Achieving a balance between low parameter count, reduced FLOPs, and high accuracy and throughput remains a central challenge in neural network design. To address this, we propose the partial channel mechanism (PCM), which leverages the inherent redundancy in feature map channels. PCM divides feature map channels into multiple groups, each processed by distinct operations such as convolution, attention, pooling, or identity mapping. Building on this, we introduce partial attention convolution (PATConv), a novel module that efficiently fuses convolution and visual attention within a unified framework. Our results demonstrate that PATConv can fully replace both standard convolution and visual attention modules, leading to significant reductions in parameters and FLOPs. Furthermore, PATConv enables three efficient visual attention variants: Partial Channel Attention, Partial Spatial Attention, and Partial Self-Attention. To further optimize the allocation of channel splits, we propose dynamic {partial convolution (DPConv), which adaptively learns the optimal split ratio for each layer, achieving a better trade-off between speed and accuracy. By integrating PATConv and DPConv, we develop a new hybrid network family, PartialNet, which achieves superior top-1 accuracy and inference speed on ImageNet-1K, and demonstrates strong performance on COCO detection and segmentation tasks.
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Model quantization is widely applied for compressing and accelerating deep neural networks (DNNs). However, conventional Quantization-Aware Training (QAT) focuses on training DNNs with uniform bit-width. The bit-width settings vary across different hardware and transmission demands, which induces considerable training and storage costs. Hence, the scheme of one-shot joint training multiple precisions is proposed to address this issue. Previous works either store a larger FP32 model to switch between different precision models for higher accuracy or store a smaller INT8 model but compromise accuracy due to using shared quantization parameters. In this paper, we introduce the Double Rounding quantization method, which fully utilizes the quantized representation range to accomplish nearly lossless bit-switching while reducing storage by using the highest integer precision instead of full precision. Furthermore, we observe a competitive interference among different precisions during one-shot joint training, primarily due to inconsistent gradients of quantization scales during backward propagation. To tackle this problem, we propose an Adaptive Learning Rate Scaling (AdaScale) technique that dynamically adapts learning rates for various precisions to optimize the training process. Additionally, we extend our Double Rounding to one-shot mixed precision training and develop a Hessian-Aware Stochastic Bit-switching (HessBit) strategy. Experimental results on the ImageNet-1K classification demonstrate that our methods have enough advantages to state-of-the-art one-shot joint QAT in both multi-precision and mixed-precision. We validate the feasibility of our method on detection and segmentation tasks, as well as on LLMs task.
Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophily
PDF ↗Graph Neural Networks (GNNs) have achieved significant success in addressing node classification tasks. However, the effectiveness of traditional GNNs degrades on heterophilic graphs, where connected nodes often belong to different labels or properties. While recent work has introduced mechanisms to improve GNN performance under heterophily, certain key limitations still exist. Most existing models apply a fixed aggregation depth across all nodes, overlooking the fact that nodes may require different propagation depths based on their local homophily levels and neighborhood structures. Moreover, many methods are tailored to either homophilic or heterophilic settings, lacking the flexibility to generalize across both regimes. To address these challenges, we develop a theoretical framework that links local structural and label characteristics to information propagation dynamics at the node level. Our analysis shows that optimal aggregation depth varies across nodes and is critical for preserving class-discriminative information. Guided by this insight, we propose a novel adaptive-depth GNN architecture that dynamically selects node-specific aggregation depths using theoretically grounded metrics. Our method seamlessly adapts to both homophilic and heterophilic patterns within a unified model. Extensive experiments demonstrate that our approach consistently enhances the performance of standard GNN backbones across diverse benchmarks.
A Stage-Aware Mixture of Experts Framework for Neurodegenerative Disease Progression Modelling
PDF ↗The long-term progression of neurodegenerative diseases is commonly conceptualized as a spatiotemporal diffusion process that consists of a graph diffusion process across the structural brain connectome and a localized reaction process within brain regions. However, modeling this progression remains challenging due to 1) the scarcity of longitudinal data obtained through irregular and infrequent subject visits and 2) the complex interplay of pathological mechanisms across brain regions and disease stages, where traditional models assume fixed mechanisms throughout disease progression. To address these limitations, we propose a novel stage-aware Mixture of Experts (MoE) framework that explicitly models how different contributing mechanisms dominate at different disease stages through time-dependent expert weighting. This architecture is a key innovation designed to maximize the utility of small datasets and provide interpretable insights into disease etiology. Data-wise, we utilize an iterative dual optimization method to properly estimate the temporal position of individual observations, constructing a cohort-level progression trajectory from irregular snapshots. Model-wise, we enhance the spatial component with an inhomogeneous graph neural diffusion model (IGND) that allows diffusivity to vary based on node states and time, providing more flexible representations of brain networks. We also introduce a localized neural reaction module to capture complex dynamics beyond standard processes.The resulting IGND-MoE model dynamically integrates these components across temporal states, offering a principled way to understand how stage-specific pathological mechanisms contribute to progression. When used to model tau pathology propagation in human brains, IGND-MoE outperforms purely pathophysiological and purely neural baselines in long-term prediction accuracy. Moreover, its stage-wise weights yield novel clinical insights that align with literature, suggesting that graph-related processes are more influential at early stages, while other unknown physical processes become dominant later on. Our findings highlight the necessity of designing hybrid and expert-constrained models that account for the evolving nature of neurodegenerative processes.
