality of implementation in varying contexts.

State-space model releases are typically coupled to fused CUDA and Triton kernels, inheriting a hard dependency on NVIDIA hardware. We show that Mamba-2's state space duality algorithm -- diagonal state structure, chunkable recurrence, and einsum-dominated compute with static control flow -- maps cleanly onto what XLA's fusion and tiling passes actually optimise, making custom kernels optional rather than required. We implement the full inference path (prefill, cached autoregressive decoding) as shaped standard primitives under XLA, without hand-written kernels, and realise the architecture's theoretical O(1) state management as a compiled on-device cache requiring no host synchronisation during generation. The implementation runs unmodified on CPU, NVIDIA GPU, and Google Cloud TPU from a single JAX source. On TPU v6e across five model scales (130M--2.7B parameters), XLA-generated code reaches approximately 140 TFLOPS on single-stream prefill (15% MFU) and up to 64% bandwidth utilisation on decode. Greedy decoding matches the PyTorch/CUDA reference token-for-token across 64 steps, with hidden-state agreement within float32 rounding tolerance. The pattern transfers to any SSM recurrence satisfying the same structural conditions, on any platform with a mature XLA backend. The implementation is publicly available at https://github.com/CosmoNaught/mamba2-jax and merged into the Bonsai JAX model library.

Recent research on remote sensing object detection has largely focused on improving the representation of oriented bounding boxes but has overlooked the unique prior knowledge presented in remote sensing scenarios. Such prior knowledge can be useful because tiny remote sensing objects may be mistakenly detected without referencing a sufficiently long-range context, and the long-range context required by different types of objects can vary. In this paper, we take these priors into account and propose the Large Selective Kernel Network (LSKNet). LSKNet can dynamically adjust its large spatial receptive field to better model the ranging context of various objects in remote sensing scenarios. To the best of our knowledge, this is the first time that large and selective kernel mechanisms have been explored in the field of remote sensing object detection. Without bells and whistles, LSKNet sets new state-of-the-art scores on standard benchmarks, i.e., HRSC2016 (98.46\% mAP), DOTA-v1.0 (81.85\% mAP) and FAIR1M-v1.0 (47.87\% mAP). Based on a similar technique, we rank 2nd place in 2022 the Greater Bay Area International Algorithm Competition. Code is available at https://github.com/zcablii/Large-Selective-Kernel-Network.

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.

Large language models have demonstrated exceptional capability in natural language understanding and generation. However, their generation speed is limited by the inherently sequential nature of their decoding process, posing challenges for real-time applications. This paper introduces Lexical Unit Decoding (LUD), a novel decoding methodology implemented in a data-driven manner, accelerating the decoding process without sacrificing output quality. The core of our approach is the observation that a pre-trained language model can confidently predict multiple contiguous tokens, forming the basis for a lexical unit, in which these contiguous tokens could be decoded in parallel. Extensive experiments validate that our method substantially reduces decoding time while maintaining generation quality, i.e., 33\% speed up on natural language generation with no quality loss, and 30\% speed up on code generation with a negligible quality loss of 3\%. Distinctively, LUD requires no auxiliary models and does not require changes to existing architectures. It can also be integrated with other decoding acceleration methods, thus achieving an even more pronounced inference efficiency boost. We posit that the foundational principles of LUD could define a new decoding paradigm for future language models, enhancing their applicability for a broader spectrum of applications. All codes are be publicly available at https://github.com/tjunlp-lab/Lexical-Unit-Decoding-LUD-. Keywords: Parallel Decoding, Lexical Unit Decoding, Large Language Model

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).

Self-supervised monocular depth estimation has emerged as a promising approach since it does not rely on labeled training data. Most methods combine convolution and Transformer to model long-distance dependencies to estimate depth accurately. However, Transformer treats 2D image features as 1D sequences, and positional encoding somewhat mitigates the loss of spatial information between different feature blocks, tending to overlook channel features, which limit the performance of depth estimation. In this paper, we propose a self-supervised monocular depth estimation network to get finer details. Specifically, we propose a decoder based on large kernel attention, which can model long-distance dependencies without compromising the two-dimension structure of features while maintaining feature channel adaptivity. In addition, we introduce a up-sampling module to accurately recover the fine details in the depth map. Our method achieves competitive results on the KITTI dataset.

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.

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.

Post-Training Quantization (PTQ) is an effective technique for compressing Large Language Models (LLMs). While many studies focus on quantizing both weights and activations, it is still a challenge to maintain the accuracy of LLM after activating quantization. To investigate the primary cause, we extend the concept of kernel from linear algebra to quantization functions to define a new term, "quantization kernel", which refers to the set of elements in activations that are quantized to zero. Through quantitative analysis of the quantization kernel, we find that these elements are crucial for maintaining the accuracy of quantized LLMs. With the decrease of quantization kernel, the precision of quantized LLMs increases. If the quantization kernel proportion is kept below 19% for OPT models and below 1% for LLaMA models, the precision loss from quantizing activations to INT8 becomes negligible. Motivated by the goal of developing a quantization method with small quantization kernel, we propose CrossQuant: a simple yet effective method for quantizing activations. CrossQuant cross-quantizes elements using row and column-wise absolute maximum vectors, achieving a quantization kernel of approximately 16% for OPT models and less than 0.1% for LLaMA models. Experimental results on LLMs (LLaMA, OPT) ranging from 6.7B to 70B parameters demonstrate that CrossQuant improves or maintains perplexity and accuracy in language modeling, zero-shot, and few-shot tasks.

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.

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.

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.

Large language models (LLMs) enable long-context tasks but face efficiency challenges due to the growing key-value (KV) cache. We propose LeanK, a learning-based method that prunes unimportant key (K) cache channels by leveraging static channel sparsity. With a novel two-stage training process, LeanK learns channel-wise static mask that could satisfy specific sparsity ratio and hardware alignment requirement. LeanK reduces GPU memory and accelerates decoding without sacrificing accuracy. Experiments demonstrate up to 70% K cache and 16%-18% V cache memory reduction. Custom decoding kernel enables 1.3x speedup for attention computation. We also provide insights into model channels and attention heads during long-context inference by analyzing the learned importance distribution. Our code is available at https://aka.ms/LeanK.

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.

Top-k decoding is a widely used method for sampling from LLMs: at each token, only the largest k next-token-probabilities are kept, and the next token is sampled after re-normalizing them to sum to unity. Top-k and other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-k decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-k decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We consider Bregman decoders obtained by minimizing a separable Bregman divergence (for both the primal and dual cases) with a sparsity-inducing ell_0 regularization. Despite the combinatorial nature of the objective, we show how to optimize it efficiently for a large class of divergences. We show that the optimal decoding strategies are greedy, and further that the loss function is discretely convex in k, so that binary search provably and efficiently finds the optimal k. We show that top-k decoding arises as a special case for the KL divergence, and identify new decoding strategies that have distinct behaviors (e.g., non-linearly up-weighting larger probabilities after re-normalization).

To alleviate the computational burden of large language models (LLMs), architectures with activation sparsity, represented by mixture-of-experts (MoE), have attracted increasing attention. However, the non-differentiable and inflexible routing of vanilla MoE hurts model performance. Moreover, while each token activates only a few parameters, these sparsely-activated architectures exhibit low chunk-level sparsity, indicating that the union of multiple consecutive tokens activates a large ratio of parameters. Such a sparsity pattern is unfriendly for acceleration under low-resource conditions (e.g., end-side devices) and incompatible with mainstream acceleration techniques (e.g., speculative decoding). To address these challenges, we introduce a novel MoE architecture, BlockFFN, as well as its efficient training and deployment techniques. Specifically, we use a router integrating ReLU activation and RMSNorm for differentiable and flexible routing. Next, to promote both token-level sparsity (TLS) and chunk-level sparsity (CLS), CLS-aware training objectives are designed, making BlockFFN more acceleration-friendly. Finally, we implement efficient acceleration kernels, combining activation sparsity and speculative decoding for the first time. The experimental results demonstrate the superior performance of BlockFFN over other MoE baselines, achieving over 80% TLS and 70% 8-token CLS. Our kernels achieve up to 3.67times speedup on real end-side devices than dense models. All codes and checkpoints are available publicly (https://github.com/thunlp/BlockFFN).

Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a regularised problem over the probability simplex that trades off model score against structural preferences and constraints. This single template recovers greedy decoding, Softmax sampling, Top-K, Top-P, and Sparsemax-style sparsity as special cases, and explains their common structure through optimality conditions. More importantly, the framework makes it easy to invent new decoders without folklore. We demonstrate this by designing Best-of-K (BoK), a KL-anchored coverage objective aimed at multi-sample pipelines (self-consistency, reranking, verifier selection). BoK targets the probability of covering good alternatives within a fixed K-sample budget and improves empirical performance. We show that such samples can improve accuracy by, for example, +18.6% for Qwen2.5-Math-7B on MATH500 at high sampling temperatures.

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.

Long-context inference is increasingly constrained by the KV cache: resident memory grows with context length, and decoding becomes limited by repeated High Bandwidth Memory (HBM) streaming rather than arithmetic. Existing methods such as eviction, windowing, quantization, and offloading reduce footprint, but often leave the critical-path bottleneck only partially addressed, especially when compressed states must still be reconstructed into dense vectors during decoding. We present Spherical KV, a long-context inference method that treats KV allocation as a rate-distortion problem grounded in attention geometry for efficient decoding. The method is built on two ideas: (i) represent directional information cheaply in the decode hot loop, and (ii) allocate retention and precision according to estimated future utility. Its first component, Angle-Domain Attention (ADA), stores keys in a spherical parameterization consisting of a scalar radius and compact angle codes, and computes attention logits directly from these codes without reconstructing dense keys. This preserves a paged, block-local, fusion-friendly decode path and directly targets HBM traffic in realistic serving settings. Its second component, Rate-Distortion Retention (RDR), jointly chooses keep/drop decisions and precision tiers per token and head under a fixed budget, producing tier-homogeneous pages with lightweight metadata and coalesced reads. Together, ADA and RDR provide a deployment-oriented mechanism for reducing KV residency while preserving decode efficiency.

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.

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.

We consider the problem of contextual kernel bandits with stochastic contexts, where the underlying reward function belongs to a known Reproducing Kernel Hilbert Space (RKHS). We study this problem under the additional constraint of joint differential privacy, where the agents needs to ensure that the sequence of query points is differentially private with respect to both the sequence of contexts and rewards. We propose a novel algorithm that improves upon the state of the art and achieves an error rate of Oleft(frac{gamma_T{T}} + gamma_T{T varepsilon}right) after T queries for a large class of kernel families, where gamma_T represents the effective dimensionality of the kernel and varepsilon > 0 is the privacy parameter. Our results are based on a novel estimator for the reward function that simultaneously enjoys high utility along with a low-sensitivity to observed rewards and contexts, which is crucial to obtain an order optimal learning performance with improved dependence on the privacy parameter.

Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits generalization to unseen noise types and levels. Existing approaches attempt to address this with extensive training data and high computational resources but they still suffer from overfitting. To address these issues, we conduct image denoising by utilizing dynamically generated kernels via efficient operations. This approach helps prevent overfitting and improves resilience to unseen noise. Specifically, our method leverages a Feature Extraction Module for robust noise-invariant features, Global Statistics and Local Correlation Modules to capture comprehensive noise characteristics and structural correlations. The Kernel Prediction Module then employs these cues to produce pixel-wise varying kernels adapted to local structures, which are then applied iteratively for denoising. This ensures both efficiency and superior restoration quality. Despite being trained on single-level Gaussian noise, our compact model (~ 0.04 M) excels across diverse noise types and levels, demonstrating the promise of iterative dynamic filtering for practical image denoising.

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.

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

Fast, scalable decoding architectures that operate in a block-wise parallel fashion across space and time are essential for real-time fault-tolerant quantum computing. We introduce a scalable AI-based pre-decoder for the surface code that performs local, parallel error correction with low decoding runtimes, removing the majority of physical errors before passing residual syndromes to a downstream global decoder. This modular architecture is backend-agnostic and composes with arbitrary global decoding algorithms designed for surface codes, and our implementation is completely open source. Integrated with uncorrelated PyMatching, the pipeline achieves end-to-end decoding runtimes of order O(1 μs) per round at large code distances on NVIDIA GB300 GPUs while reducing logical error rates (LERs) relative to global decoding alone. In a block-wise parallel decoding scheme with access to multiple GPUs, the decoding runtime can be reduced to well below O(1 μs) per round. We observe further LER improvements by training a larger model, outperforming correlated PyMatching up to distance-13. We additionally introduce a noise-learning architecture that infers decoding weights directly from experimentally accessible syndrome statistics without requiring an explicit circuit-level noise model. We show that purely data-driven graph weight estimation can nearly match uncorrelated PyMatching and exceed correlated PyMatching in certain regimes, enabling highly-optimized decoding when hardware noise models are unknown or time-varying, as well as training pre-decoders with realistic noise models. Together, these results establish a practical, modular, and high-throughput decoding framework suitable for large-distance surface-code implementations.

The segmentation of cell nuclei in tissue images stained with the blood dye hematoxylin and eosin (H&E) is essential for various clinical applications and analyses. Due to the complex characteristics of cellular morphology, a large receptive field is considered crucial for generating high-quality segmentation. However, previous methods face challenges in achieving a balance between the receptive field and computational burden. To address this issue, we propose LKCell, a high-accuracy and efficient cell segmentation method. Its core insight lies in unleashing the potential of large convolution kernels to achieve computationally efficient large receptive fields. Specifically, (1) We transfer pre-trained large convolution kernel models to the medical domain for the first time, demonstrating their effectiveness in cell segmentation. (2) We analyze the redundancy of previous methods and design a new segmentation decoder based on large convolution kernels. It achieves higher performance while significantly reducing the number of parameters. We evaluate our method on the most challenging benchmark and achieve state-of-the-art results (0.5080 mPQ) in cell nuclei instance segmentation with only 21.6% FLOPs compared with the previous leading method. Our source code and models are available at https://github.com/hustvl/LKCell.

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.

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.

During the deployment of Large Language Models (LLMs), the autoregressive decoding phase on heterogeneous NPU platforms (e.g., Ascend 910B) faces severe memory-bound challenges. This study reveals the ``Model Scaling Paradox'' caused by the static deployment of single-sized models. It also points out the kernel synchronization overhead of fine-grained speculative decoding leviathan2023fast, chen2023speculative under NPU computational graph compilation, and the severe limitations of purely relying on micro-level acceleration algorithms like Prompt LookUp Decoding (PLD)

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.

Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To address this challenge, we propose a modification of the radial basis function neural network model by equipping its Gaussian kernel with a learnable precision matrix. We show that precious information is contained in the spectrum of the precision matrix that can be extracted once the training of the model is completed. In particular, the eigenvectors explain the directions of maximum sensitivity of the model revealing the active subspace and suggesting potential applications for supervised dimensionality reduction. At the same time, the eigenvectors highlight the relationship in terms of absolute variation between the input and the latent variables, thereby allowing us to extract a ranking of the input variables based on their importance to the prediction task enhancing the model interpretability. We conducted numerical experiments for regression, classification, and feature selection tasks, comparing our model against popular machine learning models, the state-of-the-art deep learning-based embedding feature selection techniques, and a transformer model for tabular data. Our results demonstrate that the proposed model does not only yield an attractive prediction performance compared to the competitors but also provides meaningful and interpretable results that potentially could assist the decision-making process in real-world applications. A PyTorch implementation of the model is available on GitHub at the following link. https://github.com/dannyzx/Gaussian-RBFNN

We present Upsample Anything, a lightweight test-time optimization (TTO) framework that restores low-resolution features to high-resolution, pixel-wise outputs without any training. Although Vision Foundation Models demonstrate strong generalization across diverse downstream tasks, their representations are typically downsampled by 14x/16x (e.g., ViT), which limits their direct use in pixel-level applications. Existing feature upsampling approaches depend on dataset-specific retraining or heavy implicit optimization, restricting scalability and generalization. Upsample Anything addresses these issues through a simple per-image optimization that learns an anisotropic Gaussian kernel combining spatial and range cues, effectively bridging Gaussian Splatting and Joint Bilateral Upsampling. The learned kernel acts as a universal, edge-aware operator that transfers seamlessly across architectures and modalities, enabling precise high-resolution reconstruction of features, depth, or probability maps. It runs in only approx0.419 s per 224x224 image and achieves state-of-the-art performance on semantic segmentation, depth estimation, and both depth and probability map upsampling. Project page: https://seominseok0429.github.io/Upsample-Anything/{https://seominseok0429.github.io/Upsample-Anything/}

Ever since neural models were adopted in data-to-text language generation, they have invariably been reliant on extrinsic components to improve their semantic accuracy, because the models normally do not exhibit the ability to generate text that reliably mentions all of the information provided in the input. In this paper, we propose a novel decoding method that extracts interpretable information from encoder-decoder models' cross-attention, and uses it to infer which attributes are mentioned in the generated text, which is subsequently used to rescore beam hypotheses. Using this decoding method with T5 and BART, we show on three datasets its ability to dramatically reduce semantic errors in the generated outputs, while maintaining their state-of-the-art quality.

