论文检索

Deep Learning · Large Language Models

Hyeong Kyu Choi, Maxim Khanov, Hongxin Wei, Sharon Li

Dataset contamination, where evaluation datasets overlap with pre-training corpora, inflates performance metrics and undermines the reliability of model evaluations. Measuring dataset contamination thus becomes essential to ensure that performance evaluations genuinely reflect a model's ability to generalize to unseen data, rather than relying on memorized examples. To address this problem, we propose Kernel Divergence Score (KDS), a novel method that evaluates dataset contamination by computing the divergence between the kernel similarity matrix of sample embeddings, before and after fine-tuning on the benchmark dataset. Leveraging the insight that fine-tuning affects unseen samples more significantly than seen ones, KDS provides a reliable measure of contamination. Through extensive experiments on controlled contamination scenarios, KDS demonstrates a near-perfect correlation with contamination levels and outperforms existing baselines. Additionally, we perform comprehensive ablation studies to analyze the impact of key design choices, providing deeper insights into the components and effectiveness of KDS. These ablations highlight the importance of leveraging fine-grained kernel-based information and confirm the reliability of the proposed framework across diverse datasets and settings.Code is released in https://github.com/deeplearning-wisc/kernel-divergence-score.

Probabilistic Methods · Gaussian Processes

Siavash Ameli, Chris van der Heide, Liam Hodgkinson, Fred Roosta, Michael Mahoney

Calculating or accurately estimating log-determinants of large positive semi-definite matrices is of fundamental importance in many machine learning tasks. While its cubic computational complexity can already be prohibitive, in modern applications even storing the matrices themselves can pose a memory bottleneck. To address this, we derive a novel hierarchical algorithm based on block-wise computation of the LDL decomposition for large-scale log-determinant calculation in memory-constrained settings. In extreme cases where matrices are highly ill-conditioned, accurately computing the full matrix itself may be infeasible. This is particularly relevant when considering kernel matrices at scale, including the empirical Neural Tangent Kernel (NTK) of neural networks trained on large datasets. Under the assumption of neural scaling laws in the test error, we show that the ratio of pseudo-determinants satisfies a power-law relationship, enabling the derivation of corresponding scaling laws. This allows for accurate estimation of NTK log-determinants from a tiny fraction of the full dataset; in our experiments, this results in a $\sim$100,000$\times$ speedup with improved accuracy to other state-of-the-art approaches. Using these techniques, we successfully estimate log-determinants for dense matrices of extreme sizes, which were previously deemed intractable and inaccessible due to their enormous scale and computational requirements.

Deep Learning · Graph Neural Networks

Yoon Hyeok Lee, Jaemin Park, Taejin Paik, Doyun Kim, Bosun Hwang

Graph Transformers (GTs) have emerged as a powerful alternative to message-passing neural networks, yet their performance heavily depends on effectively embedding structural inductive biases. In this work, we introduce novel structural encodings (SEs) grounded in a rigorous analysis of random walks (RWs), leveraging Green and Martin kernels that we have carefully redefined for AI applications while preserving their mathematical essence.These kernels capture the long-term behavior of RWs on graphs and allow for enhanced representation of complex topologies, including non-aperiodic and directed acyclic substructures.Empirical evaluations across eight benchmark datasets demonstrate strong performance across diverse tasks, notably in molecular and circuit domains.We attribute this performance boost to the improved ability of our kernel-based SEs to encode intricate structural information, thereby strengthening the global attention and inductive bias within GTs.This work highlights the effectiveness of theoretically grounded kernel methods in advancing Transformer-based models for graph learning.