HiQ-Lip: A Hierarchical Quantum-Classical Method for Global Lipschitz Constant Estimation of ReLU Networks
PDF ↗Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities. However, precise calculations are NP-hard, and current semidefinite programming (SDP) methods face challenges such as high memory usage and slow processing speeds. In this paper, we propose HiQ-Lip, a hybrid quantum-classical hierarchical method that leverages Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant. We tackle the estimation by converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement a multilevel graph coarsening and refinement strategy to adapt to the constraints of contemporary quantum hardware. Our experimental evaluations on fully connected neural networks demonstrate that HiQ-Lip not only provides estimates comparable to state-of-the-art methods but also significantly accelerates the computation process. In specific tests involving two-layer neural networks with 256 hidden neurons, HiQ-Lip doubles the solving speed and offers more accurate upper bounds than the existing best method, LiPopt. These findings highlight the promising utility of small-scale quantum devices in advancing the estimation of neural network robustness.
As Convolutional Neural Networks (CNNs) continue to gain traction in deep learning, Winograd convolution has emerged as a key algorithm to enhance computational efficiency. Although ARM-based CPUs are increasingly prevalent in mobile devices, embedded systems and HPC servers, existing 2D Winograd convolution implementations for ARM often leave room for improvement in transformation efficiency, computational throughput, and overall versatility. Furthermore, the lack of tailored 3D Winograd convolution implementations for ARM architectures stems from the additional complexity of supporting higher-dimensional kernels. AirWino introduces a set of novel optimizations covering transformations, data layouts, micro-kernel computations, and parallelization strategies for both 2D and 3D Winograd convolution. It supports FP32 and FP16 precisions with filter sizes of 3 and 5, targeting a broad range of applications. Evaluations on four distinct ARM platforms show that AirWino consistently outperforms state-of-the-art libraries across various experimental scenarios and hardware configurations, highlighting its efficiency and portability.
The learning dynamics of modern neural networks remain an open problem in deep learning. The Neural Tangent Kernel (NTK) offers an elegant description of training dynamics in the infinite‑width limit, yet its classical formulation assumes a static data set. Modern model training practice departs from this strong assumption through the use of on‑the‑fly data augmentations (e.g. additive noise). In this work, we conduct an NTK-driven analysis of how data transformations affect a neural net's evolution in the function space. Our theoretical contributions characterize how repeated Gaussian perturbations from NTK-derived covariances can steer neural-net optimizations toward user‑specified behavior. These theoretical insights are empirically validated by controlled experiments. Taken together, our results lay the foundation for a promising future research direction that transforms the NTK from a descriptive to a prescriptive tool, enabling control of neural net training trajectories and behavior of inference generalization with grounded interventions.
Efficiently Seeking Flat Minima for Better Generalization in Fine-Tuning Large Language Models and Beyond
PDF ↗Little research explores the correlation between the expressive ability and generalization ability of the low-rank adaptation (LoRA). Sharpness-Aware Minimization (SAM) improves model generalization for both Convolutional Neural Networks (CNNs) and Transformers by encouraging convergence to locally flat minima. However, the connection between sharpness and generalization has not been fully explored for LoRA due to the lack of tools to either empirically seek flat minima or develop theoretical methods. In this work, we propose Flat Minima LoRA (FMLoRA) and its efficient version i.e., EFMLoRA, to seek flat minima for LoRA. Concretely, we theoretically demonstrate that perturbations in the full parameter space can be transferred to the low-rank subspace. This approach eliminates the potential interference introduced by perturbations across multiple matrices in the low-rank subspace. Our extensive experiments on large language models and vision-language models demonstrate that EFMLoRA achieves optimization efficiency comparable to that of LoRA while simultaneously attaining comparable or even better performance. For example, on the GLUE dataset with RoBERTa-large, EFMLoRA outperforms LoRA and full fine-tuning by 1.0% and 0.5% on average, respectively. On vision-language models e.g., Qwen-VL-Chat, there are performance improvements of 1.5% and 1.0% on the SQA and VizWiz datasets, respectively. These empirical results also verify that the generalization of LoRA is closely related to sharpness, which is omitted by previous methods.