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.

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.

Large Language Models (LLMs) have revolutionized natural language processing by understanding and generating human-like text. However, the increasing demand for more sophisticated LLMs presents significant computational challenges due to their scale and complexity. This paper introduces Hardware Accelerated Decoding (HADES), a novel approach to enhance the performance and energy efficiency of LLMs. We address the design of an LLM accelerator with hardware-level speculative decoding support, a concept not previously explored in existing literature. Our work demonstrates how speculative decoding can significantly improve the efficiency of LLM operations, paving the way for more advanced and practical applications of these models.

Large language models face significant computational and memory challenges when processing long contexts. During inference, efficient management of the key-value (KV) cache, which stores intermediate activations for autoregressive generation, is critical to reducing memory overhead and improving computational efficiency. Traditional token-level efficient KV caching methods overlook semantic information, treating tokens independently without considering their semantic relationships. Meanwhile, existing semantic-preserving KV cache management approaches often suffer from substantial memory usage and high time-to-first-token. To address these limitations, we propose SentenceKV, a novel sentence-level semantic KV caching approach designed to enhance inference efficiency while preserving semantic coherence. During prefilling, SentenceKV groups tokens based on sentence-level semantic similarity, compressing sentence representations into concise semantic vectors stored directly on the GPU, while individual KV pairs are offloaded to CPU. During decoding, SentenceKV generates tokens by selectively retrieving semantically relevant sentence-level KV entries, leveraging the semantic similarity between the prefilling-stage semantic vectors and decoding-stage queries. This ensures efficient and contextually accurate predictions, minimizing the loading of redundant or irrelevant data into GPU memory and significantly reducing memory overhead while maintaining stable inference latency, even for extremely long contexts. Extensive evaluations on benchmarks including PG-19, LongBench, and Needle-In-A-Haystack demonstrate that SentenceKV significantly outperforms state-of-the-art methods in both efficiency and memory usage, without compromising model accuracy.

Large-scale kernel ridge regression (KRR) is limited by the need to store a large kernel matrix K_t. To avoid storing the entire matrix K_t, Nystrom methods subsample a subset of columns of the kernel matrix, and efficiently find an approximate KRR solution on the reconstructed matrix. The chosen subsampling distribution in turn affects the statistical and computational tradeoffs. For KRR problems, recent works show that a sampling distribution proportional to the ridge leverage scores (RLSs) provides strong reconstruction guarantees for the approximation. While exact RLSs are as difficult to compute as a KRR solution, we may be able to approximate them well enough. In this paper, we study KRR problems in a sequential setting and introduce the INK-ESTIMATE algorithm, that incrementally computes the RLSs estimates. INK-ESTIMATE maintains a small sketch of K_t, that at each step is used to compute an intermediate estimate of the RLSs. First, our sketch update does not require access to previously seen columns, and therefore a single pass over the kernel matrix is sufficient. Second, the algorithm requires a fixed, small space budget to run dependent only on the effective dimension of the kernel matrix. Finally, our sketch provides strong approximation guarantees on the distance between the true kernel matrix and its approximation, and on the statistical risk of the approximate KRR solution at any time, because all our guarantees hold at any intermediate step.

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

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.

Weight-only quantization is widely used to mitigate the memory-bound nature of LLM inference. Codebook-based methods extend this trend by achieving strong accuracy in the extremely low-bit regime (e.g., 2-bit). However, current kernels rely on dequantization, which repeatedly fetches centroids and reconstructs weights, incurring substantial latency and cache pressure. We present CodeGEMM, a codebook-centric GEMM kernel that replaces dequantization with precomputed inner products between centroids and activations stored in a lightweight Psumbook. At inference, code indices directly gather these partial sums, eliminating per-element lookups and reducing the on-chip footprint. The kernel supports the systematic exploration of latency-memory-accuracy trade-offs under a unified implementation. On Llama-3 models, CodeGEMM delivers 1.83x (8B) and 8.93x (70B) speedups in the 2-bit configuration compared to state-of-the-art codebook-based quantization at comparable accuracy and further improves computing efficiency and memory subsystem utilization.

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.

While Key-Value (KV) cache succeeds in reducing redundant computations in auto-regressive models, it introduces significant memory overhead, limiting its practical deployment in long-sequence scenarios. Existing KV retrieval methods mitigate this by dynamically retaining only a subset of KV entries on the GPU. However, they still suffer from notable efficiency and accuracy bottlenecks due to per-token retrieval and coarse-grained page-level KV management, especially in long-output reasoning scenarios. With the emergence of large reasoning models, efficiently handling such scenarios has become increasingly important. To address this issue, we present two key observations: (1) critical KVs exhibit strong temporal locality during decoding, and (2) these KVs exhibit distinct distribution patterns across the input prompt and generated output. Building on these observations, we propose LouisKV, an efficient KV cache retrieval framework designed for various long-sequence scenarios. Specifically, LouisKV introduces a semantic-aware retrieval strategy leveraging temporal locality to trigger retrieval only at semantic boundaries, drastically reducing computation and data transfer overhead. LouisKV also designs a decoupled, fine-grained management scheme that tailors differentiated strategies for input and output sequences to create retrieval units that better match the model's attention patterns, enabling precise identification of critical KVs. Furthermore, to boost efficiency, LouisKV incorporates several kernel-level optimizations, including custom Triton and CUDA kernels to accelerate the KV clustering and retrieval. Evaluations show that LouisKV achieves up to 4.7times speedup over state-of-the-art KV retrieval methods while maintaining near-lossless accuracy across diverse long-sequence tasks, including long-input short-output, short-input long-output, and long-input long-output scenarios.

Blind image deconvolution (BID) is a classic yet challenging problem in the field of image processing. Recent advances in deep image prior (DIP) have motivated a series of DIP-based approaches, demonstrating remarkable success in BID. However, due to the high non-convexity of the inherent optimization process, these methods are notorious for their sensitivity to the initialized kernel. To alleviate this issue and further improve their performance, we propose a new framework for BID that better considers the prior modeling and the initialization for blur kernels, leveraging a deep generative model. The proposed approach pre-trains a generative adversarial network-based kernel generator that aptly characterizes the kernel priors and a kernel initializer that facilitates a well-informed initialization for the blur kernel through latent space encoding. With the pre-trained kernel generator and initializer, one can obtain a high-quality initialization of the blur kernel, and enable optimization within a compact latent kernel manifold. Such a framework results in an evident performance improvement over existing DIP-based BID methods. Extensive experiments on different datasets demonstrate the effectiveness of the proposed method.

Autoregressive decoding remains a primary bottleneck in large language model (LLM) serving, motivating speculative decoding methods that reduce expensive teacher-model invocations by verifying multiple candidate tokens per step. Tree-structured speculation further increases parallelism, but is often brittle when ported across heterogeneous backends and accelerator stacks, where attention masking, KV-cache layouts, and indexing semantics are not interchangeable. We present EAGLE-Pangu, a reproducible system that ports EAGLE-3-style tree speculative decoding to a Pangu teacher backend on Ascend NPUs. EAGLE-Pangu contributes (i) an explicit branch/commit cache manager built on the Cache API, (ii) accelerator-safe tree tensorization that removes undefined negative indices by construction and validates structural invariants, and (iii) a fused-kernel-compatible teacher verification path with a debuggable eager fallback. On 240 turns from MT-Bench and HumanEval-style prompts, EAGLE-Pangu improves end-to-end decoding throughput by 1.27x on average, up to 2.46x at p99, over teacher-only greedy decoding in the fused-kernel performance path. We also provide a fused-kernel-free reference path with structured traces and invariant checks to support reproducible debugging and ablation across execution modes and tree budgets.

