Pengcheng Zhou

Ren Wang, Pengcheng Zhou

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global topological integrity from noisy data or construct a balanced dimensionality reduction, resulting in distorted or fractured embeddings. We present an AutoEncoder-based method that integrates a manifold reconstruction layer, which uncovers latent manifold structures from noisy point clouds, and further provides regularizations on topological and geometric properties during dimensionality reduction, whereas the two components promote each other during training. Experiments on point cloud datasets demonstrate that our method outperforms baselines like t-SNE, UMAP, and Topological AutoEncoders in discovering manifold structures from noisy data and preserving them through dimensionality reduction, as validated by visualization and quantitative metrics. This work demonstrates the significance of combining manifold reconstruction with manifold learning to achieve reliable representation of the latent manifold, particularly when dealing with noisy real-world data. Code repository: https://github.com/Thanatorika/mrtg.

Pengcheng Zhou, Yinglun Feng, Zhongliang Yang

Although Retrieval-Augmented Generation (RAG) systems have been widely applied, the privacy and security risks they face, such as data leakage and data poisoning, have not been systematically addressed yet. Existing defense strategies primarily rely on heuristic filtering or enhancing retriever robustness, which suffer from limited interpretability, lack of formal security guarantees, and vulnerability to adaptive attacks. To address these challenges, this paper proposes the first provably secure framework for RAG systems(SAG). Our framework employs a pre-storage full-encryption scheme to ensure dual protection of both retrieved content and vector embeddings, guaranteeing that only authorized entities can access the data. Through formal security proofs, we rigorously verify the scheme's confidentiality and integrity under a computational security model. Extensive experiments across multiple benchmark datasets demonstrate that our framework effectively resists a range of state-of-the-art attacks. This work establishes a theoretical foundation and practical paradigm for verifiably secure RAG systems, advancing AI-powered services toward formally guaranteed security.

Fanhe Ma, Faen Zhang, Shenglan Ben et al.

In this paper, we are interested in building a domain knowledge based deep learning framework to solve the chiller plants energy optimization problems. Compared to the hotspot applications of deep learning (e.g. image classification and NLP), it is difficult to collect enormous data for deep network training in real-world physical systems. Most existing methods reduce the complex systems into linear model to facilitate the training on small samples. To tackle the small sample size problem, this paper considers domain knowledge in the structure and loss design of deep network to build a nonlinear model with lower redundancy function space. Specifically, the energy consumption estimation of most chillers can be physically viewed as an input-output monotonic problem. Thus, we can design a Neural Network with monotonic constraints to mimic the physical behavior of the system. We verify the proposed method in a cooling system of a data center, experimental results show the superiority of our framework in energy optimization compared to the existing ones.

Faen Zhang, Xinyu Fan, Hui Xu et al.

In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional distributions instead of the whole distribution, especially for small datasets. To address this problem, we proposed arbitrary quantile modeling to regulate the prediction, which achieved better performance compared to traditional loss functions. More specifically, a new distribution regression method, Deep Distribution Regression (DDR), is proposed to estimate arbitrary quantiles of the response variable. Our DDR method consists of two models: a Q model, which predicts the corresponding value for arbitrary quantile, and an F model, which predicts the corresponding quantile for arbitrary value. Furthermore, the duality between Q and F models enables us to design a novel loss function for joint training and perform a dual inference mechanism. Our experiments demonstrate that our DDR-joint and DDR-disjoint methods outperform previous methods such as AdaBoost, random forest, LightGBM, and neural networks both in terms of mean and quantile prediction.

Yenson Lau, Qing Qu, Han-Wen Kuo et al.

Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure. Variants of this problem arise in applications such as image deblurring, microscopy, neural spike sorting, and more. The problem is challenging in both theory and practice, as natural optimization formulations are nonconvex. Moreover, practical deconvolution problems involve smooth motifs (kernels) whose spectra decay rapidly, resulting in poor conditioning and numerical challenges. This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD. This is used to derive a $provable$ algorithm which exactly solves certain non-practical instances of the SaSD problem. We leverage the key ideas from this theory (sphere constraints, data-driven initialization) to develop a $practical$ algorithm, which performs well on data arising from a range of application areas. We highlight key additional challenges posed by the ill-conditioning of real SaSD problems, and suggest heuristics (acceleration, continuation, reweighting) to mitigate them. Experiments demonstrate both the performance and generality of the proposed method.

E. Kelly Buchanan, Ian Kinsella, Ding Zhou et al.

Calcium imaging has revolutionized systems neuroscience, providing the ability to image large neural populations with single-cell resolution. The resulting datasets are quite large, which has presented a barrier to routine open sharing of this data, slowing progress in reproducible research. State of the art methods for analyzing this data are based on non-negative matrix factorization (NMF); these approaches solve a non-convex optimization problem, and are effective when good initializations are available, but can break down in low-SNR settings where common initialization approaches fail. Here we introduce an approach to compressing and denoising functional imaging data. The method is based on a spatially-localized penalized matrix decomposition (PMD) of the data to separate (low-dimensional) signal from (temporally-uncorrelated) noise. This approach can be applied in parallel on local spatial patches and is therefore highly scalable, does not impose non-negativity constraints or require stringent identifiability assumptions (leading to significantly more robust results compared to NMF), and estimates all parameters directly from the data, so no hand-tuning is required. We have applied the method to a wide range of functional imaging data (including one-photon, two-photon, three-photon, widefield, somatic, axonal, dendritic, calcium, and voltage imaging datasets): in all cases, we observe ~2-4x increases in SNR and compression rates of 20-300x with minimal visible loss of signal, with no adjustment of hyperparameters; this in turn facilitates the process of demixing the observed activity into contributions from individual neurons. We focus on two challenging applications: dendritic calcium imaging data and voltage imaging data in the context of optogenetic stimulation. In both cases, we show that our new approach leads to faster and much more robust extraction of activity from the data.