Ling Zhou

Qi Dong, Rubing Huang, Chenhui Cui et al.

Short-Term Electricity-Load Forecasting (STELF) refers to the prediction of the immediate demand (in the next few hours to several days) for the power system. Various external factors, such as weather changes and the emergence of new electricity consumption scenarios, can impact electricity demand, causing load data to fluctuate and become non-linear, which increases the complexity and difficulty of STELF. In the past decade, deep learning has been applied to STELF, modeling and predicting electricity demand with high accuracy, and contributing significantly to the development of STELF. This paper provides a comprehensive survey on deep-learning-based STELF over the past ten years. It examines the entire forecasting process, including data pre-processing, feature extraction, deep-learning modeling and optimization, and results evaluation. This paper also identifies some research challenges and potential research directions to be further investigated in future work.

Luis Scoccola, Hitesh Gakhar, Johnathan Bush et al.

The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a $1$-dimensional hole in the data; the output is a map from the data into the circle that captures this hole, and that is of minimum energy in a suitable sense. However, when applied to several cohomology classes, the output circle-valued maps can be "geometrically correlated" even if the chosen cohomology classes are linearly independent. It is shown in the original work that less correlated maps can be obtained with suitable integer linear combinations of the cohomology classes, with the linear combinations being chosen by inspection. In this paper, we identify a formal notion of geometric correlation between circle-valued maps which, in the Riemannian manifold case, corresponds to the Dirichlet form, a bilinear form derived from the Dirichlet energy. We describe a systematic procedure for constructing low energy torus-valued maps on data, starting from a set of linearly independent cohomology classes. We showcase our procedure with computational examples. Our main algorithm is based on the Lenstra--Lenstra--Lovász algorithm from computational number theory.

Ling Zhou, Mingpei Wang, Xiaohua Huang et al.

Micro-expression recognition (MER) in low-resolution (LR) scenarios presents an important and complex challenge, particularly for practical applications such as group MER in crowded environments. Despite considerable advancements in super-resolution techniques for enhancing the quality of LR images and videos, few study has focused on investigate super-resolution for improving LR MER. The scarcity of investigation can be attributed to the inherent difficulty in capturing the subtle motions of micro-expressions, even in original-resolution MER samples, which becomes even more challenging in LR samples due to the loss of distinctive features. Furthermore, a lack of systematic benchmarking and thorough analysis of super-resolution-assisted MER methods has been noted. This paper tackles these issues by conducting a series of benchmark experiments that integrate both super-resolution (SR) and MER methods, guided by an in-depth literature survey. Specifically, we employ seven cutting-edge state-of-the-art (SOTA) MER techniques and evaluate their performance on samples generated from 13 SOTA SR techniques, thereby addressing the problem of super-resolution in MER. Through our empirical study, we uncover the primary challenges associated with SR-assisted MER and identify avenues to tackle these challenges by leveraging recent advancements in both SR and MER methodologies. Our analysis provides insights for progressing toward more efficient SR-assisted MER.

Quanxing Xu, Yuhao Tian, Ling Zhou et al.

Visual Question Answering (VQA), as the representative multimodal task, serves as a key benchmark for evaluating the reasoning capabilities of Multimodal Large Language Models (MLLMs). However, existing evaluations largely rely on static datasets and accuracy-based metrics, which fail to capture robustness, consistency, and generalization. Inspired by Metamorphic Testing (MT), we propose Metamorphic Robustness Assessment (MetaRA), a testing framework that employs Metamorphic Relations (MRs) to systematically probe vulnerabilities in MLLM-based VQA systems. MetaRA generates controlled variations of image-question inputs based on specific MRs and evaluates models across diverse conditions. Applying MetaRA to multiple MLLM-based VQA models across different tasks reveals nuanced failure patterns, including sensitivity to linguistic perturbations, over-reliance on superficial visual cues, and deeper weaknesses in multimodal reasoning. Experimental results demonstrate that MetaRA provides richer diagnostic insights than conventional accuracy metrics, exposing failure modes that remain hidden under standard benchmarks. Overall, this work highlights the need for systematic robustness evaluation in VQA and positions metamorphic assessment as a scalable, model-agnostic approach toward trustworthy multimodal AI.

