Qibin Zhao

Chao Li, Junhua Zeng, Zerui Tao et al. · tsinghua

Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we consider a practical variant of TN-SS, dubbed TN permutation search (TN-PS), in which we search for good mappings from tensor modes onto TN vertices (core tensors) for compact TN representations. We conduct a theoretical investigation of TN-PS and propose a practically-efficient algorithm to resolve the problem. Theoretically, we prove the counting and metric properties of search spaces of TN-PS, analyzing for the first time the impact of TN structures on these unique properties. Numerically, we propose a novel meta-heuristic algorithm, in which the searching is done by randomly sampling in a neighborhood established in our theory, and then recurrently updating the neighborhood until convergence. Numerical results demonstrate that the new algorithm can reduce the required model size of TNs in extensive benchmarks, implying the improvement in the expressive power of TNs. Furthermore, the computational cost for the new algorithm is significantly less than that in~\cite{li2020evolutionary}.

Chao Li, Junhua Zeng, Chunmei Li et al. · tsinghua

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~\cite{li2022permutation} showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, \emph{greatly} reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is \emph{reached} in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that $Ω(2^N)$ evaluations are typically required in TNLS for \emph{reaching} the objective reduction in the neighborhood, while ideally $O(N^2R)$ evaluations are sufficient in TnALE, where $N$ denotes the tensor order and $R$ reflects the \emph{``low-rankness''} of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.

Andong Wang, Chao Li, Mingyuan Bai et al. · tsinghua

Achieving efficient and robust multi-channel data learning is a challenging task in data science. By exploiting low-rankness in the transformed domain, i.e., transformed low-rankness, tensor Singular Value Decomposition (t-SVD) has achieved extensive success in multi-channel data representation and has recently been extended to function representation such as Neural Networks with t-product layers (t-NNs). However, it still remains unclear how t-SVD theoretically affects the learning behavior of t-NNs. This paper is the first to answer this question by deriving the upper bounds of the generalization error of both standard and adversarially trained t-NNs. It reveals that the t-NNs compressed by exact transformed low-rank parameterization can achieve a sharper adversarial generalization bound. In practice, although t-NNs rarely have exactly transformed low-rank weights, our analysis further shows that by adversarial training with gradient flow (GF), the over-parameterized t-NNs with ReLU activations are trained with implicit regularization towards transformed low-rank parameterization under certain conditions. We also establish adversarial generalization bounds for t-NNs with approximately transformed low-rank weights. Our analysis indicates that the transformed low-rank parameterization can promisingly enhance robust generalization for t-NNs.

Zhiqi Shao, Dai Shi, Andi Han et al. · tsinghua

Graph Neural Networks (GNNs) have emerged as one of the leading approaches for machine learning on graph-structured data. Despite their great success, critical computational challenges such as over-smoothing, over-squashing, and limited expressive power continue to impact the performance of GNNs. In this study, inspired from the time-reversal principle commonly utilized in classical and quantum physics, we reverse the time direction of the graph heat equation. The resulted reversing process yields a class of high pass filtering functions that enhance the sharpness of graph node features. Leveraging this concept, we introduce the Multi-Scaled Heat Kernel based GNN (MHKG) by amalgamating diverse filtering functions' effects on node features. To explore more flexible filtering conditions, we further generalize MHKG into a model termed G-MHKG and thoroughly show the roles of each element in controlling over-smoothing, over-squashing and expressive power. Notably, we illustrate that all aforementioned issues can be characterized and analyzed via the properties of the filtering functions, and uncover a trade-off between over-smoothing and over-squashing: enhancing node feature sharpness will make model suffer more from over-squashing, and vice versa. Furthermore, we manipulate the time again to show how G-MHKG can handle both two issues under mild conditions. Our conclusive experiments highlight the effectiveness of proposed models. It surpasses several GNN baseline models in performance across graph datasets characterized by both homophily and heterophily.

Yichun Qiu, Weijun Sun, Guoxu Zhou et al. · tsinghua

Efficient and accurate low-rank approximation (LRA) methods are of great significance for large-scale data analysis. Randomized tensor decompositions have emerged as powerful tools to meet this need, but most existing methods perform poorly in the presence of noise interference. Inspired by the remarkable performance of randomized block Krylov iteration (rBKI) in reducing the effect of tail singular values, this work designs an rBKI-based Tucker decomposition (rBKI-TK) for accurate approximation, together with a hierarchical tensor ring decomposition based on rBKI-TK for efficient compression of large-scale data. Besides, the error bound between the deterministic LRA and the randomized LRA is studied. Numerical experiences demonstrate the efficiency, accuracy and scalability of the proposed methods in both data compression and denoising.

Qi Jiang, Guoxu Zhou, Qibin Zhao · tsinghua

Concept Factorization (CF), as a novel paradigm of representation learning, has demonstrated superior performance in multi-view clustering tasks. It overcomes limitations such as the non-negativity constraint imposed by traditional matrix factorization methods and leverages kernel methods to learn latent representations that capture the underlying structure of the data, thereby improving data representation. However, existing multi-view concept factorization methods fail to consider the limited labeled information inherent in real-world multi-view data. This often leads to significant performance loss. To overcome these limitations, we propose a novel semi-supervised multi-view concept factorization model, named SMVCF. In the SMVCF model, we first extend the conventional single-view CF to a multi-view version, enabling more effective exploration of complementary information across multiple views. We then integrate multi-view CF, label propagation, and manifold learning into a unified framework to leverage and incorporate valuable information present in the data. Additionally, an adaptive weight vector is introduced to balance the importance of different views in the clustering process. We further develop targeted optimization methods specifically tailored for the SMVCF model. Finally, we conduct extensive experiments on four diverse datasets with varying label ratios to evaluate the performance of SMVCF. The experimental results demonstrate the effectiveness and superiority of our proposed approach in multi-view clustering tasks.

Reinmar J Kobler, Jun-ichiro Hirayama, Qibin Zhao et al.