Deep Learning · Graph Neural Networks

Zhiqiang Wang, Jianghao Wen, Jianqing Liang

Dynamic graph representation learning using Spiking Neural Networks (SNNs) exploits the temporal spiking behavior of neurons, offering advantages in capturing the temporal evolution and sparsity of dynamic graphs. However, existing SNN-based methods often fail to effectively capture the impact of latency in information propagation on node representations. To address this, we propose Delay-DSGN, a dynamic spiking graph neural network incorporating a learnable delay mechanism. By leveraging synaptic plasticity, the model dynamically adjusts connection weights and propagation speeds, enhancing temporal correlations and enabling historical data to influence future representations. Specifically, we introduce a Gaussian delay kernel into the neighborhood aggregation process at each time step, adaptively delaying historical information to future time steps and mitigating information forgetting. Experiments on three large-scale dynamic graph datasets demonstrate that Delay-DSGN outperforms eight state-of-the-art methods, achieving the best results in node classification tasks. We also theoretically derive the constraint conditions between the Gaussian kernel's standard deviation and size, ensuring stable training and preventing gradient explosion and vanishing issues.

General Machine Learning · Online Learning, Active Learning and Bandits

Cun-Yuan Xing, Meng-Zhang Qian, Wu-Yang Chen, Wei Gao, Zhi-Hua Zhou

Feature evolvable learning studies the scenario where old features will vanish and new features will emerge when learning with data streams, and various methods have been developed by utilizing some useful relationships from old features to new features, rather than re-training from scratch. In this work, we focus on two fundamental problems: How to characterize the relationships between two different feature spaces, and how to exploit those relationships for feature evolvable learning. We introduce the Kernel Ortho-Mapping (KOM) discrepancy to characterize relationships between two different feature spaces via kernel functions, and correlate with the optimal classifiers learned from different feature spaces. Based on this discrepancy, we develop the one-pass algorithm for feature evolvable learning, which requires going through all instances only once without storing the entire or partial training data. Our basic idea is to take online kernel learning with the random Fourier features and incorporate some feature and label relationships via the KOM discrepancy for feature evolvable learning. We finally validate the effectiveness of our proposed method both theoretically and empirically.

Wenjie Wei, Malu Zhang, Zijian Zhou, Ammar Belatreche, Yimeng Shan, Yu Liang, Honglin Cao, Jieyuan Zhang, Yang Yang

Brain-inspired Spiking Neural Networks (SNNs) leverage sparse spikes to encode information and operate in an asynchronous event-driven manner, offering a highly energy-efficient paradigm for machine intelligence. However, the current SNN community focuses primarily on performance improvement by developing large-scale models, which limits the applicability of SNNs in resource-limited edge devices. In this paper, we propose a hardware-friendly and lightweight SNN, aimed at effectively deploying high-performance SNN in resource-limited scenarios. Specifically, we first develop a baseline model that integrates uniform quantization and structured pruning, called QP-SNN baseline. While this baseline significantly reduces storage demands and computational costs, it suffers from performance decline. To address this, we conduct an in-depth analysis of the challenges in quantization and pruning that lead to performance degradation and propose solutions to enhance the baseline's performance. For weight quantization, we propose a weight rescaling strategy that utilizes bit width more effectively to enhance the model's representation capability. For structured pruning, we propose a novel pruning criterion using the singular value of spatiotemporal spike activities to enable more accurate removal of redundant kernels. Extensive experiments demonstrate that integrating two proposed methods into the baseline allows QP-SNN to achieve state-of-the-art performance and efficiency, underscoring its potential for enhancing SNN deployment in edge intelligence computing.

