Aditya Ranganath

Lawrence Livermore National Laboratory

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Mukesh Singhal

University of California, Merced

Roummel F. Marcia

University of California, Merced

Vahid Behzadan

University of New Haven

Omar DeGuchy

University of California, Merced

Pooya Tavallali

University of California, Merced

Azar Alizadeh

GE Global Research (United States)

Zach Chandler

Stanford University

Jacqueline Alvarez

University of California, Merced

Fabián Santiago

Université Paris 8

Andrew Johnson

University of Colorado Boulder

Cooperative Institutions

University of California, Merced

Lawrence Livermore National Laboratory

Florida State University

University of Colorado Boulder

John Wiley & Sons (United States)

Stanford University

University of California System

Universidad Nacional Autónoma de México

University of Colorado System

Brookhaven National Laboratory

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Symmetric Rank-One Quasi-Newton Methods for Deep Learning Using Cubic Regularization

arXiv (Cornell University) (2025)

Aditya Ranganath Mukesh Singhal Roummel F. Marcia

Stochastic gradient descent and other first-order variants, such as Adam and AdaGrad, are commonly used in the field of deep learning due to their computational efficiency and low-storage memory requirements. However, these methods do not exploit curvature information. Consequently, iterates can converge to saddle points or poor local minima. On the other hand, Quasi-Newton methods compute Hessian approximations which exploit this information with a comparable computational budget. Quasi-Newton methods re-use previously computed iterates and gradients to compute a low-rank structured update. The most widely used quasi-Newton update is the L-BFGS, which guarantees a positive semi-definite Hessian approximation, making it suitable in a line search setting. However, the loss functions in DNNs are non-convex, where the Hessian is potentially non-positive definite. In this paper, we propose using a limited-memory symmetric rank-one quasi-Newton approach which allows for indefinite Hessian approximations, enabling directions of negative curvature to be exploited. Furthermore, we use a modified adaptive regularized cubics approach, which generates a sequence of cubic subproblems that have closed-form solutions with suitable regularization choices. We investigate the performance of our proposed method on autoencoders and feed-forward neural network models and compare our approach to state-of-the-art first-order adaptive stochastic methods as well as other quasi-Newton methods.x

Regularization

Rank (graph theory)

10.48550/arxiv.2502.12298

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Quasi-Adam: Accelerating Adam using quasi-Newton approximations

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (2024)

Aditya Ranganath Ignacio Romero Mukesh Singhal Roummel F. Marcia

Approximations of π

Source

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Recurrent Nerual Imaging: An Evolutionary Approach for Mixed Possion-Gaussian Image Denoising

Aditya Ranganath Omar DeGuchy Fabián Santiago Mukesh Singhal Roummel F. Marcia

Recurrent neural networks (RNNs) are traditionally used for machine learning applications for temporal sequences such as natural language processing. Its application to image processing is relatively new. In this paper, we apply RNNs to denoise images corrupted by mixed Poisson and Gaussian noise. The motivation for using an RNN comes from viewing the denoising of the Poisson-Gaussian realization as a temporal process. The network then attempts to trace back the steps that create the noisy realization in order to arrive at the noiseless reconstruction. Numerical experiments demonstrate that our proposed RNN approach outperforms convolutional autoen-coder methods for denoising and upsampling low-resolution images from the CIFAR-10 dataset.

Upsampling

Realization (probability)

Gaussian Noise

TRACE (psycholinguistics)

10.1109/icmla55696.2022.00078

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Multi-Stage Gaussian Noise Reduction with Recurrent Neural Networks

2014 48th Asilomar Conference on Signals, Systems and Computers (2021)

Aditya Ranganath Omar DeGuchy Mukesh Singhal Roummel F. Marcia

In this paper, we implement multi-stage deep learning methods to recover signals from noisy observations. We seek an alternative to the traditional iterative optimization-based methods by exploiting the denoising properties of autoencoders. The novelty of our method is in the reformulation of the denoising problem as a multi-stage process and in the use of recurrent neural networks to gradually recover the intended signal. Numerical experiments on a modified version of the CIFAR-10 dataset show that signal recovery in multiple stages produces sharper images than a standard autoencoder approach. We present quantitative evidence of improvement using both the mean squared error and the structural similarity index.

Autoencoder

Gaussian Noise

SIGNAL (programming language)

Similarity (geometry)

10.1109/ieeeconf53345.2021.9723266

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Stochastic Induction of Decision Trees with Application to Learning Haar Trees

Azar Alizadeh Mukesh Singhal Vahid Behzadan Pooya Tavallali Aditya Ranganath

Decision trees are a convenient and established approach for any supervised learning task. Decision trees are trained by greedily splitting a leaf nodes, into two leaf nodes until a specific stopping criterion is reached. Splitting a node consists of finding the best feature and threshold that minimizes a criterion. The criterion minimization problem is solved through a costly exhaustive search algorithm. This paper proposes a novel stochastic approach for criterion minimization. The algorithm is compared with several other related state-of-the-art decision tree learning methods, including the baseline non-stochastic approach. We apply the proposed algorithm to learn a Haar tree over MNIST dataset that consists of over 200, 000 features and 60, 000 samples. The result is comparable to the performance of oblique trees while providing a significant speed-up in both inference and training times.