Hao Shu, Jicheng Li, Yu Jin et al.

Non-random missing data is a ubiquitous yet undertreated flaw in multidimensional time series, fundamentally threatening the reliability of data-driven analysis and decision-making. Pure low-rank tensor completion, as a classical data recovery method, falls short in handling non-random missingness, both methodologically and theoretically. Hankel-structured tensor completion models provide a feasible approach for recovering multidimensional time series with non-random missing patterns. However, most Hankel-based multidimensional data recovery methods both suffer from unclear sources of Hankel tensor low-rankness and lack an exact recovery theory for non-random missing data. To address these issues, we propose the temporal isometric delay-embedding transform, which constructs a Hankel tensor whose low-rankness is naturally induced by the smoothness and periodicity of the underlying time series. Leveraging this property, we develop the \textit{Low-Rank Tensor Completion with Temporal Isometric Delay-embedding Transform} (LRTC-TIDT) model, which characterizes the low-rank structure under the \textit{Tensor Singular Value Decomposition} (t-SVD) framework. Once the prescribed non-random sampling conditions and mild incoherence assumptions are satisfied, the proposed LRTC-TIDT model achieves exact recovery, as confirmed by simulation experiments under various non-random missing patterns. Furthermore, LRTC-TIDT consistently outperforms existing tensor-based methods across multiple real-world tasks, including network flow reconstruction, urban traffic estimation, and temperature field prediction. Our implementation is publicly available at https://github.com/HaoShu2000/LRTC-TIDT.

Zhenghan Tai, Hanwei Wu, Qingchen Hu et al.

Retrieval-Augmented Generation (RAG) is becoming increasingly essential for Question Answering (QA) in the financial sector, where accurate and contextually grounded insights from complex public disclosures are crucial. However, existing financial RAG systems face two significant challenges: (1) they struggle to process heterogeneous data formats, such as text, tables, and figures; and (2) they encounter difficulties in balancing general-domain applicability with company-specific adaptation. To overcome these challenges, we present VeritasFi, an innovative hybrid RAG framework that incorporates a multi-modal preprocessing pipeline alongside a cutting-edge two-stage training strategy for its re-ranking component. VeritasFi enhances financial QA through three key innovations: (1) A multi-modal preprocessing pipeline that seamlessly transforms heterogeneous data into a coherent, machine-readable format. (2) A tripartite hybrid retrieval engine that operates in parallel, combining deep multi-path retrieval over a semantically indexed document corpus, real-time data acquisition through tool utilization, and an expert-curated memory bank for high-frequency questions, ensuring comprehensive scope, accuracy, and efficiency. (3) A two-stage training strategy for the document re-ranker, which initially constructs a general, domain-specific model using anonymized data, followed by rapid fine-tuning on company-specific data for targeted applications. By integrating our proposed designs, VeritasFi presents a groundbreaking framework that greatly enhances the adaptability and robustness of financial RAG systems, providing a scalable solution for both general-domain and company-specific QA tasks. Code accompanying this work is available at https://github.com/simplew4y/VeritasFi.git.

Ling Zhou, Runtian Yuan, Yi Liu et al.

