arXiv subjects

Ganesh Sundaramoorthi

Publications and source records attributed to Ganesh Sundaramoorthi.

At least 19 recordsLinked to original sources

arXiv2026

An Information-Theoretic Framework for Feature Construction in Out-of-Distribution Detection

We present a theory for the construction of out-of-distribution (OOD) detection features for neural networks. We introduce random features for OOD through a novel information-theoretic loss functional consisting of two terms, the first based on the KL divergence separates resulting in-distribution (ID) and OOD feature distributions and the second term is the Information Bottleneck, which favors compressed features that retain the OOD information. We formulate a variational procedure to optimize the loss and obtain OOD features. Based on assumptions on OOD distributions, one can recover properties of existing OOD features, i.e., shaping functions. Furthermore, we show that our theory can predict a new shaping function that out-performs existing ones on OOD benchmarks, including both semantic and a wide range of covariate shifts. Our theory provides a general framework for constructing a variety of new features with clear explainability.

cs.LG↗

arXiv2026

Out-of-Distribution (OOD) Detectors for Open-Set RF Fingerprinting

Radio-frequency (RF) fingerprinting systems must operate in open-world environments where signals from unknown transmitters and temporal drift introduce distribution shift at test time. Out-of-distribution (OOD) detection provides a natural framework for this problem, yet its application to RF fingerprinting (RFF) remains limited. A key barrier to their adoption is that most OOD detectors require auxiliary OOD data for parameter tuning, an assumption that is difficult to satisfy in RF environments where representative OOD data is impractical to collect. In this work, we introduce a promising set of OOD detection methods from the machine learning literature to open-set RFF domain. We present these methods within a unified mathematical framework based on information theory, which is a natural framework for communication systems. Our framework allows for the systematic analysis of methods and development of new methods. We further demonstrate the applicability of recent work on tuning OOD detectors without given OOD tuning data for open-set RFF. We evaluate on the POWDER RF fingerprinting dataset, showing that detectors tuned without any given OOD data achieve performance comparable to baselines with access to true OOD tuning data and greatly out-perform baseline approaches without access to true OOD tuning data, showcasing the practical viability for the RFF problem.

cs.LG↗

arXiv2026

ODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splatting

We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods, which rely on time-conditioned deformation networks and are limited to interpolation within a fixed time window, ODE-GS eliminates timestamp dependency by modeling Gaussian parameter trajectories as continuous-time latent dynamics. Our approach first learns an interpolation model to generate accurate Gaussian trajectories within the observed window, then trains a Transformer encoder to aggregate past trajectories into a latent state evolved via a neural ODE. Finally, numerical integration produces smooth, physically plausible future Gaussian trajectories, enabling rendering at arbitrary future timestamps. On the D-NeRF, NVFi, and HyperNeRF benchmarks, ODE-GS achieves state-of-the-art extrapolation performance, improving metrics by 19.8% compared to leading baselines, demonstrating its ability to accurately represent and predict 3D scene dynamics.

cs.GR↗

arXiv2026

Tuning Out-of-Distribution (OOD) Detectors Without Given OOD Data

Existing out-of-distribution (OOD) detectors are often tuned by a separate dataset deemed OOD with respect to the training distribution of a neural network (NN). OOD detectors process the activations of NN layers and score the output, where parameters of the detectors are determined by fitting to an in-distribution (training) set and the aforementioned dataset chosen adhocly. At detector training time, this adhoc dataset may not be available or difficult to obtain, and even when it's available, it may not be representative of actual OOD data, which is often ''unknown unknowns." Current benchmarks may specify some left-out set from test OOD sets. We show that there can be significant variance in performance of detectors based on the adhoc dataset chosen in current literature, and thus even if such a dataset can be collected, the performance of the detector may be highly dependent on the choice. In this paper, we introduce and formalize the often neglected problem of tuning OOD detectors without a given ``OOD'' dataset. To this end, we present strong baselines as an attempt to approach this problem. Furthermore, we propose a new generic approach to OOD detector tuning that does not require any extra data other than those used to train the NN. We show that our approach improves over baseline methods consistently across higher-parameter OOD detector families, while being comparable across lower-parameter families.

cs.LG↗

arXiv2024

A PDE-based Explanation of Extreme Numerical Sensitivities and Edge of Stability in Training Neural Networks