While Mixture-of-Experts (MoE) scales model capacity without proportionally increasing computation, its massive total parameter footprint creates significant storage and memory-access bottlenecks, which hinder efficient end-side deployment that simultaneously requires high performance, low computational cost, and small storage overhead. To achieve these properties, we present DECO, a sparse MoE architecture designed to match the performance of dense Transformers under identical total parameter budgets and training tokens. DECO utilizes the differentiable and flexible ReLU-based routing enhanced by learnable expert-wise scaling, which adaptively balances the contributions of routed and shared experts. Furthermore, we introduce NormSiLU, an activation function that normalizes inputs prior to SiLU operators, producing a more stable trend of routed-expert activation ratio and a higher intrinsic sparsity level. We also identify an empirical advantage in using non-gated MLP experts with ReLU-based routing, indicating the possibility of MoE architecture simplification. Experiments demonstrate that DECO, activating only 20% of experts, matches dense performance and outperforms established MoE baselines. Our specialized acceleration kernel delivers a 3.00times speedup on real hardware compared with dense inference. Codes and checkpoints will be released.

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.

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

We introduce SeerAttention-R, a sparse attention framework specifically tailored for the long decoding of reasoning models. Extended from SeerAttention, SeerAttention-R retains the design of learning attention sparsity through a self-distilled gating mechanism, while removing query pooling to accommodate auto-regressive decoding. With a lightweight plug-in gating, SeerAttention-R is flexible and can be easily integrated into existing pretrained model without modifying the original parameters. We demonstrate that SeerAttention-R, trained on just 0.4B tokens, maintains near-lossless reasoning accuracy with 4K token budget in AIME benchmark under large sparse attention block sizes (64/128). Using TileLang, we develop a highly optimized sparse decoding kernel that achieves near-theoretical speedups of up to 9x over FlashAttention-3 on H100 GPU at 90% sparsity. Code is available at: https://github.com/microsoft/SeerAttention.

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.

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the classic k-means algorithm, leading to efficient algorithms that approximate k-means clusters using axis-aligned decision trees. However, interpretable variants of k-means have limited applicability in practice, where more flexible clustering methods are often needed to obtain useful partitions of the data. In this work, we investigate interpretable kernel clustering, and propose algorithms that construct decision trees to approximate the partitions induced by kernel k-means, a nonlinear extension of k-means. We further build on previous work on explainable k-means and demonstrate how a suitable choice of features allows preserving interpretability without sacrificing approximation guarantees on the interpretable model.

In recent years, many interpretability methods have been proposed to help interpret the internal states of Transformer-models, at different levels of precision and complexity. Here, to analyze encoder-decoder Transformers, we propose a simple, new method: DecoderLens. Inspired by the LogitLens (for decoder-only Transformers), this method involves allowing the decoder to cross-attend representations of intermediate encoder layers instead of using the final encoder output, as is normally done in encoder-decoder models. The method thus maps previously uninterpretable vector representations to human-interpretable sequences of words or symbols. We report results from the DecoderLens applied to models trained on question answering, logical reasoning, speech recognition and machine translation. The DecoderLens reveals several specific subtasks that are solved at low or intermediate layers, shedding new light on the information flow inside the encoder component of this important class of models.

Advances in hardware and language model architecture have spurred a revolution in natural language generation. However, autoregressive models compute probability distributions over next-token choices, and sampling from these distributions, known as decoding, has received significantly less attention than other design choices. Existing decoding strategies are largely based on heuristics, resulting in methods that are hard to apply or improve in a principled manner. We develop the theory of decoding strategies for language models by expressing popular decoding algorithms as equilibrium states in the language of ergodic theory and stating the functions they optimize. Using this, we analyze the effect of the local normalization step of top-k, nucleus, and temperature sampling, used to make probabilities sum to one. We argue that local normalization distortion is a fundamental defect of decoding strategies and quantify the size of this distortion and its effect on mathematical proxies for the quality and diversity of generated text. Contrary to the prevailing explanation, we argue that the major cause of the under-performance of top-k sampling relative to nucleus sampling is local normalization distortion. This yields conclusions for the future design of decoding algorithms and the detection of machine-generated text.

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.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs are nearly power-law distributed: their values are mostly clustered into a small number of codewords. This phenomenon encourages us to compact typical BNNs and obtain further close performance through learning non-repetitive kernels within a binary kernel subspace. Specifically, we regard the binarization process as kernel grouping in terms of a binary codebook, and our task lies in learning to select a smaller subset of codewords from the full codebook. We then leverage the Gumbel-Sinkhorn technique to approximate the codeword selection process, and develop the Permutation Straight-Through Estimator (PSTE) that is able to not only optimize the selection process end-to-end but also maintain the non-repetitive occupancy of selected codewords. Experiments verify that our method reduces both the model size and bit-wise computational costs, and achieves accuracy improvements compared with state-of-the-art BNNs under comparable budgets.

Diffusion-based large language models (dLLMs) are gaining attention for their inherent capacity for parallel decoding, offering a compelling alternative to autoregressive LLMs. Among various decoding strategies, blockwise semi-autoregressive (semi-AR) approaches are widely adopted due to their natural support for KV caching and their favorable accuracy-speed trade-off. However, this paper identifies two fundamental limitations in the conventional semi-AR decoding approach that applies a fixed block size: i) late decoding overhead, where the unmasking of high-confidence tokens outside the current block is unnecessarily delayed, and ii) premature decoding error, where low-confidence tokens inside the current block are committed too early, leading to incorrect tokens. This paper presents the first systematic investigation challenging the fixed block size assumption in semi-AR decoding. Through a statistical analysis of confidence dynamics during the denoising process, we identify a volatility band (VB) region during dLLM decoding, which encodes local semantic structure and can be used to guide adaptive block sizing. Leveraging these insights, we introduce AdaBlock-dLLM, a training-free, plug-and-play scheduler that adaptively aligns block boundaries with semantic steps by adjusting block size during runtime. Extensive experiments across diverse benchmarks show that AdaBlock-dLLM achieves up to 5.3% accuracy improvement under the same throughput budget. Beyond inference-time optimization, we hope our semantics-aware adaptive scheduling approach and confidence-based analysis will inspire future training strategies for dLLMs.

Large language models are expensive to deploy. We introduce Sparse Knowledge Distillation (SparseKD), a post-training method that compresses transformer models by combining structured SVD pruning with self-referential knowledge distillation. The key insight is simple: instead of using an external teacher, the model teaches itself by matching its own probability distribution from before compression. This self-referential setup enables surprisingly strong quality recovery after aggressive pruning. Our experiments reveal an unexpected finding: self-referential distillation alone, applied post-training under an identical objective and fixed calibration dataset, improves model quality by 39% relative to the original converged checkpoint. When combined with structured pruning, SparseKD achieves 15-65% parameter reduction with acceptable quality trade-offs. Kernel profiling shows that speedups arise entirely from reduced dense matrix multiplication in feed-forward layers while attention remains unchanged, making this approach complementary to attention optimizations. We validate across two model families (0.6B and 3.8B parameters) with multi-seed experiments confirming high reproducibility. SparseKD requires no external super-teacher, no architectural changes, and no custom inference kernels, making it immediately deployable with existing infrastructure.

We propose (G)I-DLE, a new approach to constrained decoding that leverages KL divergence minimization to preserve the intrinsic conditional probability distribution of autoregressive language models while excluding undesirable tokens. Unlike conventional methods that naively set banned tokens' logits to -infty, which can distort the conversion from raw logits to posterior probabilities and increase output variance, (G)I-DLE re-normalizes the allowed token probabilities to minimize such distortion. We validate our method on the K2-Eval dataset, specifically designed to assess Korean language fluency, logical reasoning, and cultural appropriateness. Experimental results on Qwen2.5 models (ranging from 1.5B to 14B) demonstrate that G-IDLE not only boosts mean evaluation scores but also substantially reduces the variance of output quality.

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.

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.