Ultrasound imaging is a prevalent diagnostic tool known for its simplicity and non-invasiveness. However, its inherent characteristics often introduce substantial noise, posing considerable challenges for automated lesion or organ segmentation in ultrasound video sequences. To address these limitations, we propose the Dual Semantic-Aware Network (DSANet), a novel framework designed to enhance noise robustness in ultrasound video segmentation by fostering mutual semantic awareness between local and global features. Specifically, we introduce an Adjacent-Frame Semantic-Aware (AFSA) module, which constructs a channel-wise similarity matrix to guide feature fusion across adjacent frames, effectively mitigating the impact of random noise without relying on pixel-level relationships. Additionally, we propose a Local-and-Global Semantic-Aware (LGSA) module that reorganizes and fuses temporal unconditional local features, which capture spatial details independently at each frame, with conditional global features that incorporate temporal context from adjacent frames. This integration facilitates multi-level semantic representation, significantly improving the model's resilience to noise interference. Extensive evaluations on four benchmark datasets demonstrate that DSANet substantially outperforms state-of-the-art methods in segmentation accuracy. Moreover, since our model avoids pixel-level feature dependencies, it achieves significantly higher inference FPS than video-based methods, and even surpasses some image-based models. Code can be found in \href{https://github.com/ZhouL2001/DSANet}{DSANet}

Quanxing Xu, Ling Zhou, Xian Zhong et al.

With advances in multimodal research and deep learning, Multimodal Large Language Models (MLLMs) have emerged as a powerful paradigm for a wide range of multimodal tasks. As a core problem in vision-language research, Visual Question Answering (VQA) has increasingly employed MLLMs to improve performance, particularly in open-domain settings where external knowledge is essential. In this work, we aim to further enhance retrieval-based VQA by more effectively integrating MLLMs with structured reasoning and knowledge acquisition. We introduce a logical prompting strategy that fuses Chain-of-Thought (CoT) reasoning with Visual Question Decomposition (VQD), termed CoVQD, to guide retrieval toward more accurate and relevant knowledge for MLLM inference. Building on this idea, we propose a new framework, CoVQD-guided RAG (CgRAG), which enables MLLMs to access more comprehensive and coherent external knowledge while benefiting from structured visual-text reasoning guidance, thereby improving generalization and reliability in complex cross-domain VQA scenarios. Extensive experiments on E-VQA, InfoSeek, and OKVQA benchmarks demonstrate the effectiveness of the proposed method.

Maoheng Li, Ling Zhou, Xiaohua Huang et al.

Multimodal sarcasm detection, which aims to precisely identify pragmatic incongruities between literal text and nonverbal cues, has gained substantial attention in multimodal understanding. Recent advancements have predominantly relied on na\"ıve similarity-based attention mechanisms and uniform late fusion strategies.Furthermore, given that functional entanglement restricts traditional late fusions, we incorporate a scalar congruity routing mechanism and a prior-guided contextual graph. This mechanism anchors a generalized incongruity manifold through a two-stage asymmetric optimization driven by inconsistency-aware contrastive learning, selectively fusing only the most discriminative multi-granularity evidence. Extensive experiments on the \texttt{MUStARD} benchmark and its spurious-correlation-mitigated balanced datasets demonstrate that our approach achieves new state-of-the-art performance, surpassing the strongest multimodal baseline by a substantial 3.14\% improvement in Macro-F1. By architecturally isolating atomic, composition, and contextual conflicts. This work provides a robust, decoupled paradigm for modeling subtle pragmatic incongruities in human communication.

Quanxing Xu, Ling Zhou, Feifei Zhang et al.

Large Language Models (LLMs) have become a crucial tool in Visual Question Answering (VQA) for handling knowledge-intensive questions in few-shot or zero-shot scenarios. However, their reliance on massive training datasets often causes them to inherit language biases during the acquisition of knowledge. This limitation imposes two key constraints on existing methods: (1) LLM predictions become less reliable due to bias exploitation, and (2) despite strong knowledge reasoning capabilities, LLMs still struggle with out-of-distribution (OOD) generalization. To address these issues, we propose Object Attribute Description Promoter (OAD-Promoter), a novel approach for enhancing LLM-based VQA by mitigating language bias and improving domain-shift robustness. OAD-Promoter comprises three components: the Object-concentrated Example Generation (OEG) module, the Memory Knowledge Assistance (MKA) module, and the OAD Prompt. The OEG module generates global captions and object-concentrated samples, jointly enhancing visual information input to the LLM and mitigating bias through complementary global and regional visual cues. The MKA module assists the LLM in handling OOD samples by retrieving relevant knowledge from stored examples to support questions from unseen domains. Finally, the OAD Prompt integrates the outputs of the preceding modules to optimize LLM inference. Experiments demonstrate that OAD-Promoter significantly improves the performance of LLM-based VQA methods in few-shot or zero-shot settings, achieving new state-of-the-art results.