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD), and its variants. We show numerical error (on the order of the smallest floating point bit and thus the most extreme or limiting numerical perturbations induced from floating point arithmetic in training deep nets can be amplified significantly and result in significant test accuracy variance (sensitivities), comparable to the test accuracy variance due to stochasticity in SGD. We show how this is likely traced to instabilities of the optimization dynamics that are restrained, i.e., localized over iterations and regions of the weight tensor space. We do this by presenting a theoretical framework using numerical analysis of partial differential equations (PDE), and analyzing the gradient descent PDE of convolutional neural networks (CNNs). We show that it is stable only under certain conditions on the learning rate and weight decay. We show that rather than blowing up when the conditions are violated, the instability can be restrained. We show this is a consequence of the non-linear PDE associated with the gradient descent of the CNN, whose local linearization changes when over-driving the step size of the discretization, resulting in a stabilizing effect. We link restrained instabilities to the recently discovered Edge of Stability (EoS) phenomena, in which the stable step size predicted by classical theory is exceeded while continuing to optimize the loss and still converging. Because restrained instabilities occur at the EoS, our theory provides new insights and predictions about the EoS, in particular, the role of regularization and the dependence on the network complexity.

cs.LG↗

arXiv2023

StEik: Stabilizing the Optimization of Neural Signed Distance Functions and Finer Shape Representation

We present new insights and a novel paradigm (StEik) for learning implicit neural representations (INR) of shapes. In particular, we shed light on the popular eikonal loss used for imposing a signed distance function constraint in INR. We show analytically that as the representation power of the network increases, the optimization approaches a partial differential equation (PDE) in the continuum limit that is unstable. We show that this instability can manifest in existing network optimization, leading to irregularities in the reconstructed surface and/or convergence to sub-optimal local minima, and thus fails to capture fine geometric and topological structure. We show analytically how other terms added to the loss, currently used in the literature for other purposes, can actually eliminate these instabilities. However, such terms can over-regularize the surface, preventing the representation of fine shape detail. Based on a similar PDE theory for the continuum limit, we introduce a new regularization term that still counteracts the eikonal instability but without over-regularizing. Furthermore, since stability is now guaranteed in the continuum limit, this stabilization also allows for considering new network structures that are able to represent finer shape detail. We introduce such a structure based on quadratic layers. Experiments on multiple benchmark data sets show that our new regularization and network are able to capture more precise shape details and more accurate topology than existing state-of-the-art.

cs.CV↗

arXiv2023

HAct: Out-of-Distribution Detection with Neural Net Activation Histograms

We propose a simple, efficient, and accurate method for detecting out-of-distribution (OOD) data for trained neural networks. We propose a novel descriptor, HAct - activation histograms, for OOD detection, that is, probability distributions (approximated by histograms) of output values of neural network layers under the influence of incoming data. We formulate an OOD detector based on HAct descriptors. We demonstrate that HAct is significantly more accurate than state-of-the-art in OOD detection on multiple image classification benchmarks. For instance, our approach achieves a true positive rate (TPR) of 95% with only 0.03% false-positives using Resnet-50 on standard OOD benchmarks, outperforming previous state-of-the-art by 20.67% in the false positive rate (at the same TPR of 95%). The computational efficiency and the ease of implementation makes HAct suitable for online implementation in monitoring deployed neural networks in practice at scale.

cs.LG↗

arXiv2021

Flow-Guided Video Inpainting with Scene Templates

We consider the problem of filling in missing spatio-temporal regions of a video. We provide a novel flow-based solution by introducing a generative model of images in relation to the scene (without missing regions) and mappings from the scene to images. We use the model to jointly infer the scene template, a 2D representation of the scene, and the mappings. This ensures consistency of the frame-to-frame flows generated to the underlying scene, reducing geometric distortions in flow based inpainting. The template is mapped to the missing regions in the video by a new L2-L1 interpolation scheme, creating crisp inpaintings and reducing common blur and distortion artifacts. We show on two benchmark datasets that our approach out-performs state-of-the-art quantitatively and in user studies.

cs.CV↗

arXiv2021

Class-Agnostic Segmentation Loss and Its Application to Salient Object Detection and Segmentation

In this paper we present a novel loss function, called class-agnostic segmentation (CAS) loss. With CAS loss the class descriptors are learned during training of the network. We don't require to define the label of a class a-priori, rather the CAS loss clusters regions with similar appearance together in a weakly-supervised manner. Furthermore, we show that the CAS loss function is sparse, bounded, and robust to class-imbalance. We first apply our CAS loss function with fully-convolutional ResNet101 and DeepLab-v3 architectures to the binary segmentation problem of salient object detection. We investigate the performance against the state-of-the-art methods in two settings of low and high-fidelity training data on seven salient object detection datasets. For low-fidelity training data (incorrect class label) class-agnostic segmentation loss outperforms the state-of-the-art methods on salient object detection datasets by staggering margins of around 50%. For high-fidelity training data (correct class labels) class-agnostic segmentation models perform as good as the state-of-the-art approaches while beating the state-of-the-art methods on most datasets. In order to show the utility of the loss function across different domains we then also test on general segmentation dataset, where class-agnostic segmentation loss outperforms competing losses by huge margins.