Electroencephalography (EEG) provides access to neuronal dynamics non-invasively with millisecond resolution, rendering it a viable method in neuroscience and healthcare. However, its utility is limited as current EEG technology does not generalize well across domains (i.e., sessions and subjects) without expensive supervised re-calibration. Contemporary methods cast this transfer learning (TL) problem as a multi-source/-target unsupervised domain adaptation (UDA) problem and address it with deep learning or shallow, Riemannian geometry aware alignment methods. Both directions have, so far, failed to consistently close the performance gap to state-of-the-art domain-specific methods based on tangent space mapping (TSM) on the symmetric positive definite (SPD) manifold. Here, we propose a theory-based machine learning framework that enables, for the first time, learning domain-invariant TSM models in an end-to-end fashion. To achieve this, we propose a new building block for geometric deep learning, which we denote SPD domain-specific momentum batch normalization (SPDDSMBN). A SPDDSMBN layer can transform domain-specific SPD inputs into domain-invariant SPD outputs, and can be readily applied to multi-source/-target and online UDA scenarios. In extensive experiments with 6 diverse EEG brain-computer interface (BCI) datasets, we obtain state-of-the-art performance in inter-session and -subject TL with a simple, intrinsically interpretable network architecture, which we denote TSMNet.

Longhao Yuan, Jianting Cao, Qiang Wu et al.

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high compressibility and flexibility of recently proposed tensor ring (TR) decomposition, we propose a new tensor completion approach named tensor ring weighted optimization (TR-WOPT). It finds the latent factors of the incomplete tensor by gradient descent algorithm, then the latent factors are employed to predict the missing entries of the tensor. We conduct various tensor completion experiments on synthetic data and real-world data. The simulation results show that TR-WOPT performs well in various high-dimension tensors. Furthermore, image completion results show that our proposed algorithm outperforms the state-of-the-art algorithms in many situations. Especially when the missing rate of the test images is high (e.g., over 0.9), the performance of our TR-WOPT is significantly better than the compared algorithms.

Yuning Qiu, Guoxu Zhou, Qibin Zhao et al.

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries are noise-free to provide a theoretical guarantee of exact recovery of missing entries, which is quite restrictive in practice. To remedy such drawbacks, this paper proposes a novel noisy tensor completion model, which complements the incompetence of existing works in handling the degeneration of high-order and noisy observations. Specifically, the tensor ring nuclear norm (TRNN) and least-squares estimator are adopted to regularize the underlying tensor and the observed entries, respectively. In addition, a non-asymptotic upper bound of estimation error is provided to depict the statistical performance of the proposed estimator. Two efficient algorithms are developed to solve the optimization problem with convergence guarantee, one of which is specially tailored to handle large-scale tensors by replacing the minimization of TRNN of the original tensor equivalently with that of a much smaller one in a heterogeneous tensor decomposition framework. Experimental results on both synthetic and real-world data demonstrate the effectiveness and efficiency of the proposed model in recovering noisy incomplete tensor data compared with state-of-the-art tensor completion models.

Wanqi Zhou, Shuanghao Bai, Danilo P. Mandic et al.

Pretrained vision-language models (VLMs) like CLIP exhibit exceptional generalization across diverse downstream tasks. While recent studies reveal their vulnerability to adversarial attacks, research to date has primarily focused on enhancing the robustness of image encoders against image-based attacks, with defenses against text-based and multimodal attacks remaining largely unexplored. To this end, this work presents the first comprehensive study on improving the adversarial robustness of VLMs against attacks targeting image, text, and multimodal inputs. This is achieved by proposing multimodal contrastive adversarial training (MMCoA). Such an approach strengthens the robustness of both image and text encoders by aligning the clean text embeddings with adversarial image embeddings, and adversarial text embeddings with clean image embeddings. The robustness of the proposed MMCoA is examined against existing defense methods over image, text, and multimodal attacks on the CLIP model. Extensive experiments on 15 datasets across two tasks reveal the characteristics of different adversarial defense methods under distinct distribution shifts and dataset complexities across the three attack types. This paves the way for a unified framework of adversarial robustness against different modality attacks, opening up new possibilities for securing VLMs against multimodal attacks. The code is available at https://github.com/ElleZWQ/MMCoA.git.

Binghua Li, Ziqing Chang, Tong Liang et al.

We address the challenge of parameter-efficient fine-tuning (PEFT) for three-dimensional (3D) U-Net-based denoising diffusion probabilistic models (DDPMs) in magnetic resonance imaging (MRI) image generation. Despite its practical significance, research on parameter-efficient representations of 3D convolution operations remains limited. To bridge this gap, we propose Tensor Volumetric Operator (TenVOO), a novel PEFT method specifically designed for fine-tuning DDPMs with 3D convolutional backbones. Leveraging tensor network modeling, TenVOO represents 3D convolution kernels with lower-dimensional tensors, effectively capturing complex spatial dependencies during fine-tuning with few parameters. We evaluate TenVOO on three downstream brain MRI datasets-ADNI, PPMI, and BraTS2021-by fine-tuning a DDPM pretrained on 59,830 T1-weighted brain MRI scans from the UK Biobank. Our results demonstrate that TenVOO achieves state-of-the-art performance in multi-scale structural similarity index measure (MS-SSIM), outperforming existing approaches in capturing spatial dependencies while requiring only 0.3% of the trainable parameters of the original model. Our code is available at: https://github.com/xiaovhua/tenvoo

Binghua Li, Jie Mao, Zhe Sun et al.

Automated diagnosis with artificial intelligence has emerged as a promising area in the realm of medical imaging, while the interpretability of the introduced deep neural networks still remains an urgent concern. Although contemporary works, such as XProtoNet and MProtoNet, has sought to design interpretable prediction models for the issue, the localization precision of their resulting attribution maps can be further improved. To this end, we propose a Multi-scale Attentive Prototypical part Network, termed MAProtoNet, to provide more precise maps for attribution. Specifically, we introduce a concise multi-scale module to merge attentive features from quadruplet attention layers, and produces attribution maps. The proposed quadruplet attention layers can enhance the existing online class activation mapping loss via capturing interactions between the spatial and channel dimension, while the multi-scale module then fuses both fine-grained and coarse-grained information for precise maps generation. We also apply a novel multi-scale mapping loss for supervision on the proposed multi-scale module. Compared to existing interpretable prototypical part networks in medical imaging, MAProtoNet can achieve state-of-the-art performance in localization on brain tumor segmentation (BraTS) datasets, resulting in approximately 4% overall improvement on activation precision score (with a best score of 85.8%), without using additional annotated labels of segmentation. Our code will be released in https://github.com/TUAT-Novice/maprotonet.

