NFL: Robust Learned Index via Distribution TransformationShangyu Wu, Yufei Cui, Jinghuan Yu et al.
Recent works on learned index open a new direction for the indexing field. The key insight of the learned index is to approximate the mapping between keys and positions with piece-wise linear functions. Such methods require partitioning key space for a better approximation. Although lots of heuristics are proposed to improve the approximation quality, the bottleneck is that the segmentation overheads could hinder the overall performance. This paper tackles the approximation problem by applying a \textit{distribution transformation} to the keys before constructing the learned index. A two-stage Normalizing-Flow-based Learned index framework (NFL) is proposed, which first transforms the original complex key distribution into a near-uniform distribution, then builds a learned index leveraging the transformed keys. For effective distribution transformation, we propose a Numerical Normalizing Flow (Numerical NF). Based on the characteristics of the transformed keys, we propose a robust After-Flow Learned Index (AFLI). To validate the performance, comprehensive evaluations are conducted on both synthetic and real-world workloads, which shows that the proposed NFL produces the highest throughput and the lowest tail latency compared to the state-of-the-art learned indexes.
2.1CLJan 20
Top 10 Open Challenges Steering the Future of Diffusion Language Model and Its VariantsYunhe Wang, Kai Han, Huiling Zhen et al.
The paradigm of Large Language Models (LLMs) is currently defined by auto-regressive (AR) architectures, which generate text through a sequential ``brick-by-brick'' process. Despite their success, AR models are inherently constrained by a causal bottleneck that limits global structural foresight and iterative refinement. Diffusion Language Models (DLMs) offer a transformative alternative, conceptualizing text generation as a holistic, bidirectional denoising process akin to a sculptor refining a masterpiece. However, the potential of DLMs remains largely untapped as they are frequently confined within AR-legacy infrastructures and optimization frameworks. In this Perspective, we identify ten fundamental challenges ranging from architectural inertia and gradient sparsity to the limitations of linear reasoning that prevent DLMs from reaching their ``GPT-4 moment''. We propose a strategic roadmap organized into four pillars: foundational infrastructure, algorithmic optimization, cognitive reasoning, and unified multimodal intelligence. By shifting toward a diffusion-native ecosystem characterized by multi-scale tokenization, active remasking, and latent thinking, we can move beyond the constraints of the causal horizon. We argue that this transition is essential for developing next-generation AI capable of complex structural reasoning, dynamic self-correction, and seamless multimodal integration.
5.8LGJan 20
Diffusion In Diffusion: Reclaiming Global Coherence in Semi-Autoregressive DiffusionLinrui Ma, Yufei Cui, Kai Han et al.
One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while offering benefits, can cause models to lose this global coherence at the macro level. To regain global contextual understanding while preserving the advantages of the semi-autoregressive paradigm, we propose Diffusion in Diffusion, a 'draft-then-refine' framework designed to overcome the irreversibility and myopia problems inherent in block diffusion models. Our approach first employs block diffusion to generate rapid drafts using small blocks, then refines these drafts through global bidirectional diffusion with a larger bidirectional receptive field. We utilize snapshot confidence remasking to identify the most critical tokens that require modification, and apply mix-scale training to expand the block diffusion model's global capabilities. Empirical results demonstrate that our approach sets a new benchmark for discrete diffusion models on the OpenWebText dataset. Using only 26% of the fine-tuning budget of baseline models, we reduce generative perplexity from 25.7 to 21.9, significantly narrowing the performance gap with autoregressive models.
RALAD: Bridging the Real-to-Sim Domain Gap in Autonomous Driving with Retrieval-Augmented LearningJiacheng Zuo, Haibo Hu, Zikang Zhou et al.
In the pursuit of robust autonomous driving systems, models trained on real-world datasets often struggle to adapt to new environments, particularly when confronted with corner cases such as extreme weather conditions. Collecting these corner cases in the real world is non-trivial, which necessitates the use of simulators for validation. However,the high computational cost and the domain gap in data distribution have hindered the seamless transition between real and simulated driving scenarios. To tackle this challenge, we propose Retrieval-Augmented Learning for Autonomous Driving (RALAD), a novel framework designed to bridge the real-to-sim gap at a low cost. RALAD features three primary designs, including (1) domain adaptation via an enhanced Optimal Transport (OT) method that accounts for both individual and grouped image distances, (2) a simple and unified framework that can be applied to various models, and (3) efficient fine-tuning techniques that freeze the computationally expensive layers while maintaining robustness. Experimental results demonstrate that RALAD compensates for the performance degradation in simulated environments while maintaining accuracy in real-world scenarios across three different models. Taking Cross View as an example, the mIOU and mAP metrics in real-world scenarios remain stable before and after RALAD fine-tuning, while in simulated environments,the mIOU and mAP metrics are improved by 10.30% and 12.29%, respectively. Moreover, the re-training cost of our approach is reduced by approximately 88.1%. Our code is available at https://github.com/JiachengZuo/RALAD.git.
