Mayank Goswami

Wenjia Zhang, Yikai Zhang, Xiaoling Hu et al.

The adversarial risk of a machine learning model has been widely studied. Most previous works assume that the data lies in the whole ambient space. We propose to take a new angle and take the manifold assumption into consideration. Assuming data lies in a manifold, we investigate two new types of adversarial risk, the normal adversarial risk due to perturbation along normal direction, and the in-manifold adversarial risk due to perturbation within the manifold. We prove that the classic adversarial risk can be bounded from both sides using the normal and in-manifold adversarial risks. We also show with a surprisingly pessimistic case that the standard adversarial risk can be nonzero even when both normal and in-manifold risks are zero. We finalize the paper with empirical studies supporting our theoretical results. Our results suggest the possibility of improving the robustness of a classifier by only focusing on the normal adversarial risk.

Jiachen Yao, Yikai Zhang, Songzhu Zheng et al.

Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing methods mostly assume noisy labels in different pixels are \textit{i.i.d}. However, segmentation label noise usually has strong spatial correlation and has prominent bias in distribution. In this paper, we propose a novel Markov model for segmentation noisy annotations that encodes both spatial correlation and bias. Further, to mitigate such label noise, we propose a label correction method to recover true label progressively. We provide theoretical guarantees of the correctness of the proposed method. Experiments show that our approach outperforms current state-of-the-art methods on both synthetic and real-world noisy annotations.

Sunita Khod, Akshay Dvivedi, Mayank Goswami

The 3D printing process flow requires several inputs for the best printing quality. These settings may vary from sample to sample, printer to printer, and depend upon users' previous experience. The involved operational parameters for 3D Printing are varied to test the optimality. Thirty-eight samples are printed using four commercially available 3D printers, namely: (a) Ultimaker 2 Extended+, (b) Delta Wasp, (c) Raise E2, and (d) ProJet MJP. The sample profiles contain uniform and non-uniform distribution of the assorted size of cubes and spheres with a known amount of porosity. These samples are scanned using X-Ray Computed Tomography system. Functional Imaging analysis is performed using AI-based segmentation codes to (a) characterize these 3D printers and (b) find Three-dimensional surface roughness of three teeth and one sandstone pebble (from riverbed) with naturally deposited layers is also compared with printed sample values. Teeth has best quality. It is found that ProJet MJP gives the best quality of printed samples with the least amount of surface roughness and almost near to the actual porosity value. As expected, 100% infill density value, best spatial resolution for printing or Layer height, and minimum nozzle speed give the best quality of 3D printing.

Mayank Goswami

Image data set from a multi-spectral animal imaging system is used to address two issues: (a) registering the oscillation in optical coherence tomography (OCT) images due to mouse eye movement and (b) suppressing the shadow region under the thick vessels/structures. Several classical and AI-based algorithms in combination are tested for each task to see their compatibility with data from the combined animal imaging system. Hybridization of AI with optical flow followed by Homography transformation is shown to be working (correlation value>0.7) for registration. Resnet50 backbone is shown to be working better than the famous U-net model for shadow region detection with a loss value of 0.9. A simple-to-implement analytical equation is shown to be working for brightness manipulation with a 1% increment in mean pixel values and a 77% decrease in the number of zeros. The proposed equation allows formulating a constraint optimization problem using a controlling factor α for minimization of number of zeros, standard deviation of pixel value and maximizing the mean pixel value. For Layer segmentation, the standard U-net model is used. The AI-Pipeline consists of CNN, Optical flow, RCNN, pixel manipulation model, and U-net models in sequence. The thickness estimation process has a 6% error as compared to manual annotated standard data.

Anders Aamand, Mikkel Abrahamsen, Reilly Browne et al.

