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In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks. Betti matching loss builds on techniques from topological data analysis, specifically persistent homology. A major challenge is the computational cost of computing persistence barcodes. In response to this challenge, we propose a new, highly optimized implementation of Betti matching, implemented in C++ together with a python interface, which achieves significant speedups compared to the state-of-the-art implementation Cubical Ripser. We use Betti matching 3D to train segmentation networks with the Betti matching loss and demonstrate improved topological correctness of predicted segmentations across several datasets. The source code is available at //github.com/nstucki/Betti-Matching-3D.

In this work, we investigate the impact of channel aging and electromagnetic interference (EMI) on spatially correlated reconfigurable intelligent surface (RIS) assisted cell-free massive multiple-input multiple-output (MIMO) systems. To effectively handle channel aging and EMI, we employ a novel two-phase channel estimation scheme with fractional power control-aided pilot assignment during the uplink channel estimation phase. This scheme provides improved channel estimates compared to existing approaches. The closed-form uplink and downlink spectral efficiency (SE) expressions incorporating fractional power control are derived to enable system performance evaluation. Additionally, we introduce the system's power consumption model to analyze energy efficiency (EE). Our numerical results illustrate the theoretical results and demonstrate the system performance with channel aging and EMI. Specifically, the proposed two-phase channel estimation scheme enhances estimation accuracy, compensating for performance degradation caused by channel aging and EMI. We find that increasing the number of access points (APs), RISs, antennas per AP, and elements per RIS can help to mitigate the SE performance degradation. We also find that an optimal number of APs can be selected to achieve energy efficiency (EE) maximization. However, in severe EMI environments, the benefits of deploying more RISs cannot be fully realized.

In a recent work, Gryaznov, Pudl\'{a}k, and Talebanfard (CCC' 22) introduced a stronger version of affine extractors known as directional affine extractors, together with a generalization of $\mathsf{ROBP}$s where each node can make linear queries, and showed that the former implies strong lower bound for a certain type of the latter known as strongly read-once linear branching programs ($\mathsf{SROLBP}$s). Their main result gives explicit constructions of directional affine extractors for entropy $k > 2n/3$, which implies average-case complexity $2^{n/3-o(n)}$ against $\mathsf{SROLBP}$s with exponentially small correlation. A follow-up work by Chattopadhyay and Liao (ECCC' 22) improves the hardness to $2^{n-o(n)}$ at the price of increasing the correlation to polynomially large. In this paper we show: An explicit construction of directional affine extractors with $k=o(n)$ and exponentially small error, which gives average-case complexity $2^{n-o(n)}$ against $\mathsf{SROLBP}$s with exponentially small correlation, thus answering the two open questions raised in previous works. An explicit function in $\mathsf{AC}^0$ that gives average-case complexity $2^{(1-\delta)n}$ against $\mathsf{ROBP}$s with negligible correlation, for any constant $\delta>0$. Previously, no such average-case hardness is known, and the best size lower bound for any function in $\mathsf{AC}^0$ against $\mathsf{ROBP}$s is $2^{\Omega(n)}$. One of the key ingredients in our constructions is a new linear somewhere condenser for affine sources, which is based on dimension expanders. The condenser also leads to an unconditional improvement of the entropy requirement of explicit affine extractors with negligible error. We further show that the condenser also works for general weak random sources, under the Polynomial Freiman-Ruzsa Theorem in $\mathsf{F}_2^n$.

Generating diverse samples under hard constraints is a core challenge in many areas. With this work we aim to provide an integrative view and framework to combine methods from the fields of MCMC, constrained optimization, as well as robotics, and gain insights in their strengths from empirical evaluations. We propose NLP Sampling as a general problem formulation, propose a family of restarting two-phase methods as a framework to integrated methods from across the fields, and evaluate them on analytical and robotic manipulation planning problems. Complementary to this, we provide several conceptual discussions, e.g. on the role of Lagrange parameters, global sampling, and the idea of a Diffused NLP and a corresponding model-based denoising sampler.

We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective solution. However, despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured (i.i.d.\ Gaussian and Haar orthogonal) designs. In contrast, real-world data matrices are highly structured and exhibit non-trivial correlations. To address the problem, we consider correlated Gaussian designs capturing the anisotropic nature of the features via a covariance matrix $\Sigma$. Our main result is a precise asymptotic characterization of the performance of spectral estimators. This allows us to identify the optimal preprocessing that minimizes the number of samples needed for parameter estimation. Surprisingly, such preprocessing is universal across a broad set of designs, which partly addresses a conjecture on optimal spectral estimators for rotationally invariant models. Our principled approach vastly improves upon previous heuristic methods, including for designs common in computational imaging and genetics. The proposed methodology, based on approximate message passing, is broadly applicable and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings.

In this work, we deal with the problem of re compression based image forgery detection, where some regions of an image are modified illegitimately, hence giving rise to presence of dual compression characteristics within a single image. There have been some significant researches in this direction, in the last decade. However, almost all existing techniques fail to detect this form of forgery, when the first compression factor is greater than the second. We address this problem in re compression based forgery detection, here Recently, Machine Learning techniques have started gaining a lot of importance in the domain of digital image forensics. In this work, we propose a Convolution Neural Network based deep learning architecture, which is capable of detecting the presence of re compression based forgery in JPEG images. The proposed architecture works equally efficiently, even in cases where the first compression ratio is greater than the second. In this work, we also aim to localize the regions of image manipulation based on re compression features, using the trained neural network. Our experimental results prove that the proposed method outperforms the state of the art, with respect to forgery detection and localization accuracy.

This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of this method is to utilize the information of the current iteration point to adaptively select the appropriate parameters, thus expanding the selection of the subproblem step size and improving the convergence rate of the algorithm while ensuring convergence.The advantage of this method is that it can improve the convergence rate of the algorithm as much as possible without compromising the convergence. This is very beneficial for the solution of optimization problems because the traditional linearized alternating direction multiplier method has a trade-off in the selection of the regular term coefficients: larger coefficients ensure convergence but tend to lead to small step sizes, while smaller coefficients allow for an increase in the iterative step size but tend to lead to the algorithm's non-convergence. This balance can be better handled by adaptively selecting the parameters, thus improving the efficiency of the algorithm.

When the regressors of a econometric linear model are nonorthogonal, it is well known that their estimation by ordinary least squares can present various problems that discourage the use of this model. The ridge regression is the most commonly used alternative; however, its generalized version has hardly been analyzed. The present work addresses the estimation of this generalized version, as well as the calculation of its mean squared error, goodness of fit and bootstrap inference.

In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.