Over-smoothing in Graph Neural Networks (GNNs) causes collapse in distinct node features, particularly on heterophilic graphs where adjacent nodes often have dissimilar labels. Although sheaf neural networks partially mitigate this problem, they typically rely on static or heavily parameterized sheaf structures that hinder generalization and scalability. Existing sheaf-based models either predefine restriction maps or introduce excessive complexity, yet fail to provide rigorous stability guarantees. In this paper, we introduce a novel scheme called SGPC (Sheaf GNNs with PAC-Bayes Calibration), a unified architecture that combines cellular-sheaf message passing with several mechanisms, including optimal transport-based lifting, variance-reduced diffusion, and PAC-Bayes spectral regularization for robust semi-supervised node classification. We establish performance bounds theoretically and demonstrate that end-to-end training in linear computational complexity can achieve the resulting bound-aware objective. Experiments on nine homophilic and heterophilic benchmarks show that SGPC outperforms state-of-the-art spectral and sheaf-based GNNs while providing certified confidence intervals on unseen nodes.
Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these methods effectively model the relationships between latent factors and the low-rank tensor using Dirac delta distributions. However, tensor low-rank decomposition is inherently non-unique, leading to a multimodal distribution over possible solutions. Critically, such prior knowledge is rarely available in practical scenarios, particularly regarding the optimal rank structure and contraction rules. To address this issue, we propose a score-based model that eliminates the need for predefined structural or distributional assumptions, enabling the learning of compatibility between tensors and latent factors. Specifically, a neural network is designed to learn the energy function, which is optimized via score matching to capture the gradient of the joint log-probability of tensor entries and latent factors. Our method allows for modeling structures and distributions beyond the Dirac delta assumption. Moreover, integrating the block coordinate descent (BCD) algorithm with the proposed smooth regularization enables the model to perform both tensor completion and denoising. Experimental results demonstrate significant performance improvements across various tensor types, including sparse and continuous-time tensors, as well as visual data.
Graph Neural Networks (GNNs) have received increasing attention due to their ability to handle graph-structured data, yet their explainability remains a significant challenge. An effective solution is to provide the GNN models with counterfactual explanations, which aim to answer “How should the input instance be perturbed to change the model's prediction?". However, existing works mainly focus on generating explanations that can effectively alter model predictions, while neglecting whether the explanations remain aligned with the original data distribution, leading to the distribution shift problem. To address this problem, we propose a novel method called ICExplainer for generating explanations within the original distribution. Specifically, we introduce graph diffusion-based generative model into the counterfactual reasoning, treating it as an optimization objective for graph distribution learning. Taking insights from variational inference, we use it to estimate the true distribution of the input graphs to retain essential structural and semantic information. The inferred distribution is then utilized as prior knowledge to guide the reverse process, ensuring that generated explanations are both counterfactual and distributionally coherent. Extensive experiments conducted on both synthetic and real-world datasets demonstrate the superior performance of ICExplainer over existing methods.
Mixed-precision quantization (MPQ) is crucial for deploying deep neural networks on resource-constrained devices, but finding the optimal bit-width for each layer represents a complex combinatorial optimization problem. Current state-of-the-art methods rely on computationally expensive search algorithms or local sensitivity heuristic proxies like the Hessian, which fail to capture the cascading global effects of quantization error. In this work, we argue that the quantization sensitivity of a layer should not be measured by its local properties, but by its impact on the information flow throughout the entire network. We introduce InfoQ, a novel framework for mixed-precision quantization that is training-free in the bit-width search phase. InfoQ assesses layer importance by performing a single forward pass to measure the change in mutual information in the remaining part of the network, thus creating a global sensitivity score. This approach directly quantifies how quantizing one layer degrades the information characteristics of subsequent layers. The resulting scores are used to formulate bit-width allocation as an integer linear programming problem, which is solved efficiently to minimize total sensitivity under a given budget (e.g., model size or BitOps). Our retraining-free search phase provides a superior search-time/accuracy trade-off (using two orders of magnitude less data compared to state-of-the-art methods such as LIMPQ), while yielding up to a 1% accuracy improvement for MobileNetV2 and ResNet18 on ImageNet at high compression rates (14.00x and 10.66x).