MNIST database

Minification

Alternating decision tree

Tree (set theory)

Feature (linguistics)

10.1109/icmla55696.2022.00137

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Protein-ligand binding affinity prediction using multi-instance learning with docking structures

Frontiers in Pharmacology (2025)

Hyo-Jin Kim Heesung Shim Aditya Ranganath Stewart He Garrett A. Stevenson

Recent advances in 3D structure-based deep learning approaches demonstrate improved accuracy in predicting protein-ligand binding affinity in drug discovery. These methods complement physics-based computational modeling such as molecular docking for virtual high-throughput screening. Despite recent advances and improved predictive performance, most methods in this category primarily rely on utilizing co-crystal complex structures and experimentally measured binding affinities as both input and output data for model training. Nevertheless, co-crystal complex structures are not readily available and the inaccurate predicted structures from molecular docking can degrade the accuracy of the machine learning methods. We introduce a novel structure-based inference method utilizing multiple molecular docking poses for each complex entity. Our proposed method employs multi-instance learning with an attention network to predict binding affinity from a collection of docking poses. We validate our method using multiple datasets, including PDBbind and compounds targeting the main protease of SARS-CoV-2. The results demonstrate that our method leveraging docking poses is competitive with other state-of-the-art inference models that depend on co-crystal structures. This method offers binding affinity prediction without requiring co-crystal structures, thereby increasing its applicability to protein targets lacking such data.

Docking (animal)

Protein–ligand docking

10.3389/fphar.2024.1518875

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Image Separation Using Transformer Attention Models

Aditya Ranganath Jocelyn Ornelas Muñoz Robert Smith Mukesh Singhal Roummel F. Marcia

10.1109/fmlds63805.2024.00066

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Interpretability of ReLU for Inversion

Boaz Ilan Aditya Ranganath Jacqueline Alvarez Shilpa Khatri Roummel F. Marcia

Interpretability continues to be a focus of much research in deep neural network. In this work, we focus on the mathematical interpretability of fully-connected neural networks, especially those that use a rectified linear unit (ReLU) activation function. Our analysis elucidates the difficulty of approximating the reciprocal function. Notwithstanding, using the ReLU activation function halves the error compared with a linear model. In addition, one might have expected the errors to increase only towards the singular point x = 0, but both the linear and ReLU errors are fairly oscillatory and increase near both edge points.

Interpretability

Activation function

Reciprocal

10.1109/icmla55696.2022.00192

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Novel Adversarial Defense Techniques for White-Box Attacks

Jason Van Tuinen Aditya Ranganath Goran Konjevod Mukesh Singhal Roummel F. Marcia

In this paper, we propose a novel machine learning technique to detect and correctly classify adversarially modified images. Our approach takes advantage of the adversarial training objective (to influence the prediction with small perturbations to the original image) by searching for large discrepancies in the model's output relative to the input image. We find clusters in each space, and for an image whose clusters do not agree with each other, we flag the image as potentially adversarial and use the input space cluster's prediction in place of the attacked model's output. We have found that this method tends to find adversarial samples which are more likely to be misclassified by the attacked model, and that simply deferring to the input cluster's prediction on such samples is enough to increase accuracy on adversarial data, even when the attacked model is adversarially trained.

10.1109/icmla55696.2022.00095

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Second-Order Trust-Region Optimization for Data-Limited Inference

2021 29th European Signal Processing Conference (EUSIPCO) (2021)

Aditya Ranganath Omar DeGuchy Mukesh Singhal Roummel F. Marcia

Neural networks generally require large amounts of data to adequately model the domain space. In situations where the data are limited, the predictions from these models, which are typically obtained from stochastic gradient descent (SGD) minimization algorithms, can be poor. In these cases, the use of more sophisticated optimization approaches becomes even more crucial to increase the impact of each training iteration. In this paper, we propose an optimization algorithm that uses second-derivative information that exploits curvature information for avoiding saddle points, which can result in limitations on the learning process. In particular, we utilize a Hessian-free approach where we do not explicitly store the second-derivative matrix; rather, we apply a conjugate gradient method and require the Hessian matrix only to compute matrix-vector products. Our approach is based on trust-region methods, which do not require the Hessian to be positive definite and which differentiates our approach from existing Hessian-free methods. We present numerical experiments which demonstrate the improvement in classification accuracy using our proposed approach over a standard SGD approach.

Hessian matrix

Stochastic Gradient Descent

Trust region

Matrix (chemical analysis)

Saddle point

10.23919/eusipco54536.2021.9616149

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