26.6SYMay 17, 2024
Large Language Model (LLM) for Telecommunications: A Comprehensive Survey on Principles, Key Techniques, and OpportunitiesHao Zhou, Chengming Hu, Ye Yuan et al.
Large language models (LLMs) have received considerable attention recently due to their outstanding comprehension and reasoning capabilities, leading to great progress in many fields. The advancement of LLM techniques also offers promising opportunities to automate many tasks in the telecommunication (telecom) field. After pre-training and fine-tuning, LLMs can perform diverse downstream tasks based on human instructions, paving the way to artificial general intelligence (AGI)-enabled 6G. Given the great potential of LLM technologies, this work aims to provide a comprehensive overview of LLM-enabled telecom networks. In particular, we first present LLM fundamentals, including model architecture, pre-training, fine-tuning, inference and utilization, model evaluation, and telecom deployment. Then, we introduce LLM-enabled key techniques and telecom applications in terms of generation, classification, optimization, and prediction problems. Specifically, the LLM-enabled generation applications include telecom domain knowledge, code, and network configuration generation. After that, the LLM-based classification applications involve network security, text, image, and traffic classification problems. Moreover, multiple LLM-enabled optimization techniques are introduced, such as automated reward function design for reinforcement learning and verbal reinforcement learning. Furthermore, for LLM-aided prediction problems, we discussed time-series prediction models and multi-modality prediction problems for telecom. Finally, we highlight the challenges and identify the future directions of LLM-enabled telecom networks.
A Fast Transformer-based General-Purpose Lossless CompressorYu Mao, Yufei Cui, Tei-Wei Kuo et al.
Deep-learning-based compressor has received interests recently due to much improved compression ratio. However, modern approaches suffer from long execution time. To ease this problem, this paper targets on cutting down the execution time of deep-learning-based compressors. Building history-dependencies sequentially (e.g., recurrent neural networks) is responsible for long inference latency. Instead, we introduce transformer into deep learning compressors to build history-dependencies in parallel. However, existing transformer is too heavy in computation and incompatible to compression tasks. This paper proposes a fast general-purpose lossless compressor, TRACE, by designing a compression-friendly structure based on a single-layer transformer. We first design a new metric to advise the selection part of compression model structures. Byte-grouping and Shared-ffn schemes are further proposed to fully utilize the capacity of the single-layer transformer. These features allow TRACE to achieve competitive compression ratio and a much faster speed. In addition, we further accelerate the compression procedure by designing a controller to reduce the parameter updating overhead. Experiments show that TRACE achieves an overall $\sim$3x speedup while keeps a comparable compression ratio to the state-of-the-art compressors. The source code for TRACE and links to the datasets are available at https://github.com/mynotwo/A-Fast-Transformer-based-General-Purpose-LosslessCompressor.
1.4LGJan 22
Beyond Hard Writes and Rigid Preservation: Soft Recursive Least-Squares for Lifelong LLM EditingXinyu Wang, Sicheng Lyu, Yu Gu et al.
Model editing updates a pre-trained LLM with new facts or rules without re-training, while preserving unrelated behavior. In real deployment, edits arrive as long streams, and existing editors often face a plasticity-stability dilemma: locate-then-edit "hard writes" can accumulate interference over time, while null-space-style "hard preservation" preserves only what is explicitly constrained, so past edits can be overwritten and unconstrained behaviors may deviate, degrading general capabilities in the many-edits regime. We propose RLSEdit, a recursive least-squares editor for long sequential editing. RLSEdit formulates editing as an online quadratic optimization with soft constraints, minimizing a cumulative key-value fitting objective with two regularizers that control for both deviation from the pre-trained weights and from a designated anchor mapping. The resulting update admits an efficient online recursion via the Woodbury identity, with per-edit cost independent of history length and scaling only with the current edit size. We further provide deviation bounds and an asymptotic characterization of the adherence-preservation trade-off in the many-edits regime. Experiments on multiple model families demonstrate stable scaling to 10K edits, outperforming strong baselines in both edit success and holistic stability -- crucially retaining early edits, and preserving general capabilities on GLUE and held-out reasoning/code benchmarks.