Min Fang, Zhihui Fu, Qibin Zhao et al.

Speculative decoding (SD) has emerged as an effective technique to accelerate large language model (LLM) inference without compromising output quality. However, the achievable speedup largely depends on the effectiveness of the drafting model. While model-based methods like EAGLE-2 are accurate but costly, retrieval-enhanced methods like SAM-Decoding rely on heuristic switching strategies that often trigger unnecessary retrievals. To address this, we propose ReSpec (\textbf{Re}trieval-enhanced \textbf{Spe}culative Decoding), a novel framework that transforms heuristic drafter switching into adaptive decision-making. ReSpec features three core innovations: 1) An \textbf{entropy-guided adaptive trigger} quantifies contextual predictability to initiate retrieval only when uncertainty is low, avoiding costly low-quality speculations. 2) A \textbf{feedback-driven candidate selection} leverages historical feedback to organize multiple high-quality candidates for parallel verification, maximizing retrieval utility. 3) A source-aware \textbf{relaxed verification strategy} applies strict checks to model-generated drafts while using a relaxed verification for retrieved drafts, achieving a better balance between accuracy and efficiency. Extensive experiments on Spec-Bench demonstrate that ReSpec achieves state-of-the-art acceleration,outperforming EAGLE-2 and SAM-Decoding by over $33\%$ and $25\%$, respectively, while maintaining output quality.

Guang Lin, Chao Li, Jianhai Zhang et al.

The deep neural networks are known to be vulnerable to well-designed adversarial attacks. The most successful defense technique based on adversarial training (AT) can achieve optimal robustness against particular attacks but cannot generalize well to unseen attacks. Another effective defense technique based on adversarial purification (AP) can enhance generalization but cannot achieve optimal robustness. Meanwhile, both methods share one common limitation on the degraded standard accuracy. To mitigate these issues, we propose a novel pipeline to acquire the robust purifier model, named Adversarial Training on Purification (AToP), which comprises two components: perturbation destruction by random transforms (RT) and purifier model fine-tuned (FT) by adversarial loss. RT is essential to avoid overlearning to known attacks, resulting in the robustness generalization to unseen attacks, and FT is essential for the improvement of robustness. To evaluate our method in an efficient and scalable way, we conduct extensive experiments on CIFAR-10, CIFAR-100, and ImageNette to demonstrate that our method achieves optimal robustness and exhibits generalization ability against unseen attacks.

Wanqi Zhou, Shuanghao Bai, Shujian Yu et al.

With the advancement of neural networks, diverse methods for neural Granger causality have emerged, which demonstrate proficiency in handling complex data, and nonlinear relationships. However, the existing framework of neural Granger causality has several limitations. It requires the construction of separate predictive models for each target variable, and the relationship depends on the sparsity on the weights of the first layer, resulting in challenges in effectively modeling complex relationships between variables as well as unsatisfied estimation accuracy of Granger causality. Moreover, most of them cannot grasp full-time Granger causality. To address these drawbacks, we propose a Jacobian Regularizer-based Neural Granger Causality (JRNGC) approach, a straightforward yet highly effective method for learning multivariate summary Granger causality and full-time Granger causality by constructing a single model for all target variables. Specifically, our method eliminates the sparsity constraints of weights by leveraging an input-output Jacobian matrix regularizer, which can be subsequently represented as the weighted causal matrix in the post-hoc analysis. Extensive experiments show that our proposed approach achieves competitive performance with the state-of-the-art methods for learning summary Granger causality and full-time Granger causality while maintaining lower model complexity and high scalability.

Junhua Zeng, Chao Li, Zhun Sun et al.

Tensor networks are efficient for extremely high-dimensional representation, but their model selection, known as tensor network structure search (TN-SS), is a challenging problem. Although several works have targeted TN-SS, most existing algorithms are manually crafted heuristics with poor performance, suffering from the curse of dimensionality and local convergence. In this work, we jump out of the box, studying how to harness large language models (LLMs) to automatically discover new TN-SS algorithms, replacing the involvement of human experts. By observing how human experts innovate in research, we model their common workflow and propose an automatic algorithm discovery framework called tnGPS. The proposed framework is an elaborate prompting pipeline that instruct LLMs to generate new TN-SS algorithms through iterative refinement and enhancement. The experimental results demonstrate that the algorithms discovered by tnGPS exhibit superior performance in benchmarks compared to the current state-of-the-art methods.

Guang Lin, Zerui Tao, Jianhai Zhang et al.

Diffusion model (DM) based adversarial purification (AP) has proven to be a powerful defense method that can remove adversarial perturbations and generate a purified example without threats. In principle, the pre-trained DMs can only ensure that purified examples conform to the same distribution of the training data, but it may inadvertently compromise the semantic information of input examples, leading to misclassification of purified examples. Recent advancements introduce guided diffusion techniques to preserve semantic information while removing the perturbations. However, these guidances often rely on distance measures between purified examples and diffused examples, which can also preserve perturbations in purified examples. To further unleash the robustness power of DM-based AP, we propose an adversarial guided diffusion model (AGDM) by introducing a novel adversarial guidance that contains sufficient semantic information but does not explicitly involve adversarial perturbations. The guidance is modeled by an auxiliary neural network obtained with adversarial training, considering the distance in the latent representations rather than at the pixel-level values. Extensive experiments are conducted on CIFAR-10, CIFAR-100 and ImageNet to demonstrate that our method is effective for simultaneously maintaining semantic information and removing the adversarial perturbations. In addition, comprehensive comparisons show that our method significantly enhances the robustness of existing DM-based AP, with an average robust accuracy improved by up to 7.30% on CIFAR-10.

Zerui Tao, Toshihisa Tanaka, Qibin Zhao

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional TDs are explicitly or implicitly designed based on the Gaussian distribution, which is unsuitable for discrete data. Moreover, most TDs rely on predefined multi-linear structures, such as CP and Tucker formats. Therefore, they may not be effective enough to handle complex real-world datasets. To address these issues, we propose ENTED, an \underline{E}fficient \underline{N}onparametric \underline{TE}nsor \underline{D}ecomposition for binary and count tensors. Specifically, we first employ a nonparametric Gaussian process (GP) to replace traditional multi-linear structures. Next, we utilize the \pg augmentation which provides a unified framework to establish conjugate models for binary and count distributions. Finally, to address the computational issue of GPs, we enhance the model by incorporating sparse orthogonal variational inference of inducing points, which offers a more effective covariance approximation within GPs and stochastic natural gradient updates for nonparametric models. We evaluate our model on several real-world tensor completion tasks, considering binary and count datasets. The results manifest both better performance and computational advantages of the proposed model.