A novel learning-optimization-combined 4D radar odometry model, named DNOI-4DRO, is proposed in this paper. The proposed model seamlessly integrates traditional geometric optimization with end-to-end neural network training, leveraging an innovative differentiable neural-optimization iteration operator. In this framework, point-wise motion flow is first estimated using a neural network, followed by the construction of a cost function based on the relationship between point motion and pose in 3D space. The radar pose is then refined using Gauss-Newton updates. Additionally, we design a dual-stream 4D radar backbone that integrates multi-scale geometric features and clustering-based class-aware features to enhance the representation of sparse 4D radar point clouds. Extensive experiments on the VoD and Snail-Radar datasets demonstrate the superior performance of our model, which outperforms recent classical and learning-based approaches. Notably, our method even achieves results comparable to A-LOAM with mapping optimization using LiDAR point clouds as input.
Inferring Heterogeneous Private Valuations from Offline Market Data via Entropic Risk-Sensitive Utility Maximization
PDF ↗Inferring humans' private valuations for goods from their observed market behavior is essential for evaluating market efficiency and improving trading mechanism design. A core challenge lies in uncovering the human decision function that maps private valuations and observed market states to actions. In complex market settings where humans make sequential decisions in stochastic environments, neural networks offer the flexibility to model this decision function. However, training them without access to private valuations or environment dynamics remains challenging. We tackle this challenge and study how to infer heterogeneous human valuations from offline decision data in continuous double auctions. We propose learning the decision function via risk‑sensitive utility maximization. First, we train a generative model on offline bid and ask data to simulate individual trading behavior. Using this generative model, we instantiate simulated markets composed of randomly generated buyers and sellers. Second, we introduce an agent into these simulated markets and use reinforcement learning to learn a risk-sensitive utility-maximizing decision function for the agent. Third, we formulate a bilevel optimization to jointly recover private valuations and risk preference parameters. Our extensive experiments on a large‑scale continuous double auction dataset demonstrate that our framework significantly reduces errors in inferring real human valuations.
Graph Neural Networks (GNNs) have effectively improved the performance of Cognitive Diagnosis Models (CDMs). Existing works have proposed a series of Graph-based Cognitive Diagnosis Frameworks (GCDFs) to enhance robustness to noise. However, these robust designs are often general methods for GNNs and are not designed for cognitive diagnosis, which undermines real cognitive information during the denoising process. Interestingly, a noteworthy phenomenon has been overlooked: even without robustness designs, GCDFs can still learn correct information in noisy environments. In this paper, we conduct a comprehensive empirical analysis of this issue. We found that noise primarily accumulates in lower singular components. Even in noisy environments, the principal subspaces of representations still remain stable. Based on these findings, we propose a Noise-aware Cognitive Diagnostic framework based on Low-rank Alignment, named NCDLA. The framework first performs low-rank reconstruction of the interaction matrix between students and exercises, retaining only larger singular values to achieve noise reduction. Then, the reconstructed interaction matrix and the original interaction matrix are combined with the Q matrix to form a noise-reduced heterogeneous graph and an original heterogeneous graph. In order to distinguish between the interaction patterns of correct and incorrect responses, we decompose the heterogeneous graph according to the type of response. NCDLA achieves denoising of student representations and exercises representations through a self-supervised strategy based on low-rank reconstruction and a spectral anchor regularisation method. Extensive experiments on three datasets demonstrate that NCDLA achieves optimal prediction performance and robustness.
Multi-view clustering (MVC) seeks to uncover the intrinsic group structures embedded in multi-view data, which has attracted considerable attention in recent years. Existing approaches predominantly concentrate on incorporating suitable model priors to capture consistency across views. However, these explicit constraints often fail to hold in scenarios involving significant modal differences between views or the presence of noise, thereby limiting the efficacy of these methods in more complex contexts. To address these issues, this paper introduces BONE, a lightweight and interpretable MVC framework that Bridges Optimization and Neural networks for Efficient MVC. By leveraging learnable parameters to extract high-level features from low-level features derived through classical optimization, BONE integrates the consistency information across views without the need for explicit prior constraints, while eliminating the necessity for pre-training or post-processing. Extensive experiments show that BONE achieves clustering performance comparable to or even better than existing deep MVC methods, while using only 1% of the parameters, offering a new perspective for designing efficient MVC algorithms.