The Pitfalls and Promise of Conformal Inference Under Adversarial AttacksZiquan Liu, Yufei Cui, Yan Yan et al.
In safety-critical applications such as medical imaging and autonomous driving, where decisions have profound implications for patient health and road safety, it is imperative to maintain both high adversarial robustness to protect against potential adversarial attacks and reliable uncertainty quantification in decision-making. With extensive research focused on enhancing adversarial robustness through various forms of adversarial training (AT), a notable knowledge gap remains concerning the uncertainty inherent in adversarially trained models. To address this gap, this study investigates the uncertainty of deep learning models by examining the performance of conformal prediction (CP) in the context of standard adversarial attacks within the adversarial defense community. It is first unveiled that existing CP methods do not produce informative prediction sets under the commonly used $l_{\infty}$-norm bounded attack if the model is not adversarially trained, which underpins the importance of adversarial training for CP. Our paper next demonstrates that the prediction set size (PSS) of CP using adversarially trained models with AT variants is often worse than using standard AT, inspiring us to research into CP-efficient AT for improved PSS. We propose to optimize a Beta-weighting loss with an entropy minimization regularizer during AT to improve CP-efficiency, where the Beta-weighting loss is shown to be an upper bound of PSS at the population level by our theoretical analysis. Moreover, our empirical study on four image classification datasets across three popular AT baselines validates the effectiveness of the proposed Uncertainty-Reducing AT (AT-UR).
ReFusion: Improving Natural Language Understanding with Computation-Efficient Retrieval Representation FusionShangyu Wu, Ying Xiong, Yufei Cui et al.
Retrieval-based augmentations (RA) incorporating knowledge from an external database into language models have greatly succeeded in various knowledge-intensive (KI) tasks. However, integrating retrievals in non-knowledge-intensive (NKI) tasks is still challenging. Existing works focus on concatenating retrievals with inputs to improve model performance. Unfortunately, the use of retrieval concatenation-based augmentations causes an increase in the input length, substantially raising the computational demands of attention mechanisms. This paper proposes a new paradigm of RA named \textbf{ReFusion}, a computation-efficient Retrieval representation Fusion with bi-level optimization. Unlike previous works, ReFusion directly fuses the retrieval representations into the hidden states of models. Specifically, ReFusion leverages an adaptive retrieval integrator to seek the optimal combination of the proposed ranking schemes across different model layers. Experimental results demonstrate that the proposed ReFusion can achieve superior and robust performance in various NKI tasks.
2.6CLFeb 2
InfMem: Learning System-2 Memory Control for Long-Context AgentXinyu Wang, Mingze Li, Peng Lu et al.
Reasoning over ultra-long documents requires synthesizing sparse evidence scattered across distant segments under strict memory constraints. While streaming agents enable scalable processing, their passive memory update strategy often fails to preserve low-salience bridging evidence required for multi-hop reasoning. We propose InfMem, a control-centric agent that instantiates System-2-style control via a PreThink-Retrieve-Write protocol. InfMem actively monitors evidence sufficiency, performs targeted in-document retrieval, and applies evidence-aware joint compression to update a bounded memory. To ensure reliable control, we introduce a practical SFT-to-RL training recipe that aligns retrieval, writing, and stopping decisions with end-task correctness. On ultra-long QA benchmarks from 32k to 1M tokens, InfMem consistently outperforms MemAgent across backbones. Specifically, InfMem improves average absolute accuracy by +10.17, +11.84, and +8.23 points on Qwen3-1.7B, Qwen3-4B, and Qwen2.5-7B, respectively, while reducing inference time by $3.9\times$ on average (up to $5.1\times$) via adaptive early stopping.
12.3ROMar 29, 2025
VLM-C4L: Continual Core Dataset Learning with Corner Case Optimization via Vision-Language Models for Autonomous DrivingHaibo Hu, Jiacheng Zuo, Yang Lou et al.