Zerui Tao, Toshihisa Tanaka, Qibin Zhao

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates and an effective approach for automatically adapting the tensor ring rank during the learning process. However, previous BTR method employs an Automatic Relevance Determination (ARD) prior, which can lead to sub-optimal solutions. Besides, it solely focuses on continuous data, whereas many applications involve discrete data. More importantly, it relies on the Coordinate-Ascent Variational Inference (CAVI) algorithm, which is inadequate for handling large tensors with extensive observations. These limitations greatly limit its application scales and scopes, making it suitable only for small-scale problems, such as image/video completion. To address these issues, we propose a novel BTR model that incorporates a nonparametric Multiplicative Gamma Process (MGP) prior, known for its superior accuracy in identifying latent structures. To handle discrete data, we introduce the Pólya-Gamma augmentation for closed-form updates. Furthermore, we develop an efficient Gibbs sampler for consistent posterior simulation, which reduces the computational complexity of previous VI algorithm by two orders, and an online EM algorithm that is scalable to extremely large tensors. To showcase the advantages of our model, we conduct extensive experiments on both simulation data and real-world applications.

Xuyang Zhao, Qibin Zhao, Toshihisa Tanaka

With large training datasets and massive amounts of computing sources, large language models (LLMs) achieve remarkable performance in comprehensive and generative ability. Based on those powerful LLMs, the model fine-tuned with domain-specific datasets posseses more specialized knowledge and thus is more practical like medical LLMs. However, the existing fine-tuned medical LLMs are limited to general medical knowledge with English language. For disease-specific problems, the model's response is inaccurate and sometimes even completely irrelevant, especially when using a language other than English. In this work, we focus on the particular disease of Epilepsy with Japanese language and introduce a customized LLM termed as EpilepsyLLM. Our model is trained from the pre-trained LLM by fine-tuning technique using datasets from the epilepsy domain. The datasets contain knowledge of basic information about disease, common treatment methods and drugs, and important notes in life and work. The experimental results demonstrate that EpilepsyLLM can provide more reliable and specialized medical knowledge responses.

Guanghao Li, Zhihui Fu, Min Fang et al.

As large language models (LLMs) scale up, accuracy improves, but the autoregressive (AR) nature of decoding increases latency since each token requires a serial forward pass. Speculative decoding addresses this by employing a fast drafter to propose multi-token drafts, which are then verified in parallel by the target model. However, many deployments still rely on AR drafters, where sequential passes limit wall-clock gains. We revisit the drafting stage and present DiffuSpec, a training-free drop-in framework that uses a pretrained diffusion language model (DLM) to produce multi-token drafts in a single forward pass, while remaining compatible with standard AR verifiers. Because DLM drafts are generated under bidirectional conditioning, parallel per-position candidates form a token lattice in which the locally highest-probability token at each position need not form a causal left-to-right path. Moreover, DLM drafting requires pre-specifying a draft length, inducing a speed-quality trade-off. To address these challenges, we introduce two practical components: (i) a causal-consistency path search (CPS) over this lattice that extracts a left-to-right path aligned with AR verification; and (ii) an adaptive draft-length (ADL) controller that adjusts next proposal size based on recent acceptance feedback and realized generated length. Across benchmarks, DiffuSpec yields up to 3x wall-clock speedup, establishing diffusion-based drafting as a robust alternative to autoregressive drafters for speculative decoding.

Guang Lin, Duc Thien Nguyen, Zerui Tao et al.

Deep neural networks are known to be vulnerable to well-designed adversarial attacks. Although numerous defense strategies have been proposed, many are tailored to the specific attacks or tasks and often fail to generalize across diverse scenarios. In this paper, we propose Tensor Network Purification (TNP), a novel model-free adversarial purification method by a specially designed tensor network decomposition algorithm. TNP depends neither on the pre-trained generative model nor the specific dataset, resulting in strong robustness across diverse adversarial scenarios. To this end, the key challenge lies in relaxing Gaussian-noise assumptions of classical decompositions and accommodating the unknown distribution of adversarial perturbations. Unlike the low-rank representation of classical decompositions, TNP aims to reconstruct the unobserved clean examples from an adversarial example. Specifically, TNP leverages progressive downsampling and introduces a novel adversarial optimization objective to address the challenge of minimizing reconstruction error but without inadvertently restoring adversarial perturbations. Extensive experiments conducted on CIFAR-10, CIFAR-100, and ImageNet demonstrate that our method generalizes effectively across various norm threats, attack types, and tasks, providing a versatile and promising adversarial purification technique.

Zerui Tao, Yuhta Takida, Naoki Murata et al.

Parameter-Efficient Fine-Tuning (PEFT) of text-to-image models has become an increasingly popular technique with many applications. Among the various PEFT methods, Low-Rank Adaptation (LoRA) and its variants have gained significant attention due to their effectiveness, enabling users to fine-tune models with limited computational resources. However, the approximation gap between the low-rank assumption and desired fine-tuning weights prevents the simultaneous acquisition of ultra-parameter-efficiency and better performance. To reduce this gap and further improve the power of LoRA, we propose a new PEFT method that combines two classes of adaptations, namely, transform and residual adaptations. In specific, we first apply a full-rank and dense transform to the pre-trained weight. This learnable transform is expected to align the pre-trained weight as closely as possible to the desired weight, thereby reducing the rank of the residual weight. Then, the residual part can be effectively approximated by more compact and parameter-efficient structures, with a smaller approximation error. To achieve ultra-parameter-efficiency in practice, we design highly flexible and effective tensor decompositions for both the transform and residual adaptations. Additionally, popular PEFT methods such as DoRA can be summarized under this transform plus residual adaptation scheme. Experiments are conducted on fine-tuning Stable Diffusion models in subject-driven and controllable generation. The results manifest that our method can achieve better performances and parameter efficiency compared to LoRA and several baselines.

Tenghui Li, Guoxu Zhou, Xuyang Zhao et al.