Xinyu Wang, Jijun Chi, Zhenghan Tai et al.

Leveraging large language models in real-world settings often entails a need to utilize domain-specific data and tools in order to follow the complex regulations that need to be followed for acceptable use. Within financial sectors, modern enterprises increasingly rely on Retrieval-Augmented Generation (RAG) systems to address complex compliance requirements in financial document workflows. However, existing solutions struggle to account for the inherent heterogeneity of data (e.g., text, tables, diagrams) and evolving nature of regulatory standards used in financial filings, leading to compromised accuracy in critical information extraction. We propose the FinSage framework as a solution, utilizing a multi-aspect RAG framework tailored for regulatory compliance analysis in multi-modal financial documents. FinSage introduces three innovative components: (1) a multi-modal pre-processing pipeline that unifies diverse data formats and generates chunk-level metadata summaries, (2) a multi-path sparse-dense retrieval system augmented with query expansion (HyDE) and metadata-aware semantic search, and (3) a domain-specialized re-ranking module fine-tuned via Direct Preference Optimization (DPO) to prioritize compliance-critical content. Extensive experiments demonstrate that FinSage achieves an impressive recall of 92.51% on 75 expert-curated questions derived from surpasses the best baseline method on the FinanceBench question answering datasets by 24.06% in accuracy. Moreover, FinSage has been successfully deployed as financial question-answering agent in online meetings, where it has already served more than 1,200 people.

Runtian Yuan, Mohan Chen, Jilan Xu et al.

Referring Medical Image Sequence Segmentation (Ref-MISS) is a novel and challenging task that aims to segment anatomical structures in medical image sequences (\emph{e.g.} endoscopy, ultrasound, CT, and MRI) based on natural language descriptions. This task holds significant clinical potential and offers a user-friendly advancement in medical imaging interpretation. Existing 2D and 3D segmentation models struggle to explicitly track objects of interest across medical image sequences, and lack support for nteractive, text-driven guidance. To address these limitations, we propose Text-Promptable Propagation (TPP), a model designed for referring medical image sequence segmentation. TPP captures the intrinsic relationships among sequential images along with their associated textual descriptions. Specifically, it enables the recognition of referred objects through cross-modal referring interaction, and maintains continuous tracking across the sequence via Transformer-based triple propagation, using text embeddings as queries. To support this task, we curate a large-scale benchmark, Ref-MISS-Bench, which covers 4 imaging modalities and 20 different organs and lesions. Experimental results on this benchmark demonstrate that TPP consistently outperforms state-of-the-art methods in both medical segmentation and referring video object segmentation.

Xinyu Wang, Hanwei Wu, Qingchen Hu et al.

Decoder-only rerankers are central to Retrieval-Augmented Generation (RAG). However, generalist models miss domain-specific nuances in high-stakes fields like finance and law, and naive fine-tuning causes surface-form overfitting and catastrophic forgetting. To address this challenge, we introduce R2R, a domain-aware framework that combines dynamic expert routing with a two-stage training strategy, Entity Abstraction for Generalization (EAG). EAG introduces a counter-shortcut mechanism by masking the most predictive surface cues, forcing the reranker to learn domain-invariant relevance patterns rather than memorizing dataset-specific entities. To efficiently activate domain experts, R2R employs a lightweight Latent Semantic Router that probes internal representations from the frozen backbone decoder to select the optimal LoRA expert per query. Extensive experiments across different reranker backbones and diverse domains (legal, medical, and financial) demonstrate that R2R consistently surpasses generalist and single-domain fine-tuned baselines. Our results confirm that R2R is a model-agnostic and modular approach to domain specialization with strong cross-domain robustness.