Deep Learning · Theory

Hengyu Fu, Zihao Wang, Eshaan Nichani, Jason Lee

In deep learning theory, a critical question is to understand how neural networks learn hierarchical features. In this work, we study the learning of hierarchical polynomials of multiple nonlinear features using three-layer neural networks. We examine a broad class of functions of the form $f^{\star}=g^{\star}\circ \mathbf{p}$, where $\mathbf{p}:\mathbb{R}^{d} \rightarrow \mathbb{R}^{r}$ represents multiple quadratic features with $r \ll d$ and $g^{\star}:\mathbb{R}^{r}\rightarrow \mathbb{R}$ is a polynomial of degree $p$. This can be viewed as a nonlinear generalization of the multi-index model, and also an expansion upon previous work on nonlinear feature learning that focused only on a single feature (i.e. $r = 1$). Our primary contribution shows that a three-layer neural network trained via layerwise gradient descent suffices for - complete recovery of the space spanned by the nonlinear features - efficient learning of the target function $f^{\star}=g^{\star}\circ \mathbf{p}$ or transfer learning of $f=g\circ \mathbf{p}$ with a different link function within $\widetilde{\mathcal{O}}(d^4)$ samples and polynomial time.For such hierarchical targets, our result substantially improves the sample complexity ${\Theta}(d^{2p})$ of the kernel methods, demonstrating the power of efficient feature learning. It is important to highlight that our results leverage novel techniques and thus manage to go beyond all prior settings such as single-index and multi-index models as well as models depending just on one nonlinear feature, contributing to a more comprehensive understanding of feature learning in deep learning.

Peijie Dong, Lujun Li, Yuedong Zhong, DaYou Du, Ruibo FAN, Yuhan CHEN, Zhenheng Tang, Qiang Wang, Wei Xue, Yike Guo 等

In this paper, we present the first structural binarization method for LLM compression to less than 1-bit precision. Although LLMs have achieved remarkable performance, their memory-bound nature during the inference stage hinders the adoption of resource-constrained devices. Reducing weights to 1-bit precision through binarization substantially enhances computational efficiency. We observe that randomly flipping some weights in binarized LLMs does not significantly degrade the model's performance, suggesting the potential for further compression. To exploit this, our STBLLM employs an N:M sparsity technique to achieve structural binarization of the weights. Specifically, we introduce a novel Standardized Importance (SI) metric, which considers weight magnitude and input feature norm to more accurately assess weight significance. Then, we propose a layer-wise approach, allowing different layers of the LLM to be sparsified with varying N:M ratios, thereby balancing compression and accuracy. Furthermore, we implement a fine-grained grouping strategy for less important weights, applying distinct quantization schemes to sparse, intermediate, and dense regions. Finally, we design a specialized CUDA kernel to support structural binarization. We conduct extensive experiments on LLaMA, OPT, and Mistral family. STBLLM achieves a perplexity of 11.07 at 0.55 bits per weight, outperforming the BiLLM by 3×. The results demonstrate that our approach performs better than other compressed binarization LLM methods while significantly reducing memory requirements. Code is released at https://github.com/pprp/STBLLM.

Reinforcement Learning · Deep RL

Yixian Zhang, Huaze Tang, Huijing Lin, Wenbo Ding

Achieving optimal performance in reinforcement learning requires robust policies supported by training processes that ensure both sample efficiency and stability. Modeling the policy in reproducing kernel Hilbert space (RKHS) enables efficient exploration of local optimal solutions. However, the stability of existing RKHS-based methods is hindered by significant variance in gradients, while the robustness of the learned policies is often compromised due to the sensitivity of hyperparameters. In this work, we conduct a comprehensive analysis of the significant instability in RKHS policies and reveal that the variance of the policy gradient increases substantially when a wide-bandwidth kernel is employed. To address these challenges, we propose a novel RKHS policy learning method integrated with representation learning to dynamically process observations in complex environments, enhancing the robustness of RKHS policies. Furthermore, inspired by the advantage functions, we introduce a residual layer that further stabilizes the training process by significantly reducing gradient variance in RKHS. Our novel algorithm, the Residual Kernel Policy Network (ResKPN), demonstrates state-of-the-art performance, achieving a 30% improvement in episodic rewards across complex environments.