We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to write $P$ as a union of small pieces, and in partitioning, we furthermore require the pieces to be pairwise interior-disjoint. We show that these problems are in fact equivalent: Optimum covers and partitions have the same number of pieces. For covering, a natural local search algorithm repeatedly attempts to replace $k$ pieces from a candidate cover with $k-1$ pieces. In two dimensions and for sufficiently large $k$, we show that when no such swap is possible, the cover is a $1+O(1/\sqrt k)$-approximation, hence obtaining the first PTAS for the problem. Prior to our work, the only known algorithm was a $13$-approximation that only works for polygons without holes [Abrahamsen and Rasmussen, SODA 2025]. In contrast, in the three dimensional version of the problem, for a polyhedron $P$ of complexity $n$, we show that it is NP-hard to approximate an optimal cover or partition to within a factor that is logarithmic in $n$, even if $P$ is simple, i.e., has genus $0$ and no holes.

Abhijeet Kumar, Chetan Agarwal, Pronoy B. Neogi et al.

This research explores the fusion of graphology and artificial intelligence to quantify psychological stress levels in students by analyzing their handwritten examination scripts. By leveraging Optical Character Recognition and transformer based sentiment analysis models, we present a data driven approach that transcends traditional grading systems, offering deeper insights into cognitive and emotional states during examinations. The system integrates high resolution image processing, TrOCR, and sentiment entropy fusion using RoBERTa based models to generate a numerical Stress Index. Our method achieves robustness through a five model voting mechanism and unsupervised anomaly detection, making it an innovative framework in academic forensics.

Sunita Khod, Akshay Dvivedi, Mayank Goswami

The quality of the part fabricated from the Additive Manufacturing (AM) process depends upon the process parameters used, and therefore, optimization is required for apt quality. A methodology is proposed to set these parameters non-iteratively without human intervention. It utilizes Artificial Intelligence (AI) to fully automate the process, with the capability to self-train any apt AI model by further assimilating the training data.This study includes three commercially available 3D printers for soft material printing based on the Material Extrusion (MEX) AM process. The samples are 3D printed for six different AM process parameters obtained by varying layer height and nozzle speed. The novelty part of the methodology is incorporating an AI-based image segmentation step in the decision-making stage that uses quality inspected training data from the Non-Destructive Testing (NDT) method. The performance of the trained AI model is compared with the two software tools based on the classical thresholding method. The AI-based Artificial Neural Network (ANN) model is trained from NDT-assessed and AI-segmented data to automate the selection of optimized process parameters. The AI-based model is 99.3 % accurate, while the best available commercial classical image method is 83.44 % accurate. The best value of overall R for training ANN is 0.82. The MEX process gives a 22.06 % porosity error relative to the design. The NDT-data trained two AI models integrated into a series pipeline for optimal process parameters are proposed and verified by classical optimization and mechanical testing methods.

Jiachen Yao, Mayank Goswami, Chao Chen

A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on the intricacy of the underlying latent manifold. While significant advancements have been made in understanding the geometric attributes of manifolds, it's essential to recognize that topology, too, is a fundamental characteristic of manifolds. In this study, we investigate network expressive power in terms of the latent data manifold. Integrating both topological and geometric facets of the data manifold, we present a size upper bound of ReLU neural networks.

Mayank Goswami

Relatively abundant availability of medical imaging data has provided significant support in the development and testing of Neural Network based image processing methods. Clinicians often face issues in selecting suitable image processing algorithm for medical imaging data. A strategy for the selection of a proper model is presented here. The training data set comprises optical coherence tomography (OCT) and angiography (OCT-A) images of 50 mice eyes with more than 100 days follow-up. The data contains images from treated and untreated mouse eyes. Four deep learning variants are tested for automatic (a) differentiation of tumor region with healthy retinal layer and (b) segmentation of 3D ocular tumor volumes. Exhaustive sensitivity analysis of deep learning models is performed with respect to the number of training and testing images using 8 eight performance indices to study accuracy, reliability/reproducibility, and speed. U-net with UVgg16 is best for malign tumor data set with treatment (having considerable variation) and U-net with Inception backbone for benign tumor data (with minor variation). Loss value and root mean square error (R.M.S.E.) are found most and least sensitive performance indices, respectively. The performance (via indices) is found to be exponentially improving regarding a number of training images. The segmented OCT-Angiography data shows that neovascularization drives the tumor volume. Image analysis shows that photodynamic imaging-assisted tumor treatment protocol is transforming an aggressively growing tumor into a cyst. An empirical expression is obtained to help medical professionals to choose a particular model given the number of images and types of characteristics. We recommend that the presented exercise should be taken as standard practice before employing a particular deep learning model for biomedical image analysis.