From Subtle to Significant: Prompt-Driven Self-Improving Optimization in Test-Time Graph OOD Detection
PDF ↗Graph Out-of-Distribution (OOD) detection aims to identify whether a test graph deviates from the distribution of graphs observed during training, which is critical for ensuring the reliability of Graph Neural Networks (GNNs) when deployed in open-world scenarios. Recent advances in graph OOD detection have focused on test-time training techniques that facilitate OOD detection without accessing potential supervisory information (e.g., training data). However, most of these methods employ a one-pass inference paradigm, which prevents them from progressively correcting erroneous predictions to amplify OOD signals. To this end, we propose a Self-Improving Graph Out-of-Distribution detector (SIGOOD), which is an unsupervised framework that integrates continuous self-learning with test-time training for effective graph OOD detection. Specifically, SIGOOD generates a prompt to construct a prompt-enhanced graph that amplifies potential OOD signals. To optimize prompts, SIGOOD introduces an Energy Preference Optimization (EPO) loss, which leverages energy variations between the original test graph and the prompt-enhanced graph. By iteratively optimizing the prompt by involving it into the detection model in a self-improving loop, the resulting optimal prompt-enhanced graph is ultimately used for OOD detection. Comprehensive evaluations on 21 real-world datasets confirm the effectiveness and outperformance of our SIGOOD method.
Graph anomaly detection is emerging as a critical technology for addressing increasingly complex and dynamic risk environments. Although unsupervised graph anomaly detection has advanced under the graph representation learning, directly applying these paradigms remains fundamentally misaligned with anomaly detection objectives. In this work, we highlight two key insights: graph neural networks are often suboptimal as feature extractors due to neighborhood aggregation diluting anomaly signals, and reliance on local inconsistency mining is inadequate for comprehensive anomaly detection, as it often fails to identify anomalies hidden within camouflaged communities. Based on these insights, we propose multiscale inconsistency learning for graph anomaly detection (MI-GAD), a novel framework that integrates both local and global anomaly signals. Specifically, individual node representations are projected onto a common hypersphere to ensure uniformity. At the local scale, the graph structure is leveraged for affinity-aware modeling via group discrimination. At the global scale, we introduce node deviation, a metric that distinguishes anomalies by optimizing representation centers. This unified approach enables robust and comprehensive detection of diverse graph anomalies. Experiments on seven real datasets demonstrate that our method consistently outperforms state-of-the-art baselines in both effectiveness and scalability.
T-SKM-Net: Trainable Neural Network Framework for Linear Constraint Satisfaction via Sampling Kaczmarz-Motzkin Method
PDF ↗Neural network constraint satisfaction is crucial for safety-critical applications such as power system optimization, robotic path planning, and autonomous driving. However, existing constraint satisfaction methods face efficiency-applicability trade-offs, with hard constraint methods suffering from either high computational complexity or restrictive assumptions on constraint structures. The Sampling Kaczmarz-Motzkin (SKM) method is a randomized iterative algorithm for solving large-scale linear inequality systems with favorable convergence properties, but its argmax operations introduce non-differentiability, posing challenges for neural network applications. This work proposes the Trainable Sampling Kaczmarz-Motzkin Network (T-SKM-Net) framework and, for the first time, systematically integrates SKM-type methods into neural network constraint satisfaction. The framework transforms mixed constraint problems into pure inequality problems through null space transformation, employs SKM for iterative solving, and maps solutions back to the original constraint space, efficiently handling both equality and inequality constraints. We provide theoretical proof of post-processing effectiveness in expectation and end-to-end trainability guarantees based on unbiased gradient estimators, demonstrating that despite non-differentiable operations, the framework supports standard backpropagation. On the DCOPF case118 benchmark, our method achieves 4.27ms/item GPU serial forward inference with 0.0025% max optimality gap with post-processing mode and 5.25ms/item with 0.0008% max optimality gap with joint training mode, delivering over 25× speedup compared to the pandapower solver while maintaining zero constraint violations under given tolerance.
Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this paper, we introduce a novel dual-decomposition framework that relaxes the single coupling equality u=x with an augmented Lagrange multiplier and splits the problem into a vanilla MIP and a constrained NN block. Each part is tackled by the solver that suits it best-branch and cut for the MIP subproblem, first-order optimisation for the NN subproblem, so the model remains modular, the number of integer variables never grows with network depth, and the per-iteration cost scales only linearly with the NN size. On the public SurrogateLIB benchmark, our method proves scalable, modular, and adaptable: it runs 120x faster than an exact Big-M formulation on the largest test case; the NN sub-solver can be swapped from a log-barrier interior step to a projected-gradient routine with no code changes; and swapping the MLP for an LSTM backbone still completes the full optimisation in 47s without any bespoke adaptation.