Large language models have demonstrated predictable scaling behaviors with respect to model parameters and training data. This study investigates whether a similar scaling relationship exist for vision-language models with respect to the number of vision tokens. A mathematical framework is developed to characterize a relationship between vision token number and the expected divergence of distance between vision-referencing sequences. The theoretical analysis reveals two distinct scaling regimes: sublinear scaling for less vision tokens and linear scaling for more vision tokens. This aligns with model performance relationships of the form \(S(n) \approx c / n^{α(n)}\), where the scaling exponent relates to the correlation structure between vision token representations. Empirical validations across multiple vision-language benchmarks show that model performance matches the prediction from scaling relationship. The findings contribute to understanding vision token scaling in transformers through a theoretical framework that complements empirical observations.

Jian Xu, Wei Chen, Shigui Li et al.

Diffusion models have achieved remarkable success in low-light image enhancement through Retinex-based decomposition, yet their requirement for hundreds of iterative sampling steps severely limits practical deployment. While recent consistency models offer promising one-step generation for \textit{unconditional synthesis}, their application to \textit{conditional enhancement} remains unexplored. We present \textbf{Consist-Retinex}, the first framework adapting consistency modeling to Retinex-based low-light enhancement. Our key insight is that conditional enhancement requires fundamentally different training dynamics than unconditional generation standard consistency training focuses on low-noise regions near the data manifold, while conditional mapping critically depends on large-noise regimes that bridge degraded inputs to enhanced outputs. We introduce two core innovations: (1) a \textbf{dual-objective consistency loss} combining temporal consistency with ground-truth alignment under randomized time sampling, providing full-spectrum supervision for stable convergence; and (2) an \textbf{adaptive noise-emphasized sampling strategy} that prioritizes training on large-noise regions essential for one-step conditional generation. On VE-LOL-L, Consist-Retinex achieves \textbf{state-of-the-art performance with single-step sampling} (\textbf{PSNR: 25.51 vs. 23.41, FID: 44.73 vs. 49.59} compared to Diff-Retinex++), while requiring only \textbf{1/8 of the training budget} relative to the 1000-step Diff-Retinex baseline.

Jian Xu, Qibin Zhao, John Paisley et al.

Deep Gaussian processes (DGPs) enable expressive hierarchical Bayesian modeling but pose substantial challenges for posterior inference, especially over inducing variables. Denoising diffusion variational inference (DDVI) addresses this by modeling the posterior as a time-reversed diffusion from a simple Gaussian prior. However, DDVI's fixed unconditional starting distribution remains far from the complex true posterior, resulting in inefficient inference trajectories and slow convergence. In this work, we propose Diffusion Bridge Variational Inference (DBVI), a principled extension of DDVI that initiates the reverse diffusion from a learnable, data-dependent initial distribution. This initialization is parameterized via an amortized neural network and progressively adapted using gradients from the ELBO objective, reducing the posterior gap and improving sample efficiency. To enable scalable amortization, we design the network to operate on the inducing inputs, which serve as structured, low-dimensional summaries of the dataset and naturally align with the inducing variables' shape. DBVI retains the mathematical elegance of DDVI, including Girsanov-based ELBOs and reverse-time SDEs,while reinterpreting the prior via a Doob-bridged diffusion process. We derive a tractable training objective under this formulation and implement DBVI for scalable inference in large-scale DGPs. Across regression, classification, and image reconstruction tasks, DBVI consistently outperforms DDVI and other variational baselines in predictive accuracy, convergence speed, and posterior quality.

Wei Chen, Shigui Li, Jiacheng Li et al.

Estimating density ratios is a fundamental problem in machine learning, but existing methods often trade off accuracy for efficiency. We propose \textit{Interval-annealed Secant Alignment Density Ratio Estimation (ISA-DRE)}, a framework that enables accurate, any-step estimation without numerical integration. Instead of modeling infinitesimal tangents as in prior methods, ISA-DRE learns a global secant function, defined as the expectation of all tangents over an interval, with provably lower variance, making it more suitable for neural approximation. This is made possible by the \emph{Secant Alignment Identity}, a self-consistency condition that formally connects the secant with its underlying tangent representations. To mitigate instability during early training, we introduce \emph{Contraction Interval Annealing}, a curriculum strategy that gradually expands the alignment interval during training. This process induces a contraction mapping, which improves convergence and training stability. Empirically, ISA-DRE achieves competitive accuracy with significantly fewer function evaluations compared to prior methods, resulting in much faster inference and making it well suited for real-time and interactive applications.

Jian Xu, Yican Liu, Qibin Zhao et al.

Learning stochastic functions from partially observed context-target pairs is a fundamental problem in probabilistic modeling. Traditional models like Gaussian Processes (GPs) face scalability issues with large datasets and assume Gaussianity, limiting their applicability. While Neural Processes (NPs) offer more flexibility, they struggle with capturing complex, multi-modal target distributions. Neural Diffusion Processes (NDPs) enhance expressivity through a learned diffusion process but rely solely on conditional signals in the denoising network, resulting in weak input coupling from an unconditional forward process and semantic mismatch at the diffusion endpoint. In this work, we propose Neural Bridge Processes (NBPs), a novel method for modeling stochastic functions where inputs x act as dynamic anchors for the entire diffusion trajectory. By reformulating the forward kernel to explicitly depend on x, NBP enforces a constrained path that strictly terminates at the supervised target. This approach not only provides stronger gradient signals but also guarantees endpoint coherence. We validate NBPs on synthetic data, EEG signal regression and image regression tasks, achieving substantial improvements over baselines. These results underscore the effectiveness of DDPM-style bridge sampling in enhancing both performance and theoretical consistency for structured prediction tasks.

Weichen Dai, Yuxuan Huang, Li Zhu et al.