With the widespread adoption and deployment of autonomous driving, handling complex environments has become an unavoidable challenge. Due to the scarcity and diversity of extreme scenario datasets, current autonomous driving models struggle to effectively manage corner cases. This limitation poses a significant safety risk, according to the National Highway Traffic Safety Administration (NHTSA), autonomous vehicle systems have been involved in hundreds of reported crashes annually in the United States, occurred in corner cases like sun glare and fog, which caused a few fatal accident. Furthermore, in order to consistently maintain a robust and reliable autonomous driving system, it is essential for models not only to perform well on routine scenarios but also to adapt to newly emerging scenarios, especially those corner cases that deviate from the norm. This requires a learning mechanism that incrementally integrates new knowledge without degrading previously acquired capabilities. However, to the best of our knowledge, no existing continual learning methods have been proposed to ensure consistent and scalable corner case learning in autonomous driving. To address these limitations, we propose VLM-C4L, a continual learning framework that introduces Vision-Language Models (VLMs) to dynamically optimize and enhance corner case datasets, and VLM-C4L combines VLM-guided high-quality data extraction with a core data replay strategy, enabling the model to incrementally learn from diverse corner cases while preserving performance on previously routine scenarios, thus ensuring long-term stability and adaptability in real-world autonomous driving. We evaluate VLM-C4L on large-scale real-world autonomous driving datasets, including Waymo and the corner case dataset CODA.
2.4AIJan 14
Thinking Long, but Short: Stable Sequential Test-Time Scaling for Large Reasoning ModelsMichael R. Metel, Yufei Cui, Boxing Chen et al.
Sequential test-time scaling is a promising training-free method to improve large reasoning model accuracy, but as currently implemented, significant limitations have been observed. Inducing models to think for longer can increase their accuracy, but as the length of reasoning is further extended, it has also been shown to result in accuracy degradation and model instability. This work presents a novel sequential test-time scaling method, Min-Seek, which improves model accuracy significantly over a wide range of induced thoughts, stabilizing the accuracy of sequential scaling, and removing the need for reasoning length fine-tuning. Beyond improving model accuracy over a variety of reasoning tasks, our method is inherently efficient, as only the KV pairs of one additional induced thought are kept in the KV cache during reasoning. With a custom KV cache which stores keys without position embeddings, by dynamically encoding them contiguously before each new generated thought, our method can continue to reason well beyond a model's maximum context length, and under mild conditions has linear computational complexity.
7.8ROOct 2, 2025
Nav-EE: Navigation-Guided Early Exiting for Efficient Vision-Language Models in Autonomous DrivingHaibo Hu, Lianming Huang, Xinyu Wang et al.
Vision-Language Models (VLMs) are increasingly applied in autonomous driving for unified perception and reasoning, but high inference latency hinders real-time deployment. Early-exit reduces latency by terminating inference at intermediate layers, yet its task-dependent nature limits generalization across diverse scenarios. We observe that this limitation aligns with autonomous driving: navigation systems can anticipate upcoming contexts (e.g., intersections, traffic lights), indicating which tasks will be required. We propose Nav-EE, a navigation-guided early-exit framework that precomputes task-specific exit layers offline and dynamically applies them online based on navigation priors. Experiments on CODA, Waymo, and BOSCH show that Nav-EE achieves accuracy comparable to full inference while reducing latency by up to 63.9%. Real-vehicle integration with Autoware Universe further demonstrates reduced inference latency (600ms to 300ms), supporting faster decision-making in complex scenarios. These results suggest that coupling navigation foresight with early-exit offers a viable path toward efficient deployment of large models in autonomous systems. Code and data are available at our anonymous repository: https://anonymous.4open.science/r/Nav-EE-BBC4
14.4LGSep 30, 2025
GRPO-$λ$: Credit Assignment improves LLM ReasoningPrasanna Parthasarathi, Mathieu Reymond, Boxing Chen et al. · mila
Large language models (LLMs) are increasingly deployed for tasks requiring complex reasoning, prompting significant interest in improving their reasoning abilities through post-training. Especially RL based methods using verifiable reward, like the state-of-the-art GRPO, have shown to tremendously improve reasoning behaviors when applied as post-training methods. However, the lack of an explicit reward or critic model limits GRPO's ability to assign fine-grained credit across token sequences. In this work, we present GRPO-$λ$, a novel extension to GRPO that enhances credit assignment in RL finetuning of LLMs for complex reasoning tasks. We approximate learning from $λ$-return with a reformulation of eligibility traces using token-level log-probabilities applied after each sequence generation, and a novel critic-free approximation of the temporal-difference error. We introduce a few variations for the weighting of the $λ$-return, and their applications to the eligibility-trace, where all the variations provide significant gains over GRPO. We compare GRPO-$λ$ against GRPO by training models from 1.5B to 7B parameters on $4$ different math reasoning datasets. The training plots demonstrate 30-40% improved performance during RL training on both LLaMA-3.1 and Qwen-2.5 architectures. Finally, we show that with GRPO-$λ$, the resulting average performance on AIME24, Math500, OlympiadMath, MinervaMath, and AMC improves over GRPO by over $3$ points and a $4.5$ points improvement on the 7B model.