Deep Learning · Large Language Models

Jiachen Jiang, Jinxin Zhou, Zhihui Zhu

Analyzing the similarity of internal representations within and across different models has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such as those based on Centered Kernel Alignment (CKA), rely on statistical properties of the representations for a set of data points. In this paper, we focus on transformer models and study the similarity of representations between the hidden layers of individual transformers. In this context, we show that a simple sample-wise cosine similarity metric is capable of capturing the similarity and aligns with the complicated CKA. Our experimental results on common transformers reveal that representations across layers are positively correlated, with similarity increasing when layers get closer. We provide a theoretical justification for this phenomenon under the geodesic curve assumption for the learned transformer, a property that may approximately hold for residual networks. We then show that an increase in representation similarity implies an increase in predicted probability when directly applying the last-layer classifier to any hidden layer representation. This offers a justification for {\it saturation events}, where the model's top prediction remains unchanged across subsequent layers, indicating that the shallow layer has already learned the necessary knowledge. We then propose an aligned training method to improve the effectiveness of shallow layer by enhancing the similarity between internal representations, with trained models that enjoy the following properties: (1) more early saturation events, (2) layer-wise accuracies monotonically increase and reveal the minimal depth needed for the given task, (3) when served as multi-exit models, they achieve on-par performance with standard multi-exit architectures which consist of additional classifiers designed for early exiting in shallow layers. To our knowledge, our work is the first to show that one common classifier is sufficient for multi-exit models. We conduct experiments on both vision and NLP tasks to demonstrate the performance of the proposed aligned training.

Deep Learning · Graph Neural Networks

Mahalakshmi Sabanayagam, Lukas Gosch, Stephan Günnemann, Debarghya Ghoshdastidar

Machine learning models are highly vulnerable to label flipping, i.e., the adversarial modification (poisoning) of training labels to compromise performance. Thus, deriving robustness certificates is important to guarantee that test predictions remain unaffected and to understand worst-case robustness behavior. However, for Graph Neural Networks (GNNs), the problem of certifying label flipping has so far been unsolved. We change this by introducing an exact certification method, deriving both sample-wise and collective certificates. Our method leverages the Neural Tangent Kernel (NTK) to capture the training dynamics of wide networks enabling us to reformulate the bilevel optimization problem representing label flipping into a Mixed-Integer Linear Program (MILP). We apply our method to certify a broad range of GNN architectures in node classification tasks. Thereby, concerning the worst-case robustness to label flipping: $(i)$ we establish hierarchies of GNNs on different benchmark graphs; $(ii)$ quantify the effect of architectural choices such as activations, depth and skip-connections; and surprisingly, $(iii)$ uncover a novel phenomenon of the robustness plateauing for intermediate perturbation budgets across all investigated datasets and architectures. While we focus on GNNs, our certificates are applicable to sufficiently wide NNs in general through their NTK. Thus, our work presents the first exact certificate to a poisoning attack ever derived for neural networks, which could be of independent interest. The code is available at https://github.com/saper0/qpcert.

Deep Learning · Large Language Models

Yiliao Song, Zhenqiao Yuan, Shuhai Zhang, Zhen Fang, Jun Yu, Feng Liu

Recent studies demonstrate that two-sample test can effectively detect machine-generated texts (MGTs) with excellent adaptation ability to texts generated by newer LLMs. However, two-sample test-based detection relies on the assumption that human-written texts (HWTs) must follow the distribution of seen HWTs. As a result, it tends to make mistakes in identifying HWTs that deviate from the seen HWT distribution, limiting their use in sensitive areas like academic integrity verification. To address this issue, we propose to employ non-parametric kernel relative test to detect MGTs by testing whether it is statistically significant that the distribution of a text to be tested is closer to the distribution of HWTs than to the MGTs' distribution. We further develop a kernel optimisation algorithm in relative test to select the best kernel that can enhance the testing capability for MGT detection. As relative test does not assume that a text to be tested must belong exclusively to either MGTs or HWTs, relative test can largely reduce the false positive error compared to two-sample test, offering significant advantages in practice. Extensive experiments demonstrate the superior performance of our method, compared to state-of-the-art non-parametric and parametric detectors. The code and demo are available: https://github.com/xLearn-AU/R-Detect.