Quanxing Xu, Ling Zhou, Xian Zhong et al.

Existing debiasing approaches in Visual Question Answering (VQA) primarily focus on enhancing visual learning, integrating auxiliary models, or employing data augmentation strategies. However, these methods exhibit two major drawbacks. First, current debiasing techniques fail to capture the superior relation between images and texts because prevalent learning frameworks do not enable models to extract deeper correlations from highly contrasting samples. Second, they do not assess the relevance between the input question and image during inference, as no prior work has examined the degree of input relevance in debiasing studies. Motivated by these limitations, we propose a novel framework, Optimized Question-Image Relation Learning (QIRL), which employs a generation-based self-supervised learning strategy. Specifically, two modules are introduced to address the aforementioned issues. The Negative Image Generation (NIG) module automatically produces highly irrelevant question-image pairs during training to enhance correlation learning, while the Irrelevant Sample Identification (ISI) module improves model robustness by detecting and filtering irrelevant inputs, thereby reducing prediction errors. Furthermore, to validate our concept of reducing output errors through filtering unrelated question-image inputs, we propose a specialized metric to evaluate the performance of the ISI module. Notably, our approach is model-agnostic and can be integrated with various VQA models. Extensive experiments on VQA-CPv2 and VQA-v2 demonstrate the effectiveness and generalization ability of our method. Among data augmentation strategies, our approach achieves state-of-the-art results.

Zhiyao Tan, Ling Zhou, Huazhen Lin

We investigate the impact of the input dimension on the generalization error in generative adversarial networks (GANs). In particular, we first provide both theoretical and practical evidence to validate the existence of an optimal input dimension (OID) that minimizes the generalization error. Then, to identify the OID, we introduce a novel framework called generalized GANs (G-GANs), which includes existing GANs as a special case. By incorporating the group penalty and the architecture penalty developed in the paper, G-GANs have several intriguing features. First, our framework offers adaptive dimensionality reduction from the initial dimension to a dimension necessary for generating the target distribution. Second, this reduction in dimensionality also shrinks the required size of the generator network architecture, which is automatically identified by the proposed architecture penalty. Both reductions in dimensionality and the generator network significantly improve the stability and the accuracy of the estimation and prediction. Theoretical support for the consistent selection of the input dimension and the generator network is provided. Third, the proposed algorithm involves an end-to-end training process, and the algorithm allows for dynamic adjustments between the input dimension and the generator network during training, further enhancing the overall performance of G-GANs. Extensive experiments conducted with simulated and benchmark data demonstrate the superior performance of G-GANs. In particular, compared to that of off-the-shelf methods, G-GANs achieves an average improvement of 45.68% in the CT slice dataset, 43.22% in the MNIST dataset and 46.94% in the FashionMNIST dataset in terms of the maximum mean discrepancy or Frechet inception distance. Moreover, the features generated based on the input dimensions identified by G-GANs align with visually significant features.

Wen Wang, Shihao Wu, Ziwei Zhu et al.

Fusing regression coefficients into homogenous groups can unveil those coefficients that share a common value within each group. Such groupwise homogeneity reduces the intrinsic dimension of the parameter space and unleashes sharper statistical accuracy. We propose and investigate a new combinatorial grouping approach called $L_0$-Fusion that is amenable to mixed integer optimization (MIO). On the statistical aspect, we identify a fundamental quantity called grouping sensitivity that underpins the difficulty of recovering the true groups. We show that $L_0$-Fusion achieves grouping consistency under the weakest possible requirement of the grouping sensitivity: if this requirement is violated, then the minimax risk of group misspecification will fail to converge to zero. Moreover, we show that in the high-dimensional regime, one can apply $L_0$-Fusion coupled with a sure screening set of features without any essential loss of statistical efficiency, while reducing the computational cost substantially. On the algorithmic aspect, we provide a MIO formulation for $L_0$-Fusion along with a warm start strategy. Simulation and real data analysis demonstrate that $L_0$-Fusion exhibits superiority over its competitors in terms of grouping accuracy.