cs.CV↗

arXiv2021

Shape-Tailored Deep Neural Networks

We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural for segmentation, where descriptors should describe regions (e.g., of objects) that have diverse shape. We formulate these descriptors through the Poisson partial differential equation (PDE), which can be used to generalize convolution to arbitrary regions. We stack multiple PDE layers to generalize a deep CNN to arbitrary regions, and apply it to segmentation. We show that ST-DNN are covariant to translations and rotations and robust to domain deformations, natural for segmentation, which existing CNN based methods lack. ST-DNN are 3-4 orders of magnitude smaller then CNNs used for segmentation. We show that they exceed segmentation performance compared to state-of-the-art CNN-based descriptors using 2-3 orders smaller training sets on the texture segmentation problem.

cs.CV↗

arXiv2020

Class-Agnostic Segmentation Loss and Its Application to Salient Object Detection and Segmentation

In this paper we present a novel loss function, called class-agnostic segmentation (CAS) loss. With CAS loss the class descriptors are learned during training of the network. We don't require to define the label of a class a-priori, rather the CAS loss clusters regions with similar appearance together in a weakly-supervised manner. Furthermore, we show that the CAS loss function is sparse, bounded, and robust to class-imbalance. We apply our CAS loss function with fully-convolutional ResNet101 and DeepLab-v3 architectures to the binary segmentation problem of salient object detection. We investigate the performance against the state-of-the-art methods in two settings of low and high-fidelity training data on seven salient object detection datasets. For low-fidelity training data (incorrect class label) class-agnostic segmentation loss outperforms the state-of-the-art methods on salient object detection datasets by staggering margins of around 50%. For high-fidelity training data (correct class labels) class-agnostic segmentation models perform as good as the state-of-the-art approaches while beating the state-of-the-art methods on most datasets. In order to show the utility of the loss function across different domains we also test on general segmentation dataset, where class-agnostic segmentation loss outperforms cross-entropy based loss by huge margins on both region and edge metrics.

cs.CV↗

arXiv2020

Channel-Directed Gradients for Optimization of Convolutional Neural Networks

We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. The method requires only simple processing of existing stochastic gradients, can be used in conjunction with any optimizer, and has only a linear overhead (in the number of parameters) compared to computation of the stochastic gradient. The method works by computing the gradient of the loss function with respect to output-channel directed re-weighted L2 or Sobolev metrics, which has the effect of smoothing components of the gradient across a certain direction of the parameter tensor. We show that defining the gradients along the output channel direction leads to a performance boost, while other directions can be detrimental. We present the continuum theory of such gradients, its discretization, and application to deep networks. Experiments on benchmark datasets, several networks and baseline optimizers show that optimizers can be improved in generalization error by simply computing the stochastic gradient with respect to output-channel directed metrics.

cs.LG↗

arXiv2020

Phase Consistent Ecological Domain Adaptation

We introduce two criteria to regularize the optimization involved in learning a classifier in a domain where no annotated data are available, leveraging annotated data in a different domain, a problem known as unsupervised domain adaptation. We focus on the task of semantic segmentation, where annotated synthetic data are aplenty, but annotating real data is laborious. The first criterion, inspired by visual psychophysics, is that the map between the two image domains be phase-preserving. This restricts the set of possible learned maps, while enabling enough flexibility to transfer semantic information. The second criterion aims to leverage ecological statistics, or regularities in the scene which are manifest in any image of it, regardless of the characteristics of the illuminant or the imaging sensor. It is implemented using a deep neural network that scores the likelihood of each possible segmentation given a single un-annotated image. Incorporating these two priors in a standard domain adaptation framework improves performance across the board in the most common unsupervised domain adaptation benchmarks for semantic segmentation.

cs.CV↗

arXiv2019

Translation Insensitive CNNs

We address the problem that state-of-the-art Convolution Neural Networks (CNN) classifiers are not invariant to small shifts. The problem can be solved by the removal of sub-sampling operations such as stride and max pooling, but at a cost of severely degraded training and test efficiency. We present a novel usage of Gaussian-Hermite basis to efficiently approximate arbitrary filters within the CNN framework to obtain translation invariance. This is shown to be invariant to small shifts, and preserves the efficiency of training. Further, to improve efficiency in memory usage as well as computational speed, we show that it is still possible to sub-sample with this approach and retain a weaker form of invariance that we call \emph{translation insensitivity}, which leads to stability with respect to shifts. We prove these claims analytically and empirically. Our analytic methods further provide a framework for understanding any architecture in terms of translation insensitivity, and provide guiding principles for design.