2.7CLAug 20, 2025
Beyond Semantic Similarity: Reducing Unnecessary API Calls via Behavior-Aligned RetrieverYixin Chen, Ying Xiong, Shangyu Wu et al.
Tool-augmented large language models (LLMs) leverage external functions to extend their capabilities, but inaccurate function calls can lead to inefficiencies and increased costs.Existing methods address this challenge by fine-tuning LLMs or using demonstration-based prompting, yet they often suffer from high training overhead and fail to account for inconsistent demonstration samples, which misguide the model's invocation behavior. In this paper, we trained a behavior-aligned retriever (BAR), which provides behaviorally consistent demonstrations to help LLMs make more accurate tool-using decisions. To train the BAR, we construct a corpus including different function-calling behaviors, i.e., calling or non-calling.We use the contrastive learning framework to train the BAR with customized positive/negative pairs and a dual-negative contrastive loss, ensuring robust retrieval of behaviorally consistent examples.Experiments demonstrate that our approach significantly reduces erroneous function calls while maintaining high task performance, offering a cost-effective and efficient solution for tool-augmented LLMs.
3.6CVJun 4, 2025
AD-EE: Early Exiting for Fast and Reliable Vision-Language Models in Autonomous DrivingLianming Huang, Haibo Hu, Yufei Cui et al.
With the rapid advancement of autonomous driving, deploying Vision-Language Models (VLMs) to enhance perception and decision-making has become increasingly common. However, the real-time application of VLMs is hindered by high latency and computational overhead, limiting their effectiveness in time-critical driving scenarios. This challenge is particularly evident when VLMs exhibit over-inference, continuing to process unnecessary layers even after confident predictions have been reached. To address this inefficiency, we propose AD-EE, an Early Exit framework that incorporates domain characteristics of autonomous driving and leverages causal inference to identify optimal exit layers. We evaluate our method on large-scale real-world autonomous driving datasets, including Waymo and the corner-case-focused CODA, as well as on a real vehicle running the Autoware Universe platform. Extensive experiments across multiple VLMs show that our method significantly reduces latency, with maximum improvements reaching up to 57.58%, and enhances object detection accuracy, with maximum gains of up to 44%.
3.6CVMay 15, 2025
Advancing Multiple Instance Learning with Continual Learning for Whole Slide ImagingXianrui Li, Yufei Cui, Jun Li et al.
Advances in medical imaging and deep learning have propelled progress in whole slide image (WSI) analysis, with multiple instance learning (MIL) showing promise for efficient and accurate diagnostics. However, conventional MIL models often lack adaptability to evolving datasets, as they rely on static training that cannot incorporate new information without extensive retraining. Applying continual learning (CL) to MIL models is a possible solution, but often sees limited improvements. In this paper, we analyze CL in the context of attention MIL models and find that the model forgetting is mainly concentrated in the attention layers of the MIL model. Using the results of this analysis we propose two components for improving CL on MIL: Attention Knowledge Distillation (AKD) and the Pseudo-Bag Memory Pool (PMP). AKD mitigates catastrophic forgetting by focusing on retaining attention layer knowledge between learning sessions, while PMP reduces the memory footprint by selectively storing only the most informative patches, or ``pseudo-bags'' from WSIs. Experimental evaluations demonstrate that our method significantly improves both accuracy and memory efficiency on diverse WSI datasets, outperforming current state-of-the-art CL methods. This work provides a foundation for CL in large-scale, weakly annotated clinical datasets, paving the way for more adaptable and resilient diagnostic models.
GeneQuery: A General QA-based Framework for Spatial Gene Expression Predictions from Histology ImagesYing Xiong, Linjing Liu, Yufei Cui et al.