Deep Learning · Attention Mechanisms

Guoxia Wang, Jinle Zeng, Xiyuan Xiao, Siming Wu, Jiabin Yang, Lujing Zheng, Zeyu Chen, Jiang Bian, Dianhai Yu, Haifeng Wang

The computational and memory demands of vanilla attention scale quadratically with the sequence length $N$, posing significant challenges for processing long sequences in Transformer models. FlashAttention alleviates these challenges by eliminating the $\mathcal{O}(N^2)$ memory dependency and reducing attention latency through IO-aware memory optimizations. However, its native support for certain attention mask types is limited, and it does not inherently accommodate more complex masking requirements. Previous approaches resort to using dense masks with $\mathcal{O}(N^2)$ memory complexity, leading to inefficiencies. In this paper, we propose \ours{}, an extension of FlashAttention that introduces a column-wise sparse representation of attention masks. This approach efficiently represents a wide range of mask types and facilitates the development of optimized kernel implementations. By adopting this novel representation, \ours{} achieves linear memory complexity $\mathcal{O}(N)$, making it suitable for modeling long-context sequences. Moreover, this representation enables kernel optimizations that eliminate unnecessary computations by leveraging sparsity in the attention mask, without sacrificing computational accuracy, resulting in higher computational efficiency. We evaluate \ours{}'s performance in fine-tuning and alignment training of LLMs such as SFT, LoRA, DPO, and RM. \ours{} achieves significant throughput improvements, with end-to-end speedups ranging from 1.65x to 3.22x compared to existing FlashAttention dense method. Additionally, our kernel-level comparisons demonstrate that \ours{} surpasses the latest counterpart, FlexAttention, by 12.1\% to 60.7\% in terms of kernel TFLOPs/s, achieving 37.8\% to 62.3\% of the theoretical maximum FLOPs/s on the A100 GPU. The code is open-sourced on PaddlePaddle\footnote{\url{https://github.com/PaddlePaddle/Paddle}} and integrated into PaddleNLP\footnote{\url{https://github.com/PaddlePaddle/PaddleNLP}}, supporting models with over 100 billion parameters for contexts extending up to 128K tokens.

Xuan Shen, Hangyu Zheng, Yifan Gong, Zhenglun Kong, Changdi Yang, Zheng Zhan, Yushu Wu, Xue Lin, Yanzhi Wang, Pu Zhao 等

Transformer models have been widely investigated in different domains by providing long-range dependency handling and global contextual awareness, driving the development of popular AI applications such as ChatGPT, Gemini, and Alexa.State Space Models (SSMs) have emerged as strong contenders in the field of sequential modeling, challenging the dominance of Transformers. SSMs incorporate a selective mechanism that allows for dynamic parameter adjustment based on input data, enhancing their performance.However, this mechanism also comes with increasing computational complexity and bandwidth demands, posing challenges for deployment on resource-constraint mobile devices.To address these challenges without sacrificing the accuracy of the selective mechanism, we propose a sparse learning framework that integrates architecture-aware compiler optimizations. We introduce an end-to-end solution--$\mathbf{C}_4^n$ kernel sparsity, which prunes $n$ elements from every four contiguous weights, and develop a compiler-based acceleration solution to ensure execution efficiency for this sparsity on mobile devices.Based on the kernel sparsity, our framework generates optimized sparse models targeting specific sparsity or latency requirements for various model sizes. We further leverage pruned weights to compensate for the remaining weights, enhancing downstream task performance.For practical hardware acceleration, we propose $\mathbf{C}_4^n$-specific optimizations combined with a layout transformation elimination strategy. This approach mitigates inefficiencies arising from fine-grained pruning in linear layers and improves performance across other operations. Experimental results demonstrate that our method achieves superior task performance compared to other semi-structured pruning methods and achieves up-to 7$\times$ speedup compared to llama.cpp framework on mobile devices.