Qirong Mao, Ling Zhou, Wenming Zheng et al.

Micro-expression recognition (\textbf{MER}) has attracted lots of researchers' attention in a decade. However, occlusion will occur for MER in real-world scenarios. This paper deeply investigates an interesting but unexplored challenging issue in MER, \ie, occlusion MER. First, to research MER under real-world occlusion, synthetic occluded micro-expression databases are created by using various mask for the community. Second, to suppress the influence of occlusion, a \underline{R}egion-inspired \underline{R}elation \underline{R}easoning \underline{N}etwork (\textbf{RRRN}) is proposed to model relations between various facial regions. RRRN consists of a backbone network, the Region-Inspired (\textbf{RI}) module and Relation Reasoning (\textbf{RR}) module. More specifically, the backbone network aims at extracting feature representations from different facial regions, RI module computing an adaptive weight from the region itself based on attention mechanism with respect to the unobstructedness and importance for suppressing the influence of occlusion, and RR module exploiting the progressive interactions among these regions by performing graph convolutions. Experiments are conducted on handout-database evaluation and composite database evaluation tasks of MEGC 2018 protocol. Experimental results show that RRRN can significantly explore the importance of facial regions and capture the cooperative complementary relationship of facial regions for MER. The results also demonstrate RRRN outperforms the state-of-the-art approaches, especially on occlusion, and RRRN acts more robust to occlusion.

Xiaoqing Tan, Chung-Chou H. Chang, Ling Zhou et al.

Accurately estimating personalized treatment effects within a study site (e.g., a hospital) has been challenging due to limited sample size. Furthermore, privacy considerations and lack of resources prevent a site from leveraging subject-level data from other sites. We propose a tree-based model averaging approach to improve the estimation accuracy of conditional average treatment effects (CATE) at a target site by leveraging models derived from other potentially heterogeneous sites, without them sharing subject-level data. To our best knowledge, there is no established model averaging approach for distributed data with a focus on improving the estimation of treatment effects. Specifically, under distributed data networks, our framework provides an interpretable tree-based ensemble of CATE estimators that joins models across study sites, while actively modeling the heterogeneity in data sources through site partitioning. The performance of this approach is demonstrated by a real-world study of the causal effects of oxygen therapy on hospital survival rate and backed up by comprehensive simulation results.

Ling Zhou, Qirong Mao, Xiaohua Huang et al.

Micro-Expression Recognition has become challenging, as it is extremely difficult to extract the subtle facial changes of micro-expressions. Recently, several approaches proposed several expression-shared features algorithms for micro-expression recognition. However, they do not reveal the specific discriminative characteristics, which lead to sub-optimal performance. This paper proposes a novel Feature Refinement ({FR}) with expression-specific feature learning and fusion for micro-expression recognition. It aims to obtain salient and discriminative features for specific expressions and also predict expression by fusing the expression-specific features. FR consists of an expression proposal module with attention mechanism and a classification branch. First, an inception module is designed based on optical flow to obtain expression-shared features. Second, in order to extract salient and discriminative features for specific expression, expression-shared features are fed into an expression proposal module with attention factors and proposal loss. Last, in the classification branch, labels of categories are predicted by a fusion of the expression-specific features. Experiments on three publicly available databases validate the effectiveness of FR under different protocol. Results on public benchmarks demonstrate that our FR provides salient and discriminative information for micro-expression recognition. The results also show our FR achieves better or competitive performance with the existing state-of-the-art methods on micro-expression recognition.