cs.CV↗

arXiv2019

Minimum Delay Object Detection From Video

We consider the problem of detecting objects, as they come into view, from videos in an online fashion. We provide the first real-time solution that is guaranteed to minimize the delay, i.e., the time between when the object comes in view and the declared detection time, subject to acceptable levels of detection accuracy. The method leverages modern CNN-based object detectors that operate on a single frame, to aggregate detection results over frames to provide reliable detection at a rate, specified by the user, in guaranteed minimal delay. To do this, we formulate the problem as a Quickest Detection problem, which provides the aforementioned guarantees. We derive our algorithms from this theory. We show in experiments, that with an overhead of just 50 fps, we can increase the number of correct detections and decrease the overall computational cost compared to running a modern single-frame detector.

cs.CV↗

arXiv2018

Accelerated PDE's for efficient solution of regularized inversion problems

We further develop a new framework, called PDE Acceleration, by applying it to calculus of variations problems defined for general functions on $\mathbb{R}^n$, obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDE's. While the resulting family of PDE's and numerical schemes are quite general, we give special attention to their application for regularized inversion problems, with particular illustrative examples on some popular image processing applications. The method is a generalization of momentum, or accelerated, gradient descent to the PDE setting. For elliptic problems, the descent equations are a nonlinear damped wave equation, instead of a diffusion equation, and the acceleration is realized as an improvement in the CFL condition from $Δt\sim Δx^{2}$ (for diffusion) to $Δt\sim Δx$ (for wave equations). We work out several explicit as well as a semi-implicit numerical schemes, together with their necessary stability constraints, and include recursive update formulations which allow minimal-effort adaptation of existing gradient descent PDE codes into the accelerated PDE framework. We explore these schemes more carefully for a broad class of regularized inversion applications, with special attention to quadratic, Beltrami, and Total Variation regularization, where the accelerated PDE takes the form of a nonlinear wave equation. Experimental examples demonstrate the application of these schemes for image denoising, deblurring, and inpainting, including comparisons against Primal Dual, Split Bregman, and ADMM algorithms.

math.NA↗

arXiv2018

Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms

We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by generalizing Nesterov accelerated optimization to the manifold of diffeomorphisms. While our framework is general for infinite dimensional manifolds, we specifically treat the case of diffeomorphisms, motivated by optical flow problems in computer vision. This is accomplished by building on a recent variational approach to a general class of accelerated optimization methods by Wibisono, Wilson and Jordan, which applies in finite dimensions. We generalize that approach to infinite dimensional manifolds. We derive the surprisingly simple continuum evolution equations, which are partial differential equations, for accelerated gradient descent, and relate it to simple mechanical principles from fluid mechanics. Our approach has natural connections to the optimal mass transport problem. This is because one can think of our approach as an evolution of an infinite number of particles endowed with mass (represented with a mass density) that moves in an energy landscape. The mass evolves with the optimization variable, and endows the particles with dynamics. This is different than the finite dimensional case where only a single particle moves and hence the dynamics does not depend on the mass. We derive the theory, compute the PDEs for accelerated optimization, and illustrate the behavior of these new accelerated optimization schemes.

math.OC↗

arXiv2017

Accelerated Optimization in the PDE Framework: Formulations for the Active Contour Case

Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are either inapplicable or impractical. Not only does accelerated gradient descent converge considerably faster than traditional gradient descent, but it also performs a more robust local search of the parameter space by initially overshooting and then oscillating back as it settles into a final configuration, thereby selecting only local minimizers with a basis of attraction large enough to contain the initial overshoot. This behavior has made accelerated and stochastic gradient search methods particularly popular within the machine learning community. In their recent PNAS 2016 paper, Wibisono, Wilson, and Jordan demonstrate how a broad class of accelerated schemes can be cast in a variational framework formulated around the Bregman divergence, leading to continuum limit ODE's. We show how their formulation may be further extended to infinite dimension manifolds (starting here with the geometric space of curves and surfaces) by substituting the Bregman divergence with inner products on the tangent space and explicitly introducing a distributed mass model which evolves in conjunction with the object of interest during the optimization process. The co-evolving mass model, which is introduced purely for the sake of endowing the optimization with helpful dynamics, also links the resulting class of accelerated PDE based optimization schemes to fluid dynamical formulations of optimal mass transport.

math.NA↗