Speculative decoding emerges as a pivotal technique for enhancing the inference speed of Large Language Models (LLMs). Despite recent research aiming to improve prediction efficiency, multi-sample speculative decoding has been overlooked due to varying numbers of accepted tokens within a batch in the verification phase. Vanilla method adds padding tokens in order to ensure that the number of new tokens remains consistent across samples. However, this increases the computational and memory access overhead, thereby reducing the speedup ratio. We propose a novel method that can resolve the issue of inconsistent tokens accepted by different samples without necessitating an increase in memory or computing overhead. Furthermore, our proposed method can handle the situation where the prediction tokens of different samples are inconsistent without the need to add padding tokens. Sufficient experiments demonstrate the efficacy of our method. Our code is available at https://github.com/niyunsheng/EMS-SD.

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 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.

Early exiting has recently emerged as a promising technique for accelerating large language models (LLMs) by effectively reducing the hardware computation and memory access. In this paper, we present SpecEE, a fast LLM inference engine with speculative early exiting. (1) At the algorithm level, we propose the speculation-based lightweight predictor design by exploiting the probabilistic correlation between the speculative tokens and the correct results and high parallelism of GPUs. (2) At the system level, we point out that not all layers need a predictor and design the two-level heuristic predictor scheduling engine based on skewed distribution and contextual similarity. (3) At the mapping level, we point out that different decoding methods share the same essential characteristics, and propose the context-aware merged mapping for predictor with efficient GPU implementations to support speculative decoding, and form a framework for various existing orthogonal acceleration techniques (e.g., quantization and sparse activation) on cloud and personal computer (PC) scenarios, successfully pushing the Pareto frontier of accuracy and speedup. It is worth noting that SpecEE can be applied to any LLM by negligible training overhead in advance without affecting the model original parameters. Extensive experiments show that SpecEE achieves 2.25x and 2.43x speedup with Llama2-7B on cloud and PC scenarios respectively.

Diffusion language models (DLMs) generate text through iterative denoising, but inference requires full-sequence attention at every iteration, resulting in substantial redundant computation on masked tokens. Block-wise diffusion can reduce this cost, yet it typically relies on retraining and constrained update orders, limiting its direct applicability to pretrained DLMs. Our token-level analysis reveals pronounced structural locality in DLM inference. Decoding is driven by a small set of prefix-localized active tokens; the influence of distant undecoded context diminishes rapidly, and decoded tokens exhibit stage-wise temporal stability, enabling reuse of intermediate representations except for a brief post-decode transient. Motivated by these observations, we propose \placeholderThe source code is available at https://github.com/vhicrgit/Window-Diffusion., a window-based token pruning and caching method for inference. We maintain a local computation window that slides rightward as denoising progresses, and partition undecoded tokens into: (i) active tokens that are computed online, (ii) buffer tokens whose KV states are cached and periodically refreshed, and (iii) far-field tokens that are pruned outside the window. Computation is restricted to active and buffer tokens within the window, while far-field tokens are omitted at each stage. Experiments on LLaDA and Dream show that, under matched compute budgets, our method achieves up to 99times inference speedup while largely preserving generation performance.

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.

Despite the progress in machine translation quality estimation and evaluation in the last years, decoding in neural machine translation (NMT) is mostly oblivious to this and centers around finding the most probable translation according to the model (MAP decoding), approximated with beam search. In this paper, we bring together these two lines of research and propose quality-aware decoding for NMT, by leveraging recent breakthroughs in reference-free and reference-based MT evaluation through various inference methods like N-best reranking and minimum Bayes risk decoding. We perform an extensive comparison of various possible candidate generation and ranking methods across four datasets and two model classes and find that quality-aware decoding consistently outperforms MAP-based decoding according both to state-of-the-art automatic metrics (COMET and BLEURT) and to human assessments. Our code is available at https://github.com/deep-spin/qaware-decode.

Speculative Decoding (SD) has emerged as a widely used paradigm to accelerate the inference of large language models (LLMs) without compromising generation quality. It works by efficiently drafting multiple tokens using a compact model and then verifying them in parallel using the target LLM. Notably, Self-Speculative Decoding proposes skipping certain layers to construct the draft model, which eliminates the need for additional parameters or training. Despite its strengths, we observe in this work that drafting with layer skipping exhibits significant sensitivity to domain shifts, leading to a substantial drop in acceleration performance. To enhance the domain generalizability of this paradigm, we introduce KNN-SSD, an algorithm that leverages K-Nearest Neighbor (KNN) search to match different skipped layers with various domain inputs. We evaluated our algorithm in various models and multiple tasks, observing that its application leads to 1.3x-1.6x speedup in LLM inference.

Autoregressive decoding of large language models (LLMs) is memory bandwidth bounded, resulting in high latency and significant wastes of the parallel processing power of modern accelerators. Existing methods for accelerating LLM decoding often require a draft model (e.g., speculative decoding), which is nontrivial to obtain and unable to generalize. In this paper, we introduce Lookahead decoding, an exact, parallel decoding algorithm that accelerates LLM decoding without needing auxiliary models or data stores. It allows trading per-step log(FLOPs) to reduce the number of total decoding steps, is more parallelizable on single or multiple modern accelerators, and is compatible with concurrent memory-efficient attention (e.g., FlashAttention). Our implementation of Lookahead decoding can speed up autoregressive decoding by up to 1.8x on MT-bench and 4x with strong scaling on multiple GPUs in code completion tasks. Our code is avialable at https://github.com/hao-ai-lab/LookaheadDecoding

While most autoregressive LLMs are constrained to one-by-one decoding, diffusion LLMs (dLLMs) have attracted growing interest for their potential to dramatically accelerate inference through parallel decoding. Despite this promise, the conditional independence assumption in dLLMs causes parallel decoding to ignore token dependencies, inevitably degrading generation quality when these dependencies are strong. However, existing works largely overlook these inherent challenges, and evaluations on standard benchmarks (e.g., math and coding) are not sufficient to capture the quality degradation caused by parallel decoding. To address this gap, we first provide an information-theoretic analysis of parallel decoding. We then conduct case studies on analytically tractable synthetic list operations from both data distribution and decoding strategy perspectives, offering quantitative insights that highlight the fundamental limitations of parallel decoding. Building on these insights, we propose ParallelBench, the first benchmark specifically designed for dLLMs, featuring realistic tasks that are trivial for humans and autoregressive LLMs yet exceptionally challenging for dLLMs under parallel decoding. Using ParallelBench, we systematically analyze both dLLMs and autoregressive LLMs, revealing that: (i) dLLMs under parallel decoding can suffer dramatic quality degradation in real-world scenarios, and (ii) current parallel decoding strategies struggle to adapt their degree of parallelism based on task difficulty, thus failing to achieve meaningful speedup without compromising quality. Our findings underscore the pressing need for innovative decoding methods that can overcome the current speed-quality trade-off. We release our benchmark to help accelerate the development of truly efficient dLLMs.

In this work, we propose FastCoT, a model-agnostic framework based on parallel decoding without any further training of an auxiliary model or modification to the LLM itself. FastCoT uses a size-varying context window whose size changes with position to conduct parallel decoding and auto-regressive decoding simultaneously, thus fully utilizing GPU computation resources. In FastCoT, the parallel decoding part provides the LLM with a quick glance of the future composed of approximate tokens, which could lead to faster answers compared to regular autoregressive decoding used by causal transformers. We also provide an implementation of parallel decoding within LLM, which supports KV-cache generation and batch processing. Through extensive experiments, we demonstrate that FastCoT saves inference time by nearly 20% with only a negligible performance drop compared to the regular approach. Additionally, we show that the context window size exhibits considerable robustness for different tasks.

Inference from large autoregressive models like Transformers is slow - decoding K tokens takes K serial runs of the model. In this work we introduce speculative decoding - an algorithm to sample from autoregressive models faster without any changes to the outputs, by computing several tokens in parallel. At the heart of our approach lie the observations that (1) hard language-modeling tasks often include easier subtasks that can be approximated well by more efficient models, and (2) using speculative execution and a novel sampling method, we can make exact decoding from the large models faster, by running them in parallel on the outputs of the approximation models, potentially generating several tokens concurrently, and without changing the distribution. Our method can accelerate existing off-the-shelf models without retraining or architecture changes. We demonstrate it on T5-XXL and show a 2X-3X acceleration compared to the standard T5X implementation, with identical outputs.