Humans possess a remarkable capacity for spatial cognition, allowing for self-localization even in novel or unfamiliar environments. While hippocampal neurons encoding position and orientation are well documented, the large-scale neural dynamics supporting spatial representation, particularly during naturalistic, passive experience, remain poorly understood. Here, we demonstrate for the first time that non-invasive brain-computer interfaces (BCIs) based on electroencephalography (EEG) can decode spontaneous, fine-grained egocentric 6D pose, comprising three-dimensional position and orientation, during passive viewing of egocentric video. Despite EEG's limited spatial resolution and high signal noise, we find that spatially coherent visual input (i.e., continuous and structured motion) reliably evokes decodable spatial representations, aligning with participants' subjective sense of spatial engagement. Decoding performance further improves when visual input is presented at a frame rate of 100 ms per image, suggesting alignment with intrinsic neural temporal dynamics. Using gradient-based backpropagation through a neural decoding model, we identify distinct EEG channels contributing to position -- and orientation specific -- components, revealing a distributed yet complementary neural encoding scheme. These findings indicate that the brain's spatial systems operate spontaneously and continuously, even under passive conditions, challenging traditional distinctions between active and passive spatial cognition. Our results offer a non-invasive window into the automatic construction of egocentric spatial maps and advance our understanding of how the human mind transforms everyday sensory experience into structured internal representations.

Dai Shi, Zhiqi Shao, Yi Guo et al.

This paper presents a comprehensive theoretical analysis of the graph p-Laplacian regularized framelet network (pL-UFG) to establish a solid understanding of its properties. We conduct a convergence analysis on pL-UFG, addressing the gap in the understanding of its asymptotic behaviors. Further by investigating the generalized Dirichlet energy of pL-UFG, we demonstrate that the Dirichlet energy remains non-zero throughout convergence, ensuring the avoidance of over-smoothing issues. Additionally, we elucidate the energy dynamic perspective, highlighting the synergistic relationship between the implicit layer in pL-UFG and graph framelets. This synergy enhances the model's adaptability to both homophilic and heterophilic data. Notably, we reveal that pL-UFG can be interpreted as a generalized non-linear diffusion process, thereby bridging the gap between pL-UFG and differential equations on the graph. Importantly, these multifaceted analyses lead to unified conclusions that offer novel insights for understanding and implementing pL-UFG, as well as other graph neural network (GNN) models. Finally, based on our dynamic analysis, we propose two novel pL-UFG models with manually controlled energy dynamics. We demonstrate empirically and theoretically that our proposed models not only inherit the advantages of pL-UFG but also significantly reduce computational costs for training on large-scale graph datasets.

Yu-Bang Zheng, Xi-Le Zhao, Junhua Zeng et al.

Tensor network (TN) representation is a powerful technique for computer vision and machine learning. TN structure search (TN-SS) aims to search for a customized structure to achieve a compact representation, which is a challenging NP-hard problem. Recent "sampling-evaluation"-based methods require sampling an extensive collection of structures and evaluating them one by one, resulting in prohibitively high computational costs. To address this issue, we propose a novel TN paradigm, named SVD-inspired TN decomposition (SVDinsTN), which allows us to efficiently solve the TN-SS problem from a regularized modeling perspective, eliminating the repeated structure evaluations. To be specific, by inserting a diagonal factor for each edge of the fully-connected TN, SVDinsTN allows us to calculate TN cores and diagonal factors simultaneously, with the factor sparsity revealing a compact TN structure. In theory, we prove a convergence guarantee for the proposed method. Experimental results demonstrate that the proposed method achieves approximately 100 to 1000 times acceleration compared to the state-of-the-art TN-SS methods while maintaining a comparable level of representation ability.

Yuyuan Yu, Guoxu Zhou, Haonan Huang et al.

Distinguishing the importance of views has proven to be quite helpful for semi-supervised multi-view learning models. However, existing strategies cannot take advantage of semi-supervised information, only distinguishing the importance of views from a data feature perspective, which is often influenced by low-quality views then leading to poor performance. In this paper, by establishing a link between labeled data and the importance of different views, we propose an auto-weighted strategy to evaluate the importance of views from a label perspective to avoid the negative impact of unimportant or low-quality views. Based on this strategy, we propose a transductive semi-supervised auto-weighted multi-view classification model. The initialization of the proposed model can be effectively determined by labeled data, which is practical. The model is decoupled into three small-scale sub-problems that can efficiently be optimized with a local convergence guarantee. The experimental results on classification tasks show that the proposed method achieves optimal or sub-optimal classification accuracy at the lowest computational cost compared to other related methods, and the weight change experiments show that our proposed strategy can distinguish view importance more accurately than other related strategies on multi-view datasets with low-quality views.

Yuning Qiu, Guoxu Zhou, Zhenhao Huang et al.

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor recovery tasks. However, due to the large-scale tensor data in real-world applications, previous TRPCA models often suffer from high computational complexity. In this letter, we propose an efficient TRPCA under hybrid model of Tucker and TT. Specifically, in theory we reveal that TT nuclear norm (TTNN) of the original big tensor can be equivalently converted to that of a much smaller tensor via a Tucker compression format, thereby significantly reducing the computational cost of singular value decomposition (SVD). Numerical experiments on both synthetic and real-world tensor data verify the superiority of the proposed model.

Tenghui Li, Guoxu Zhou, Yuning Qiu et al.

We make an attempt to understanding convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall characteristics of neural networks without being disturbed by the horribly complex architectures. Specifically, we attempt to convert the basic structures of a convolutional neural network (CNN) and their combinations to the form of Volterra convolutions. The results show that most of convolutional neural networks can be approximated in the form of Volterra convolution, where the approximated proxy kernels preserve the characteristics of the original network. Analyzing these proxy kernels may give valuable insight about the original network. Base on this setup, we presented methods to approximating the order-zero and order-one proxy kernels, and verified the correctness and effectiveness of our results.

Xinhai Zhao, Yuyuan Yu, Guoxu Zhou et al.

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data. However, the existing methods such as graph regularized tensor ring decomposition (GNTR) only models the pair-wise similarities of objects. For tensor data with complex manifold structure, the graph can not exactly construct similarity relationships. In this paper, in order to effectively utilize the higher-dimensional and complicated similarities among objects, we introduce hypergraph to the framework of NTR to further enhance the feature extraction, upon which a hypergraph regularized nonnegative tensor ring decomposition (HGNTR) method is developed. To reduce the computational complexity and suppress the noise, we apply the low-rank approximation trick to accelerate HGNTR (called LraHGNTR). Our experimental results show that compared with other state-of-the-art algorithms, the proposed HGNTR and LraHGNTR can achieve higher performance in clustering tasks, in addition, LraHGNTR can greatly reduce running time without decreasing accuracy.

Hejia Qiu, Chao Li, Ying Weng et al.

