Akshay Kumar

Hyam Omar Ali, Sahar Alhesseen, Lamis Elkhair et al.

Mycetoma is a neglected tropical disease caused by fungi or bacteria leading to severe tissue damage and disabilities. It affects poor and rural communities and presents medical challenges and socioeconomic burdens on patients and healthcare systems in endemic regions worldwide. Mycetoma diagnosis is a major challenge in mycetoma management, particularly in low-resource settings where expert pathologists are limited. To address this challenge, this paper presents an overview of the Mycetoma MicroImage: Detect and Classify Challenge (mAIcetoma) which was organized to advance mycetoma diagnosis through AI solutions. mAIcetoma focused on developing automated models for segmenting mycetoma grains and classifying mycetoma types from histopathological images. The challenge attracted the attention of several teams worldwide to participate and five finalist teams fulfilled the challenge objectives. The teams proposed various deep learning architectures for the ultimate goal of this challenge. Mycetoma database (MyData) was provided to participants as a standardized dataset to run the proposed models. Those models were evaluated using evaluation metrics. Results showed that all the models achieved high segmentation accuracy, emphasizing the necessitate of grain detection as a critical step in mycetoma diagnosis. In addition, the top-performing models show a significant performance in classifying mycetoma types.

Shailaja Keyur Sampat, Akshay Kumar, Yezhou Yang et al.

Most existing research on visual question answering (VQA) is limited to information explicitly present in an image or a video. In this paper, we take visual understanding to a higher level where systems are challenged to answer questions that involve mentally simulating the hypothetical consequences of performing specific actions in a given scenario. Towards that end, we formulate a vision-language question answering task based on the CLEVR (Johnson et. al., 2017) dataset. We then modify the best existing VQA methods and propose baseline solvers for this task. Finally, we motivate the development of better vision-language models by providing insights about the capability of diverse architectures to perform joint reasoning over image-text modality. Our dataset setup scripts and codes will be made publicly available at https://github.com/shailaja183/clevr_hyp.

Akshay Kumar, Jarvis Haupt

This paper examines gradient flow dynamics of two-homogeneous neural networks for small initializations, where all weights are initialized near the origin. For both square and logistic losses, it is shown that for sufficiently small initializations, the gradient flow dynamics spend sufficient time in the neighborhood of the origin to allow the weights of the neural network to approximately converge in direction to the Karush-Kuhn-Tucker (KKT) points of a neural correlation function that quantifies the correlation between the output of the neural network and corresponding labels in the training data set. For square loss, it has been observed that neural networks undergo saddle-to-saddle dynamics when initialized close to the origin. Motivated by this, this paper also shows a similar directional convergence among weights of small magnitude in the neighborhood of certain saddle points.

Akshay Kumar, Jarvis Haupt

This paper studies the gradient flow dynamics that arise when training deep homogeneous neural networks assumed to have locally Lipschitz gradients and an order of homogeneity strictly greater than two. It is shown here that for sufficiently small initializations, during the early stages of training, the weights of the neural network remain small in (Euclidean) norm and approximately converge in direction to the Karush-Kuhn-Tucker (KKT) points of the recently introduced neural correlation function. Additionally, this paper also studies the KKT points of the neural correlation function for feed-forward networks with (Leaky) ReLU and polynomial (Leaky) ReLU activations, deriving necessary and sufficient conditions for rank-one KKT points.

Akshay Kumar, Jarvis Haupt

Recent works exploring the training dynamics of homogeneous neural network weights under gradient flow with small initialization have established that in the early stages of training, the weights remain small and near the origin, but converge in direction. Building on this, the current paper studies the gradient flow dynamics of homogeneous neural networks with locally Lipschitz gradients, after they escape the origin. Insights gained from this analysis are used to characterize the first saddle point encountered by gradient flow after escaping the origin. Also, it is shown that for homogeneous feed-forward neural networks, under certain conditions, the sparsity structure emerging among the weights before the escape is preserved after escaping the origin and until reaching the next saddle point.

Akshay Kumar, Jarvis Haupt

The first part of this paper studies the evolution of gradient flow for homogeneous neural networks near a class of saddle points exhibiting a sparsity structure. The choice of these saddle points is motivated from previous works on homogeneous networks, which identified the first saddle point encountered by gradient flow after escaping the origin. It is shown here that, when initialized sufficiently close to such saddle points, gradient flow remains near the saddle point for a sufficiently long time, during which the set of weights with small norm remain small but converge in direction. Furthermore, important empirical observations are made on the behavior of gradient descent after escaping these saddle points. The second part of the paper, motivated by these results, introduces a greedy algorithm to train deep neural networks called Neuron Pursuit (NP). It is an iterative procedure which alternates between expanding the network by adding neuron(s) with carefully chosen weights, and minimizing the training loss using this augmented network. The efficacy of the proposed algorithm is validated using numerical experiments.

Vinay Damodaran, Sharanya Chakravarthy, Akshay Kumar et al.

Visual Question Answering (VQA) is of tremendous interest to the research community with important applications such as aiding visually impaired users and image-based search. In this work, we explore the use of scene graphs for solving the VQA task. We conduct experiments on the GQA dataset which presents a challenging set of questions requiring counting, compositionality and advanced reasoning capability, and provides scene graphs for a large number of images. We adopt image + question architectures for use with scene graphs, evaluate various scene graph generation techniques for unseen images, propose a training curriculum to leverage human-annotated and auto-generated scene graphs, and build late fusion architectures to learn from multiple image representations. We present a multi-faceted study into the use of scene graphs for VQA, making this work the first of its kind.

Akshay Kumar, Jarvis Haupt

This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et al., 2012], we derive simple characterizations of the convex hulls of the corresponding atomic sets for this problem under several different constraints on the weights and biases of the network, thus obtaining equivalent convex formulations for these problems. A modest extension of our proposed framework to a binary classification problem is also presented. We explore the efficacy of the resulting formulations experimentally, and compare with networks trained via gradient descent.