Distributed representations of words encode lexical semantic information, but what type of information is encoded and how? Focusing on the skip-gram with negative-sampling method, we found that the squared norm of static word embedding encodes the information gain conveyed by the word; the information gain is defined by the Kullback-Leibler divergence of the co-occurrence distribution of the word to the unigram distribution. Our findings are explained by the theoretical framework of the exponential family of probability distributions and confirmed through precise experiments that remove spurious correlations arising from word frequency. This theory also extends to contextualized word embeddings in language models or any neural networks with the softmax output layer. We also demonstrate that both the KL divergence and the squared norm of embedding provide a useful metric of the informativeness of a word in tasks such as keyword extraction, proper-noun discrimination, and hypernym discrimination.

We present a novel method for reconstructing a 3D implicit surface from a large-scale, sparse, and noisy point cloud. Our approach builds upon the recently introduced Neural Kernel Fields (NKF) representation. It enjoys similar generalization capabilities to NKF, while simultaneously addressing its main limitations: (a) We can scale to large scenes through compactly supported kernel functions, which enable the use of memory-efficient sparse linear solvers. (b) We are robust to noise, through a gradient fitting solve. (c) We minimize training requirements, enabling us to learn from any dataset of dense oriented points, and even mix training data consisting of objects and scenes at different scales. Our method is capable of reconstructing millions of points in a few seconds, and handling very large scenes in an out-of-core fashion. We achieve state-of-the-art results on reconstruction benchmarks consisting of single objects, indoor scenes, and outdoor scenes.

Large language models rely on kv-caches to avoid redundant computation during autoregressive decoding, but as context length grows, reading and writing the cache can quickly saturate GPU memory bandwidth. Recent work has explored KV-cache compression, yet most approaches neglect the data-dependent nature of kv-caches and their variation across layers. We introduce KV-CoRE KV-cache Compressibility by Rank Evaluation), an SVD-based method for quantifying the data-dependent low-rank compressibility of kv-caches. KV-CoRE computes the optimal low-rank approximation under the Frobenius norm and, being gradient-free and incremental, enables efficient dataset-level, layer-wise evaluation. Using this method, we analyze multiple models and datasets spanning five English domains and sixteen languages, uncovering systematic patterns that link compressibility to model architecture, training data, and language coverage. As part of this analysis, we employ the Normalized Effective Rank as a metric of compressibility and show that it correlates strongly with performance degradation under compression. Our study establishes a principled evaluation framework and the first large-scale benchmark of kv-cache compressibility in LLMs, offering insights for dynamic, data-aware compression and data-centric model development.

Recent advances in vision transformers (ViTs) have demonstrated the advantage of global modeling capabilities, prompting widespread integration of large-kernel convolutions for enlarging the effective receptive field (ERF). However, the quadratic scaling of parameter count and computational complexity (FLOPs) with respect to kernel size poses significant efficiency and optimization challenges. This paper introduces RecConv, a recursive decomposition strategy that efficiently constructs multi-frequency representations using small-kernel convolutions. RecConv establishes a linear relationship between parameter growth and decomposing levels which determines the effective kernel size ktimes 2^ell for a base kernel k and ell levels of decomposition, while maintaining constant FLOPs regardless of the ERF expansion. Specifically, RecConv achieves a parameter expansion of only ell+2 times and a maximum FLOPs increase of 5/3 times, compared to the exponential growth (4^ell) of standard and depthwise convolutions. RecNeXt-M3 outperforms RepViT-M1.1 by 1.9 AP^{box} on COCO with similar FLOPs. This innovation provides a promising avenue towards designing efficient and compact networks across various modalities. Codes and models can be found at https://github.com/suous/RecNeXt.

Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing the prior of the kernel (or induced) error. However, how to design a suitable prior for the kernel (or induced) error remains challenging. Hand-crafted prior, incorporating domain knowledge, generally performs well but may lead to poor performance when kernel (or induced) error is complex. Data-driven prior, which excessively depends on the diversity and abundance of training data, is vulnerable to out-of-distribution blurs and images. To address this challenge, we suggest a dataset-free deep residual prior for the kernel induced error (termed as residual) expressed by a customized untrained deep neural network, which allows us to flexibly adapt to different blurs and images in real scenarios. By organically integrating the respective strengths of deep priors and hand-crafted priors, we propose an unsupervised semi-blind deblurring model which recovers the latent image from the blurry image and inaccurate blur kernel. To tackle the formulated model, an efficient alternating minimization algorithm is developed. Extensive experiments demonstrate the favorable performance of the proposed method as compared to data-driven and model-driven methods in terms of image quality and the robustness to the kernel error.

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.

This paper introduces an information-aware quantization framework that adaptively compresses the key-value (KV) cache in large language models (LLMs). Although prior work has underscored the distinct roles of key and value cache during inference, our systematic analysis -- examining singular value distributions, spectral norms, and Frobenius norms -- reveals, for the first time, that key matrices consistently exhibit higher norm values and are more sensitive to quantization than value matrices. Furthermore, our theoretical analysis shows that matrices with higher spectral norms amplify quantization errors more significantly. Motivated by these insights, we propose a mixed-precision quantization strategy, KV-AdaQuant, which allocates more bit-width for keys and fewer for values since key matrices have higher norm values. With the same total KV bit budget, this approach effectively mitigates error propagation across transformer layers while achieving significant memory savings. Our extensive experiments on multiple LLMs (1B--70B) demonstrate that our mixed-precision quantization scheme maintains high model accuracy even under aggressive compression. For instance, using 4-bit for Key and 2-bit for Value achieves an accuracy of 75.2%, whereas reversing the assignment (2-bit for Key and 4-bit for Value) yields only 54.7% accuracy. The code is available at https://tinyurl.com/kv-adaquant

Diffusion language models decode text by iteratively denoising masked token sequences, making the choice of which positions to decode a central inference-time decision. Most training-free decoding strategies use model confidence for position selection, assuming that high-confidence positions are ready to be decoded. In this work, we revisit this assumption by studying when confidence misleads fully non-autoregressive (fully non-AR) decoding. EOT tokens can receive high confidence and cause incomplete generation; inserting a suffix anchor can mitigate this issue but introduces local overconfidence near the anchor, causing anchor-adjacent tokens to be decoded too early. To address these issues, we propose Suffix-Anchored Confidence Modulation, a simple training-free method that inserts a short suffix anchor to encourage response completion and modulates confidence near the anchor according to decoding progress. This preserves the response-completion benefit of suffix anchoring while reducing premature decoding of anchor-adjacent tokens. Across text-only reasoning, vision-language reasoning, and code-generation benchmarks, our method consistently improves confidence-based fully non-AR decoding, outperforms explicit EOT suppression, and preserves the parallel decoding advantage of fully non-AR generation.

Speculative decoding is a relatively new decoding framework that leverages small and efficient draft models to reduce the latency of LLMs. In this study, we introduce GliDe and CaPE, two low-hassle modifications to vanilla speculative decoding to further improve the decoding speed of a frozen LLM. Specifically, GliDe is a modified draft model architecture that reuses the cached keys and values from the target LLM, while CaPE is a proposal expansion method that uses the draft model's confidence scores to help select additional candidate tokens for verification. Extensive experiments on different benchmarks demonstrate that our proposed GliDe draft model significantly reduces the expected decoding latency. Additional evaluation using walltime reveals that GliDe can accelerate Vicuna models up to 2.17x and further extend the improvement to 2.61x with CaPE. We will release our code, data, and the trained draft models.

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out, including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.

The auto-regressive decoding of Large Language Models (LLMs) results in significant overheads in their hardware performance. While recent research has investigated various speculative decoding techniques for multi-token generation, these efforts have primarily focused on improving processing speed such as throughput. Crucially, they often neglect other metrics essential for real-life deployments, such as memory consumption and training cost. To overcome these limitations, we propose a novel parallel prompt decoding that requires only 0.0002% trainable parameters, enabling efficient training on a single A100-40GB GPU in just 16 hours. Inspired by the human natural language generation process, PPD approximates outputs generated at future timesteps in parallel by using multiple prompt tokens. This approach partially recovers the missing conditional dependency information necessary for multi-token generation, resulting in up to a 28% higher acceptance rate for long-range predictions. Furthermore, we present a hardware-aware dynamic sparse tree technique that adaptively optimizes this decoding scheme to fully leverage the computational capacities on different GPUs. Through extensive experiments across LLMs ranging from MobileLlama to Vicuna-13B on a wide range of benchmarks, our approach demonstrates up to 2.49times speedup and maintains a minimal runtime memory overhead of just 0.0004%. More importantly, our parallel prompt decoding can serve as an orthogonal optimization for synergistic integration with existing speculative decoding, showing up to 1.22times further speed improvement. Our code is available at https://github.com/hmarkc/parallel-prompt-decoding.