Tensor-power (TP) recurrent model is a family of non-linear dynamical systems, of which the recurrence relation consists of a p-fold (a.k.a., degree-p) tensor product. Despite such the model frequently appears in the advanced recurrent neural networks (RNNs), to this date there is limited study on its memory property, a critical characteristic in sequence tasks. In this work, we conduct a thorough investigation of the memory mechanism of TP recurrent models. Theoretically, we prove that a large degree p is an essential condition to achieve the long memory effect, yet it would lead to unstable dynamical behaviors. Empirically, we tackle this issue by extending the degree p from discrete to a differentiable domain, such that it is efficiently learnable from a variety of datasets. Taken together, the new model is expected to benefit from the long memory effect in a stable manner. We experimentally show that the proposed model achieves competitive performance compared to various advanced RNNs in both the single-cell and seq2seq architectures.

Cesar F. Caiafa, Ziyao Wang, Jordi Solé-Casals et al.

In this paper, the problem of training a classifier on a dataset with incomplete features is addressed. We assume that different subsets of features (random or structured) are available at each data instance. This situation typically occurs in the applications when not all the features are collected for every data sample. A new supervised learning method is developed to train a general classifier, such as a logistic regression or a deep neural network, using only a subset of features per sample, while assuming sparse representations of data vectors on an unknown dictionary. Sufficient conditions are identified, such that, if it is possible to train a classifier on incomplete observations so that their reconstructions are well separated by a hyperplane, then the same classifier also correctly separates the original (unobserved) data samples. Extensive simulation results on synthetic and well-known datasets are presented that validate our theoretical findings and demonstrate the effectiveness of the proposed method compared to traditional data imputation approaches and one state-of-the-art algorithm.

Wei He, Quanming Yao, Chao Li et al.

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) restoration, which includes the tasks of denoising, compressed HSI reconstruction and inpainting. Unfortunately, while its restoration performance benefits from more spectral bands, its runtime also substantially increases. In this paper, we claim that the HSI lies in a global spectral low-rank subspace, and the spectral subspaces of each full band patch group should lie in this global low-rank subspace. This motivates us to propose a unified paradigm combining the spatial and spectral properties for HSI restoration. The proposed paradigm enjoys performance superiority from the non-local spatial denoising and light computation complexity from the low-rank orthogonal basis exploration. An efficient alternating minimization algorithm with rank adaptation is developed. It is done by first solving a fidelity term-related problem for the update of a latent input image, and then learning a low-dimensional orthogonal basis and the related reduced image from the latent input image. Subsequently, non-local low-rank denoising is developed to refine the reduced image and orthogonal basis iteratively. Finally, the experiments on HSI denoising, compressed reconstruction, and inpainting tasks, with both simulated and real datasets, demonstrate its superiority with respect to state-of-the-art HSI restoration methods.

Yuyuan Yu, Guoxu Zhou, Ning Zheng et al.

Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition and graph regularized NTR (GNTR) decomposition are proposed, where the former equips TR decomposition with local feature extraction by imposing nonnegativity on the core tensors and the latter is additionally able to capture manifold geometry information of tensor data, both significantly extend the applications of TR decomposition for nonnegative multiway representation learning. Accelerated proximal gradient based methods are derived for NTR and GNTR. The experimental result demonstrate that the proposed algorithms can extract parts-based basis with rich colors and rich lines from tensor objects that provide more interpretable and meaningful representation, and hence yield better performance than the state-of-the-art tensor based methods in clustering and classification tasks.

Zihao Huang, Chao Li, Feng Duan et al.

It is a challenging task to restore images from their variants with combined distortions. In the existing works, a promising strategy is to apply parallel "operations" to handle different types of distortion. However, in the feature fusion phase, a small number of operations would dominate the restoration result due to the features' heterogeneity by different operations. To this end, we introduce the tensor 1x1 convolutional layer by imposing high-order tensor (outer) product, by which we not only harmonize the heterogeneous features but also take additional non-linearity into account. To avoid the unacceptable kernel size resulted from the tensor product, we construct the kernels with tensor network decomposition, which is able to convert the exponential growth of the dimension to linear growth. Armed with the new layer, we propose High-order OWAN for multi-distorted image restoration. In the numerical experiments, the proposed net outperforms the previous state-of-the-art and shows promising performance even in more difficult tasks.

Wei He, Yong Chen, Naoto Yokoya et al.

Hyperspectral super-resolution (HSR) fuses a low-resolution hyperspectral image (HSI) and a high-resolution multispectral image (MSI) to obtain a high-resolution HSI (HR-HSI). In this paper, we propose a new model, named coupled tensor ring factorization (CTRF), for HSR. The proposed CTRF approach simultaneously learns high spectral resolution core tensor from the HSI and high spatial resolution core tensors from the MSI, and reconstructs the HR-HSI via tensor ring (TR) representation (Figure~\ref{fig:framework}). The CTRF model can separately exploit the low-rank property of each class (Section \ref{sec:analysis}), which has been never explored in the previous coupled tensor model. Meanwhile, it inherits the simple representation of coupled matrix/CP factorization and flexible low-rank exploration of coupled Tucker factorization. Guided by Theorem~\ref{th:1}, we further propose a spectral nuclear norm regularization to explore the global spectral low-rank property. The experiments have demonstrated the advantage of the proposed nuclear norm regularized CTRF (NCTRF) as compared to previous matrix/tensor and deep learning methods.

Tatsuya Yokota, Hidekata Hontani, Qibin Zhao et al.

Deep image prior (DIP), which utilizes a deep convolutional network (ConvNet) structure itself as an image prior, has attracted attentions in computer vision and machine learning communities. It empirically shows the effectiveness of ConvNet structure for various image restoration applications. However, why the DIP works so well is still unknown, and why convolution operation is useful for image reconstruction or enhancement is not very clear. In this study, we tackle these questions. The proposed approach is dividing the convolution into ``delay-embedding'' and ``transformation (\ie encoder-decoder)'', and proposing a simple, but essential, image/tensor modeling method which is closely related to dynamical systems and self-similarity. The proposed method named as manifold modeling in embedded space (MMES) is implemented by using a novel denoising-auto-encoder in combination with multi-way delay-embedding transform. In spite of its simplicity, the image/tensor completion, super-resolution, deconvolution, and denoising results of MMES are quite similar even competitive to DIP in our extensive experiments, and these results would help us for reinterpreting/characterizing the DIP from a perspective of ``low-dimensional patch-manifold prior''.