Songzhu Zheng, Yikai Zhang, Hubert Wagner et al.

Deep neural networks are known to have security issues. One particular threat is the Trojan attack. It occurs when the attackers stealthily manipulate the model's behavior through Trojaned training samples, which can later be exploited. Guided by basic neuroscientific principles we discover subtle -- yet critical -- structural deviation characterizing Trojaned models. In our analysis we use topological tools. They allow us to model high-order dependencies in the networks, robustly compare different networks, and localize structural abnormalities. One interesting observation is that Trojaned models develop short-cuts from input to output layers. Inspired by these observations, we devise a strategy for robust detection of Trojaned models. Compared to standard baselines it displays better performance on multiple benchmarks.

Yikai Zhang, Songzhu Zheng, Pengxiang Wu et al.

Label noise is frequently observed in real-world large-scale datasets. The noise is introduced due to a variety of reasons; it is heterogeneous and feature-dependent. Most existing approaches to handling noisy labels fall into two categories: they either assume an ideal feature-independent noise, or remain heuristic without theoretical guarantees. In this paper, we propose to target a new family of feature-dependent label noise, which is much more general than commonly used i.i.d. label noise and encompasses a broad spectrum of noise patterns. Focusing on this general noise family, we propose a progressive label correction algorithm that iteratively corrects labels and refines the model. We provide theoretical guarantees showing that for a wide variety of (unknown) noise patterns, a classifier trained with this strategy converges to be consistent with the Bayes classifier. In experiments, our method outperforms SOTA baselines and is robust to various noise types and levels.

Yikai Zhang, Wenjia Zhang, Sammy Bald et al.

Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a prominent one being algorithmic stability [18]. However, there are no known examples of smooth loss functions for which the analysis can be shown to be tight. Furthermore, apart from the properties of the loss function, data distribution has also been shown to be an important factor in generalization performance. This raises the question: is the stability analysis of [18] tight for smooth functions, and if not, for what kind of loss functions and data distributions can the stability analysis be improved? In this paper we first settle open questions regarding tightness of bounds in the data-independent setting: we show that for general datasets, the existing analysis for convex and strongly-convex loss functions is tight, but it can be improved for non-convex loss functions. Next, we give a novel and improved data-dependent bounds: we show stability upper bounds for a large class of convex regularized loss functions, with negligible regularization parameters, and improve existing data-dependent bounds in the non-convex setting. We hope that our results will initiate further efforts to better understand the data-dependent setting under non-convex loss functions, leading to an improved understanding of the generalization abilities of deep networks.

Pengxiang Wu, Songzhu Zheng, Mayank Goswami et al.

Noisy labels can impair the performance of deep neural networks. To tackle this problem, in this paper, we propose a new method for filtering label noise. Unlike most existing methods relying on the posterior probability of a noisy classifier, we focus on the much richer spatial behavior of data in the latent representational space. By leveraging the high-order topological information of data, we are able to collect most of the clean data and train a high-quality model. Theoretically we prove that this topological approach is guaranteed to collect the clean data with high probability. Empirical results show that our method outperforms the state-of-the-arts and is robust to a broad spectrum of noise types and levels.

Songzhu Zheng, Pengxiang Wu, Aman Goswami et al.

To collect large scale annotated data, it is inevitable to introduce label noise, i.e., incorrect class labels. To be robust against label noise, many successful methods rely on the noisy classifiers (i.e., models trained on the noisy training data) to determine whether a label is trustworthy. However, it remains unknown why this heuristic works well in practice. In this paper, we provide the first theoretical explanation for these methods. We prove that the prediction of a noisy classifier can indeed be a good indicator of whether the label of a training data is clean. Based on the theoretical result, we propose a novel algorithm that corrects the labels based on the noisy classifier prediction. The corrected labels are consistent with the true Bayesian optimal classifier with high probability. We incorporate our label correction algorithm into the training of deep neural networks and train models that achieve superior testing performance on multiple public datasets.