Convolutional models have been widely used in multiple domains. However, most existing models only use local convolution, making the model unable to handle long-range dependency efficiently. Attention overcomes this problem by aggregating global information but also makes the computational complexity quadratic to the sequence length. Recently, Gu et al. [2021] proposed a model called S4 inspired by the state space model. S4 can be efficiently implemented as a global convolutional model whose kernel size equals the input sequence length. S4 can model much longer sequences than Transformers and achieve significant gains over SoTA on several long-range tasks. Despite its empirical success, S4 is involved. It requires sophisticated parameterization and initialization schemes. As a result, S4 is less intuitive and hard to use. Here we aim to demystify S4 and extract basic principles that contribute to the success of S4 as a global convolutional model. We focus on the structure of the convolution kernel and identify two critical but intuitive principles enjoyed by S4 that are sufficient to make up an effective global convolutional model: 1) The parameterization of the convolutional kernel needs to be efficient in the sense that the number of parameters should scale sub-linearly with sequence length. 2) The kernel needs to satisfy a decaying structure that the weights for convolving with closer neighbors are larger than the more distant ones. Based on the two principles, we propose a simple yet effective convolutional model called Structured Global Convolution (SGConv). SGConv exhibits strong empirical performance over several tasks: 1) With faster speed, SGConv surpasses S4 on Long Range Arena and Speech Command datasets. 2) When plugging SGConv into standard language and vision models, it shows the potential to improve both efficiency and performance.

Long-context decoding in LLMs is IO-bound: each token re-reads an ever-growing KV cache. Prior accelerations cut bytes via compression, which lowers fidelity, or selection/eviction, which restricts what remains accessible, and both can degrade delayed recall and long-form generation. We introduce MAC-Attention, a fidelity- and access-preserving alternative that accelerates decoding by reusing prior attention computations for semantically similar recent queries. It starts with a match stage that performs pre-RoPE L2 matching over a short local window; an amend stage rectifies the reused attention by recomputing a small band near the match boundary; and a complete stage fuses the rectified results with fresh attention computed on the KV tail through a numerically stable merge. On a match hit, the compute and bandwidth complexity is constant regardless of context length. The method is model-agnostic and composes with IO-aware kernels, paged-KV managers, and MQA/GQA. Across LongBench v2 (120K), RULER (120K), and LongGenBench (16K continuous generation), compared to the latest FlashInfer library, MAC-Attention reduces KV accesses by up to 99%, cuts token generation latency by over 60% at 128K, and achieves over 14.3x attention-phase speedups, up to 2.6x end-to-end, while maintaining full-attention quality. By reusing computation, MAC-Attention delivers long-context inference that is both fast and faithful. Code is available here: https://github.com/YJHMITWEB/MAC-Attention.git

Large language model (LLM) decoding involves generating a sequence of tokens based on a given context, where each token is predicted one at a time using the model's learned probabilities. The typical autoregressive decoding method requires a separate forward pass through the model for each token generated, which is computationally inefficient and poses challenges for deploying LLMs in latency-sensitive scenarios. The main limitations of current decoding methods stem from their inefficiencies and resource demands. Existing approaches either necessitate fine-tuning smaller models, which is resource-intensive, or rely on fixed retrieval schemes to construct drafts for the next tokens, which lack adaptability and fail to generalize across different models and contexts. To address these issues, we introduce a novel methodology called ADED, which accelerates LLM decoding without requiring fine-tuning. Our approach involves an adaptive draft-verification process that evolves over time to improve efficiency. We utilize a tri-gram matrix-based LLM representation to dynamically approximate the output distribution of the LLM, allowing the model to adjust to changing token probabilities during the decoding process. Additionally, we implement a draft construction mechanism that effectively balances exploration and exploitation, ensuring that the drafts generated are both diverse and close to the true output distribution of the LLM. The importance of this design lies in its ability to optimize the draft distribution adaptively, leading to faster and more accurate decoding. Through extensive experiments on various benchmark datasets and LLM architectures, we demonstrate that ADED significantly accelerates the decoding process while maintaining high accuracy, making it suitable for deployment in a wide range of practical applications.

Existing techniques for accelerating language model inference, such as speculative decoding, require training auxiliary speculator models and building and deploying complex inference pipelines. We consider a new approach for converting a pretrained autoregressive language model from a slow single next token prediction model into a fast standalone multi-token prediction model using a simple online distillation objective. The final model retains the exact same implementation as the pretrained initial checkpoint and is deployable without the addition of any auxiliary verifier or other specialized inference code. On GSM8K, our method produces models that can decode more than 3times faster on average at <5% drop in accuracy relative to single token decoding performance.

Autoregressive decoding limits the efficiency of transformers for Machine Translation (MT). The community proposed specific network architectures and learning-based methods to solve this issue, which are expensive and require changes to the MT model, trading inference speed at the cost of the translation quality. In this paper, we propose to address the problem from the point of view of decoding algorithms, as a less explored but rather compelling direction. We propose to reframe the standard greedy autoregressive decoding of MT with a parallel formulation leveraging Jacobi and Gauss-Seidel fixed-point iteration methods for fast inference. This formulation allows to speed up existing models without training or modifications while retaining translation quality. We present three parallel decoding algorithms and test them on different languages and models showing how the parallelization introduces a speedup up to 38% w.r.t. the standard autoregressive decoding and nearly 2x when scaling the method on parallel resources. Finally, we introduce a decoding dependency graph visualizer (DDGviz) that let us see how the model has learned the conditional dependence between tokens and inspect the decoding procedure.

Speculative decoding (SD) has become a popular technique to accelerate Large Language Model (LLM) inference, yet its real-world effectiveness remains unclear as prior evaluations rely on research prototypes and unrealistically small batch sizes. We present, to our knowledge, the first systematic study of SD on a production-grade and widely deployed inference engine (vLLM), covering multiple SD variants (n-gram, EAGLE/EAGLE-3, Draft-Model, Multi-Token Prediction) across diverse workloads, model scales, and batch sizes. We analyze key factors governing SD performance, and quantify a theoretical upper bound on SD speedup. Our results show that verification by the target model dominates the execution, while acceptance length varies markedly across output token positions, requests, and datasets. Comparing measured performance with theoretical bounds reveals substantial gaps between observed and theoretical upper bounds, and we leverage this observation to highlight new research opportunities that our study opens up in improving SD.

Speculative decoding has emerged as a powerful method to improve latency and throughput in hosting large language models. However, most existing implementations focus on generating a single sequence. Real-world generative AI applications often require multiple responses and how to perform speculative decoding in a batched setting while preserving its latency benefits poses non-trivial challenges. This paper describes a system of batched speculative decoding that sets a new state of the art in multi-sequence generation latency and that demonstrates superior GPU utilization as well as quality of generations within a time budget. For example, for a 7.8B-size model on a single A100 GPU and with a batch size of 8, each sequence is generated at an average speed of 5.8ms per token, the overall throughput being 1.1K tokens per second. These results represent state-of-the-art latency and a 2.15X speed-up over optimized regular decoding. Within a time budget that regular decoding does not finish, our system is able to generate sequences with HumanEval Pass@First of 43% and Pass@All of 61%, far exceeding what's feasible with single-sequence speculative decoding. Our peak GPU utilization during decoding reaches as high as 15.8%, more than 3X the highest of that of regular decoding and around 10X of single-sequence speculative decoding.

Model pruning is an effective approach for compressing large language models. However, this process often leads to significant degradation of model capabilities. While post-training techniques such as instruction tuning are commonly employed to recover model performance, existing methods often overlook the uneven deterioration of model capabilities and incur high computational costs. Moreover, some instruction data irrelevant to model capability recovery may introduce negative effects. To address these challenges, we propose the Post-training dAta Selection method for Efficient pruned large language model Recovery (PASER). PASER aims to identify instructions where model capabilities are most severely compromised within a certain recovery data budget. Our approach first applies manifold learning and spectral clustering to group recovery data in the semantic space, revealing capability-specific instruction sets. We then adaptively allocate the data budget to different clusters based on the degrees of model capability degradation. In each cluster, we prioritize data samples where model performance has declined dramatically. To mitigate potential negative transfer, we also detect and filter out conflicting or irrelevant recovery data. Extensive experiments demonstrate that PASER significantly outperforms conventional baselines, effectively recovering the general capabilities of pruned LLMs while utilizing merely 4\%-20\% of the original post-training data.