Paul Pu Liang, Zhun Liu, Yao-Hung Hubert Tsai et al.

There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result of imperfect modalities, missing entries or noise corruption. To address these concerns, we present a regularization method based on tensor rank minimization. Our method is based on the observation that high-dimensional multimodal time series data often exhibit correlations across time and modalities which leads to low-rank tensor representations. However, the presence of noise or incomplete values breaks these correlations and results in tensor representations of higher rank. We design a model to learn such tensor representations and effectively regularize their rank. Experiments on multimodal language data show that our model achieves good results across various levels of imperfection.

Jinshi Yu, Chao Li, Qibin Zhao et al.

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally demanding. In addition, the determination of the optimal TR rank is a tough work in practice. To overcome these drawbacks, we first introduce a class of new tensor nuclear norms by using tensor circular unfolding. Then we theoretically establish connection between the rank of the circularly-unfolded matrices and the TR ranks. We also develop an efficient tensor completion algorithm by minimizing the proposed tensor nuclear norm. Extensive experimental results demonstrate that our proposed tensor completion method outperforms the conventional tensor completion methods in the image/video in-painting problem with striped missing values.

Giuseppe G. Calvi, Ahmad Moniri, Mahmoud Mahfouz et al.

This work aims to help resolve the two main stumbling blocks in the application of Deep Neural Networks (DNNs), that is, the exceedingly large number of trainable parameters and their physical interpretability. This is achieved through a tensor valued approach, based on the proposed Tucker Tensor Layer (TTL), as an alternative to the dense weight-matrices of DNNs. This allows us to treat the weight-matrices of general DNNs as a matrix unfolding of a higher order weight-tensor. By virtue of the compression properties of tensor decompositions, this enables us to introduce a novel and efficient framework for exploiting the multi-way nature of the weight-tensor in order to dramatically reduce the number of DNN parameters. We also derive the tensor valued back-propagation algorithm within the TTL framework, by extending the notion of matrix derivatives to tensors. In this way, the physical interpretability of the Tucker decomposition is exploited to gain physical insights into the NN training, through the process of computing gradients with respect to each factor matrix. The proposed framework is validated on both synthetic data, and the benchmark datasets MNIST, Fashion-MNIST, and CIFAR-10. Overall, through the ability to provide the relative importance of each data feature in training, the TTL back-propagation is shown to help mitigate the "black-box" nature inherent to NNs. Experiments also illustrate that the TTL achieves a 66.63-fold compression on MNIST and Fashion-MNIST, while, by simplifying the VGG-16 network, it achieves a 10\% speed up in training time, at a comparable performance.

Longhao Yuan, Chao Li, Jianting Cao et al.

Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR decomposition algorithms suffer from high computational cost when facing large-scale data. In this paper, taking advantages of the recently proposed tensor random projection method, we propose two TR decomposition algorithms. By employing random projection on every mode of the large-scale tensor, the TR decomposition can be processed at a much smaller scale. The simulation experiment shows that the proposed algorithms are $4-25$ times faster than traditional algorithms without loss of accuracy, and our algorithms show superior performance in deep learning dataset compression and hyperspectral image reconstruction experiments compared to other randomized algorithms.

Wei He, Quanming Yao, Chao Li et al.

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately, with more spectral bands for HSI, while the running time of these methods significantly increases, their denoising performance benefits little. In this paper, we claim that the HSI underlines a global spectral low-rank subspace, and the spectral subspaces of each full band patch groups should underlie this global low-rank subspace. This motivates us to propose a unified spatial-spectral paradigm for HSI denoising. As the new model is hard to optimize, we further propose an efficient algorithm for optimization, which is motivated by alternating minimization. This is done by first learning a low-dimensional projection and the related reduced image from the noisy HSI. Then, the non-local low-rank denoising and iterative regularization are developed to refine the reduced image and projection, respectively. Finally, experiments on synthetic and both real datasets demonstrate the superiority against the other state-of-the-arts HSI denoising methods.

Tomasz M. Rutkowski, Qibin Zhao, Masao S. Abe et al.

Dementia and especially Alzheimer's disease (AD) are the most common causes of cognitive decline in elderly people. A spread of the above mentioned mental health problems in aging societies is causing a significant medical and economic burden in many countries around the world. According to a recent World Health Organization (WHO) report, it is approximated that currently, worldwide, about 47 million people live with a dementia spectrum of neurocognitive disorders. This number is expected to triple by 2050, which calls for possible application of AI-based technologies to support an early screening for preventive interventions and a subsequent mental wellbeing monitoring as well as maintenance with so-called digital-pharma or beyond a pill therapeutical approaches. This paper discusses our attempt and preliminary results of brainwave (EEG) techniques to develop digital biomarkers for dementia progress detection and monitoring. We present an information geometry-based classification approach for automatic EEG-derived event related responses (ERPs) discrimination of low versus high task-load auditory or tactile stimuli recognition, of which amplitude and latency variabilities are similar to those in dementia. The discussed approach is a step forward to develop AI, and especially machine learning (ML) approaches, for the subsequent application to mild-cognitive impairment (MCI) and AD diagnostics.

Chao Li, Zhun Sun, Jinshi Yu et al.

Although the convolutional neural networks (CNNs) have become popular for various image processing and computer vision task recently, it remains a challenging problem to reduce the storage cost of the parameters for resource-limited platforms. In the previous studies, tensor decomposition (TD) has achieved promising compression performance by embedding the kernel of a convolutional layer into a low-rank subspace. However the employment of TD is naively on the kernel or its specified variants. Unlike the conventional approaches, this paper shows that the kernel can be embedded into more general or even random low-rank subspaces. We demonstrate this by compressing the convolutional layers via randomly-shuffled tensor decomposition (RsTD) for a standard classification task using CIFAR-10. In addition, we analyze how the spatial similarity of the training data influences the low-rank structure of the kernels. The experimental results show that the CNN can be significantly compressed even if the kernels are randomly shuffled. Furthermore, the RsTD-based method yields more stable classification accuracy than the conventional TD-based methods in a large range of compression ratios.

Longhao Yuan, Chao Li, Danilo Mandic et al.

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.