Miscellaneous Aspects of Machine Learning · Representation Learning

Harel Mendelman, Ronen Talmon

In this paper, we introduce Supervised Diffusion Maps (SDM) and Semi-Supervised Diffusion Maps (SSDM), which transform the well-known unsupervised dimensionality reduction algorithm, Diffusion Maps, into supervised and semi-supervised learning tools. The proposed methods, SDM and SSDM, are based on our new approach that treats the labels as a second view of the data. This unique framework allows us to incorporate ideas from multi-view learning. Specifically, we propose constructing two affinity kernels corresponding to the data and the labels. We then propose a multiplicative interpolation scheme of the two kernels, whose purpose is twofold. First, our scheme extracts the common structure underlying the data and the labels by defining a diffusion process driven by the data and the labels. This label-driven diffusion produces an embedding that emphasizes the properties relevant to the label-related task. Second, the proposed interpolation scheme balances the influence of the two kernels. We show on multiple benchmark datasets that the embedding learned by SDM and SSDM is more effective in downstream regression and classification tasks than existing unsupervised, supervised, and semi-supervised nonlinear dimension reduction methods.

Deep Learning · Generative Models and Autoencoders

Muyang Li, Yujun Lin, Zhekai Zhang, Tianle Cai, Xiuyu Li, Junxian Guo, Enze Xie, Chenlin Meng, Jun-Yan Zhu, Song Han

Diffusion models can effectively generate high-quality images. However, as they scale, rising memory demands and higher latency pose substantial deployment challenges. In this work, we aim to accelerate diffusion models by quantizing their weights and activations to 4 bits. At such an aggressive level, both weights and activations are highly sensitive, where existing post-training quantization methods like smoothing become insufficient. To overcome this limitation, we propose *SVDQuant*, a new 4-bit quantization paradigm. Different from smoothing, which redistributes outliers between weights and activations, our approach *absorbs* these outliers using a low-rank branch. We first consolidate the outliers by shifting them from activations to weights. Then, we use a high-precision, low-rank branch to take in the weight outliers with Singular Value Decomposition (SVD), while a low-bit quantized branch handles the residuals. This process eases the quantization on both sides. However, naively running the low-rank branch independently incurs significant overhead due to extra data movement of activations, negating the quantization speedup. To address this, we co-design an inference engine *Nunchaku* that fuses the kernels of the low-rank branch into those of the low-bit branch to cut off redundant memory access. It can also seamlessly support off-the-shelf low-rank adapters (LoRAs) without re-quantization. Extensive experiments on SDXL, PixArt-$\Sigma$, and FLUX.1 validate the effectiveness of SVDQuant in preserving image quality. We reduce the memory usage for the 12B FLUX.1 models by 3.5×, achieving 3.0× speedup over the 4-bit weight-only quantization (W4A16) baseline on the 16GB laptop 4090 GPU with INT4 precision. On the latest RTX 5090 desktop with Blackwell architecture, we achieve a 3.1× speedup compared to the W4A16 model using NVFP4 precision. Our quantization library and inference engine are available at https://github.com/mit-han-lab/deepcompressor/ and https://github.com/mit-han-lab/nunchaku/, correspondingly.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Yi Zhang, Siwei Wang, Jiyuan Liu, Shengju Yu, Zhibin Dong, Suyuan Liu, Xinwang Liu, En Zhu

Recent advancements in multiple kernel clustering (MKC) have highlighted the effectiveness of late fusion strategies, particularly in enhancing computational efficiency to near-linear complexity while achieving promising clustering performance. However, existing methods encounter three significant limitations: (1) reliance on fixed base partition matrices that do not adaptively optimize during the clustering process, thereby constraining their performance to the inherent representational capabilities of these matrices; (2) a focus on adjusting kernel weights to explore inter-view consistency and complementarity, which often neglects the intrinsic high-order correlations among views, thereby limiting the extraction of comprehensive multiple kernel information; (3) a lack of adaptive mechanisms to accommodate varying distributions within the data, which limits robustness and generalization. To address these challenges, this paper proposes a novel algorithm termed Dynamic Late Fusion Multiple Kernel Clustering with Robust {Tensor Learning via min-max optimization (DLEFT-MKC), which effectively overcomes the representational bottleneck of base partition matrices and facilitates the learning of meaningful high-order cross-view information. Specifically, it is the first to incorporate a min-max optimization paradigm into tensor-based MKC, enhancing algorithm robustness and generalization. Additionally, it dynamically reconstructs decision layers to enhance representation capabilities and subsequently stacks the reconstructed representations for tensor learning that promotes the capture of high-order associations and cluster structures across views, ultimately yielding consensus clustering partitions. To solve the resultant optimization problem, we innovatively design a strategy that combines reduced gradient descent with the alternating direction method of multipliers, ensuring convergence to local optima while maintaining high computational efficiency. Extensive experimental results across various benchmark datasets validate the superior effectiveness and efficiency of the proposed DLEFT-MKC.