Gene expression profiling provides profound insights into molecular mechanisms, but its time-consuming and costly nature often presents significant challenges. In contrast, whole-slide hematoxylin and eosin (H&E) stained histological images are readily accessible and allow for detailed examinations of tissue structure and composition at the microscopic level. Recent advancements have utilized these histological images to predict spatially resolved gene expression profiles. However, state-of-the-art works treat gene expression prediction as a multi-output regression problem, where each gene is learned independently with its own weights, failing to capture the shared dependencies and co-expression patterns between genes. Besides, existing works can only predict gene expression values for genes seen during training, limiting their ability to generalize to new, unseen genes. To address the above limitations, this paper presents GeneQuery, which aims to solve this gene expression prediction task in a question-answering (QA) manner for better generality and flexibility. Specifically, GeneQuery takes gene-related texts as queries and whole-slide images as contexts and then predicts the queried gene expression values. With such a transformation, GeneQuery can implicitly estimate the gene distribution by introducing the gene random variable. Besides, the proposed GeneQuery consists of two architecture implementations, i.e., spot-aware GeneQuery for capturing patterns between images and gene-aware GeneQuery for capturing patterns between genes. Comprehensive experiments on spatial transcriptomics datasets show that the proposed GeneQuery outperforms existing state-of-the-art methods on known and unseen genes. More results also demonstrate that GeneQuery can potentially analyze the tissue structure.
2.0CVApr 17, 2024
BAHOP: Similarity-based Basin Hopping for A fast hyper-parameter search in WSI classificationJun Wang, Yu Mao, Yufei Cui et al.
Pre-processing whole slide images (WSIs) can impact classification performance. Our study shows that using fixed hyper-parameters for pre-processing out-of-domain WSIs can significantly degrade performance. Therefore, it is critical to search domain-specific hyper-parameters during inference. However, searching for an optimal parameter set is time-consuming. To overcome this, we propose BAHOP, a novel Similarity-based Basin Hopping optimization for fast parameter tuning to enhance inference performance on out-of-domain data. The proposed BAHOP achieves 5\% to 30\% improvement in accuracy with $\times5$ times faster on average.
4.4LGFeb 6, 2021
Weight Rescaling: Effective and Robust Regularization for Deep Neural Networks with Batch NormalizationZiquan Liu, Yufei Cui, Jia Wan et al.
Weight decay is often used to ensure good generalization in the training practice of deep neural networks with batch normalization (BN-DNNs), where some convolution layers are invariant to weight rescaling due to the normalization. In this paper, we demonstrate that the practical usage of weight decay still has some unsolved problems in spite of existing theoretical work on explaining the effect of weight decay in BN-DNNs. On the one hand, when the non-adaptive learning rate e.g. SGD with momentum is used, the effective learning rate continues to increase even after the initial training stage, which leads to an overfitting effect in many neural architectures. On the other hand, in both SGDM and adaptive learning rate optimizers e.g. Adam, the effect of weight decay on generalization is quite sensitive to the hyperparameter. Thus, finding an optimal weight decay parameter requires extensive parameter searching. To address those weaknesses, we propose to regularize the weight norm using a simple yet effective weight rescaling (WRS) scheme as an alternative to weight decay. WRS controls the weight norm by explicitly rescaling it to the unit norm, which prevents a large increase to the gradient but also ensures a sufficiently large effective learning rate to improve generalization. On a variety of computer vision applications including image classification, object detection, semantic segmentation and crowd counting, we show the effectiveness and robustness of WRS compared with weight decay, implicit weight rescaling (weight standardization) and gradient projection (AdamP).
Variational Nested DropoutYufei Cui, Yu Mao, Ziquan Liu et al.
Nested dropout is a variant of dropout operation that is able to order network parameters or features based on the pre-defined importance during training. It has been explored for: I. Constructing nested nets: the nested nets are neural networks whose architectures can be adjusted instantly during testing time, e.g., based on computational constraints. The nested dropout implicitly ranks the network parameters, generating a set of sub-networks such that any smaller sub-network forms the basis of a larger one. II. Learning ordered representation: the nested dropout applied to the latent representation of a generative model (e.g., auto-encoder) ranks the features, enforcing explicit order of the dense representation over dimensions. However, the dropout rate is fixed as a hyper-parameter during the whole training process. For nested nets, when network parameters are removed, the performance decays in a human-specified trajectory rather than in a trajectory learned from data. For generative models, the importance of features is specified as a constant vector, restraining the flexibility of representation learning. To address the problem, we focus on the probabilistic counterpart of the nested dropout. We propose a variational nested dropout (VND) operation that draws samples of multi-dimensional ordered masks at a low cost, providing useful gradients to the parameters of nested dropout. Based on this approach, we design a Bayesian nested neural network that learns the order knowledge of the parameter distributions. We further exploit the VND under different generative models for learning ordered latent distributions. In experiments, we show that the proposed approach outperforms the nested network in terms of accuracy, calibration, and out-of-domain detection in classification tasks. It also outperforms the related generative models on data generation tasks.