Autoregressive decoding in large language models (LLMs) requires O(n) sequential steps for n tokens, fundamentally limiting inference throughput. Recent diffusion-based LLMs (dLLMs) enable parallel token generation through iterative denoising. However, current parallel decoding strategies rely on fixed, input-agnostic heuristics (e.g., confidence thresholds), which fail to adapt to input-specific characteristics, resulting in suboptimal speed-quality trade-offs across diverse NLP tasks. In this work, we explore a more flexible and dynamic approach to parallel decoding. We propose Learning to Parallel Decode (Learn2PD), a framework that trains a lightweight and adaptive filter model to predict, for each token position, whether the current prediction matches the final output. This learned filter approximates an oracle parallel decoding strategy that unmasks tokens only when correctly predicted. Importantly, the filter model is learned in a post-training manner, requiring only a small amount of computation to optimize it (minute-level GPU time). Additionally, we introduce End-of-Text Prediction (EoTP) to detect decoding completion at the end of sequence, avoiding redundant decoding of padding tokens. Experiments on the LLaDA benchmark demonstrate that our method achieves up to 22.58times speedup without any performance drop, and up to 57.51times when combined with KV-Cache.

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 key-value (KV) cache accelerates LLMs decoding by storing KV tensors from previously generated tokens. It reduces redundant computation at the cost of increased memory usage. To mitigate this overhead, existing approaches compress KV tensors into lower-bit representations; however, quantization errors can accumulate as more tokens are generated, potentially resulting in undesired outputs. In this paper, we introduce SQuat (Subspace-orthogonal KV cache quantization). It first constructs a subspace spanned by query tensors to capture the most critical task-related information. During key tensor quantization, it enforces that the difference between the (de)quantized and original keys remains orthogonal to this subspace, minimizing the impact of quantization errors on the attention mechanism's outputs. SQuat requires no model fine-tuning, no additional calibration dataset for offline learning, and is grounded in a theoretical framework we develop. Through numerical experiments, we show that our method reduces peak memory by 2.17 to 2.82, improves throughput by 2.45 to 3.60, and achieves more favorable benchmark scores than existing KV cache quantization algorithms.

In this reproduction study, we revisit recent claims that self-attention implements kernel principal component analysis (KPCA) (Teo et al., 2024), positing that (i) value vectors V capture the eigenvectors of the Gram matrix of the keys, and (ii) that self-attention projects queries onto the principal component axes of the key matrix K in a feature space. Our analysis reveals three critical inconsistencies: (1) No alignment exists between learned self-attention value vectors and what is proposed in the KPCA perspective, with average similarity metrics (optimal cosine similarity leq 0.32, linear CKA (Centered Kernel Alignment) leq 0.11, kernel CKA leq 0.32) indicating negligible correspondence; (2) Reported decreases in reconstruction loss J_proj, arguably justifying the claim that the self-attention minimizes the projection error of KPCA, are misinterpreted, as the quantities involved differ by orders of magnitude (sim!10^3); (3) Gram matrix eigenvalue statistics, introduced to justify that V captures the eigenvector of the gram matrix, are irreproducible without undocumented implementation-specific adjustments. Across 10 transformer architectures, we conclude that the KPCA interpretation of self-attention lacks empirical support.

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.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

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.

Large language models have high compute, latency, and memory requirements. While specialized accelerators such as GPUs and TPUs typically run these workloads, CPUs are more widely available and consume less energy. Accelerating LLMs with CPUs enables broader AI access at a lower cost and power consumption. This acceleration potential for CPUs is especially relevant during the memory-bound decoding stage of LLM inference, which processes one token at a time and is becoming increasingly utilized with reasoning models. We utilize Advanced Matrix Extensions (AMX) support on the latest Intel CPUs together with unstructured sparsity to achieve a 1.42 times reduction in end-to-end latency compared to the current PyTorch implementation by applying our technique in linear layers. We provide a set of open-source customized sparse kernels that can speed up any PyTorch model by automatically replacing all linear layers with our custom sparse implementation. Furthermore, we demonstrate for the first time the use of unstructured sparsity in the attention computation achieving a 1.14 times speedup over the current systems without compromising accuracy. Code: https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning/tree/main/SparAMX

Large Language Models (LLMs) are increasingly deployed in scenarios demanding ultra-long context reasoning, such as agentic workflows and deep research understanding. However, long-context inference is constrained by the KV cache, a transient memory structure that grows linearly with sequence length and batch size, quickly dominating GPU memory usage. Existing memory reduction techniques, including eviction and quantization, often rely on static heuristics and suffer from degraded quality under tight budgets. In this paper, we propose ARKV, a lightweight and adaptive framework that dynamically allocates precision levels to cached tokens based on per-layer attention dynamics and token-level importance. During a short prefill phase, ARKV estimates the original quantization (OQ) ratio of each layer by computing statistical scores such as attention entropy, variance and kurtosis. During decoding, tokens are assigned to one of three states, Original (full precision), Quantization (low precision), or Eviction, according to a fast heavy-hitter scoring strategy. Our experiments on LLaMA3 and Qwen3 models across diverse long- and short-context tasks demonstrate that ARKV preserves ~97% of baseline accuracy on long-context benchmarks while reducing KV memory usage by 4x, with minimal throughput loss. On short-context tasks, ARKV matches full-precision baselines; on GSM8K math reasoning, it significantly outperforms uniform quantization. These results highlight the practical viability of ARKV for scalable LLM deployment, offering fine-grained, data-driven memory control without retraining or architectural modifications. The source code and artifacts can be found in: https://github.com/Large-scale-Sustainable-Computing-LSC/ARKV

To mitigate the high inference latency stemming from autoregressive decoding in Large Language Models (LLMs), Speculative Decoding has emerged as a novel decoding paradigm for LLM inference. In each decoding step, this method first efficiently drafts several future tokens and then verifies them in parallel. Unlike autoregressive decoding, Speculative Decoding facilitates the simultaneous decoding of multiple tokens per step, thereby accelerating inference. This paper presents a comprehensive overview and analysis of this promising decoding paradigm. We begin by providing a formal definition and formulation of Speculative Decoding. Then, we organize in-depth discussions on its key facets, including current leading techniques, the challenges faced, and potential future directions in this field. We aim for this work to serve as a catalyst for further research on Speculative Decoding, ultimately contributing to more efficient LLM inference.

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.

Feature preprocessing continues to play a critical role when applying machine learning and statistical methods to tabular data. In this paper, we propose the use of the kernel density integral transformation as a feature preprocessing step. Our approach subsumes the two leading feature preprocessing methods as limiting cases: linear min-max scaling and quantile transformation. We demonstrate that, without hyperparameter tuning, the kernel density integral transformation can be used as a simple drop-in replacement for either method, offering protection from the weaknesses of each. Alternatively, with tuning of a single continuous hyperparameter, we frequently outperform both of these methods. Finally, we show that the kernel density transformation can be profitably applied to statistical data analysis, particularly in correlation analysis and univariate clustering.

One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space complexity to O(nm) by sampling m columns from K_n. Uniform sampling preserves KRR accuracy (up to epsilon) only when m is proportional to the maximum degree of freedom of K_n, which may require O(n) columns for datasets with high coherence. Sampling columns according to their ridge leverage scores (RLS) gives accurate Nystrom approximations with m proportional to the effective dimension, but computing exact RLS also requires O(n^2) space. (Calandriello et al. 2016) propose INK-Estimate, an algorithm that processes the dataset incrementally and updates RLS, effective dimension, and Nystrom approximations on-the-fly. Its space complexity scales with the effective dimension but introduces a dependency on the largest eigenvalue of K_n, which in the worst case is O(n). In this paper we introduce SQUEAK, a new algorithm that builds on INK-Estimate but uses unnormalized RLS. As a consequence, the algorithm is simpler, does not need to estimate the effective dimension for normalization, and achieves a space complexity that is only a constant factor worse than exact RLS sampling.