Applications · Everything Else

Junchao Gong, Siwei Tu, Weidong Yang, Ben Fei, Kun Chen, Wenlong Zhang, Xiaokang Yang, Wanli Ouyang, LEI BAI

Precipitation nowcasting plays a pivotal role in socioeconomic sectors, especially in severe convective weather warnings. Although notable progress has been achieved by approaches mining the spatiotemporal correlations with deep learning, these methods still suffer severe blurriness as the lead time increases, which hampers accurate predictions for extreme precipitation. To alleviate blurriness, researchers explore generative methods conditioned on blurry predictions. However, the pairs of blurry predictions and corresponding ground truth need to be given in advance, making the training pipeline cumbersome and limiting the generality of generative models within blurry modes that appear in training data. By rethinking the blurriness in precipitation nowcasting as a blur kernel acting on predictions, we propose an unsupervised postprocessing method to eliminate the blurriness without the requirement of training with the pairs of blurry predictions and corresponding ground truth. Specifically, we utilize blurry predictions to guide the generation process of a pre-trained unconditional denoising diffusion probabilistic model (DDPM) to obtain high-fidelity predictions with eliminated blurriness. A zero-shot blur kernel estimation mechanism and an auto-scale denoise guidance strategy are introduced to adapt the unconditional DDPM to any blurriness modes varying from datasets and lead times in precipitation nowcasting. Extensive experiments are conducted on 7 precipitation radar datasets, demonstrating the generality and superiority of our method.

Probabilistic Methods · Everything Else

Jonghyeok Lee, Chen Xu, Yao Xie

Conformal prediction has been a popular distribution-free framework for uncertainty quantification. In this work, we present a novel conformal prediction method for time-series, which we call Kernel-based Optimally Weighted Conformal Prediction Intervals ($\texttt{KOWCPI}$). Specifically, $\texttt{KOWCPI}$ adapts the classic Reweighted Nadaraya-Watson (RNW) estimator for quantile regression on dependent data and learns optimal data-adaptive weights. Theoretically, we tackle the challenge of establishing a conditional coverage guarantee for non-exchangeable data under strong mixing conditions on the non-conformity scores. We demonstrate the superior performance of $\texttt{KOWCPI}$ on real time-series against state-of-the-art methods, where $\texttt{KOWCPI}$ achieves narrower confidence intervals without losing coverage.

Deep Learning · Sequential Models, Time series

Fusheng Liu, Qianxiao Li

Current methods for initializing state space model (SSM) parameters primarily rely on the HiPPO framework \citep{gu2023how}, which is based on online function approximation with the SSM kernel basis. However, the HiPPO framework does not explicitly account for the effects of the temporal structures of input sequences on the optimization of SSMs.In this paper, we take a further step to investigate the roles of SSM initialization schemes by considering the autocorrelation of input sequences. Specifically, we: (1) rigorously characterize the dependency of the SSM timescale on sequence length based on sequence autocorrelation; (2) find that with a proper timescale, allowing a zero real part for the eigenvalues of the SSM state matrix mitigates the curse of memory while still maintaining stability at initialization; (3) show that the imaginary part of the eigenvalues of the SSM state matrix determines the conditioning of SSM optimization problems, and uncover an approximation-estimation tradeoff when training SSMs with a specific class of target functions.