Ling Zhou, Qirong Mao, Ming Dong

Micro-Expression Recognition (MER) is a challenging task as the subtle changes occur over different action regions of a face. Changes in facial action regions are formed as Action Units (AUs), and AUs in micro-expressions can be seen as the actors in cooperative group activities. In this paper, we propose a novel deep neural network model for objective class-based MER, which simultaneously detects AUs and aggregates AU-level features into micro-expression-level representation through Graph Convolutional Networks (GCN). Specifically, we propose two new strategies in our AU detection module for more effective AU feature learning: the attention mechanism and the balanced detection loss function. With those two strategies, features are learned for all the AUs in a unified model, eliminating the error-prune landmark detection process and tedious separate training for each AU. Moreover, our model incorporates a tailored objective class-based AU knowledge-graph, which facilitates the GCN to aggregate the AU-level features into a micro-expression-level feature representation. Extensive experiments on two tasks in MEGC 2018 show that our approach significantly outperforms the current state-of-the-arts in MER. Additionally, we also report our single model-based micro-expression AU detection results.

Fei Wang, Ling Zhou, Lu Tang et al.

Simultaneous inference after model selection is of critical importance to address scientific hypotheses involving a set of parameters. In this paper, we consider high-dimensional linear regression model in which a regularization procedure such as LASSO is applied to yield a sparse model. To establish a simultaneous post-model selection inference, we propose a method of contraction and expansion (MOCE) along the line of debiasing estimation that enables us to balance the bias-and-variance trade-off so that the super-sparsity assumption may be relaxed. We establish key theoretical results for the proposed MOCE procedure from which the expanded model can be selected with theoretical guarantees and simultaneous confidence regions can be constructed by the joint asymptotic normal distribution. In comparison with existing methods, our proposed method exhibits stable and reliable coverage at a nominal significance level with substantially less computational burden, and thus it is trustworthy for its application in solving real-world problems.

Xiao Dong, Ling Zhou

A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the Riemannian geometry of network complexity plays a key role in understanding the basic properties of over-parameterizaed deep networks, including the generalization, convergence and parameter sensitivity. We also point out deep networks share lots of similarities with quantum computation systems. This can be regarded as a strong support of our proposal that geometrization is not only the bible for physics, it is also the key idea to understand deep learning systems.

Xiao Dong, Ling Zhou

How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum computation and this may result in a new scheme to reveal the rule of the physical world. By comparing the geometry of image matching and deep networks, we show that geometrization of deep networks can be used to understand existing deep learning systems and it may also help to solve the interpretability problem of deep learning systems.

Tong Qin, Ling Zhou, Dongbin Xiu

For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit sphere, as opposed to the entire space, and the threshold can be trained in a bounded interval, as opposed to the real line. We show that the NNs in the reduced parameter space are mathematically equivalent to the standard NNs with parameters in the whole space. The reduced parameter space shall facilitate the optimization procedure for the network training, as the search space becomes (much) smaller. We demonstrate the improved training performance using numerical examples.

Xiao Dong, Jiasong Wu, Ling Zhou

The astonishing success of AlphaGo Zero\cite{Silver_AlphaGo} invokes a worldwide discussion of the future of our human society with a mixed mood of hope, anxiousness, excitement and fear. We try to dymystify AlphaGo Zero by a qualitative analysis to indicate that AlphaGo Zero can be understood as a specially structured GAN system which is expected to possess an inherent good convergence property. Thus we deduct the success of AlphaGo Zero may not be a sign of a new generation of AI.

Xiao Dong, Jiasong Wu, Ling Zhou

Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric structures, the geometry of quantum computations and the geometry of the diffeomorphic template matching. In this framework, we give the geometric structures of different deep learning systems including convolutional neural networks, residual networks, recursive neural networks, recurrent neural networks and the equilibrium prapagation framework. We can also analysis the relationship between the geometrical structures and their performance of different networks in an algorithmic level so that the geometric framework may guide the design of the structures and algorithms of deep learning systems.