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Ubiquitous applications of Deep neural networks (DNNs) in different artificial intelligence systems have led to their adoption in solving challenging visualization problems in recent years. While sophisticated DNNs offer an impressive generalization, it is imperative to comprehend the quality, confidence, robustness, and uncertainty associated with their prediction. A thorough understanding of these quantities produces actionable insights that help application scientists make informed decisions. Unfortunately, the intrinsic design principles of the DNNs cannot beget prediction uncertainty, necessitating separate formulations for robust uncertainty-aware models for diverse visualization applications. To that end, this contribution demonstrates how the prediction uncertainty and sensitivity of DNNs can be estimated efficiently using various methods and then interactively compared and contrasted for deep image synthesis tasks. Our inspection suggests that uncertainty-aware deep visualization models generate illustrations of informative and superior quality and diversity. Furthermore, prediction uncertainty improves the robustness and interpretability of deep visualization models, making them practical and convenient for various scientific domains that thrive on visual analyses.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss., Comment: To appear at ICLR 2024

With the rising popularity of Large Language Models (LLMs), there has been an increasing interest in compression techniques that enable their efficient deployment. This study focuses on the Post-Training Quantization (PTQ) of LLMs. Drawing from recent advances, our work introduces QuantEase, a layer-wise quantization framework where individual layers undergo separate quantization. The problem is framed as a discrete-structured non-convex optimization, prompting the development of algorithms rooted in Coordinate Descent (CD) techniques. These CD-based methods provide high-quality solutions to the complex non-convex layer-wise quantization problems. Notably, our CD-based approach features straightforward updates, relying solely on matrix and vector operations, circumventing the need for matrix inversion or decomposition. We also explore an outlier-aware variant of our approach, allowing for retaining significant weights (outliers) with complete precision. Our proposal attains state-of-the-art performance in terms of perplexity and zero-shot accuracy in empirical evaluations across various LLMs and datasets, with relative improvements up to 15% over methods such as GPTQ. Leveraging careful linear algebra optimizations, QuantEase can quantize models like Falcon-180B on a single NVIDIA A100 GPU in $\sim$3 hours. Particularly noteworthy is our outlier-aware algorithm's capability to achieve near or sub-3-bit quantization of LLMs with an acceptable drop in accuracy, obviating the need for non-uniform quantization or grouping techniques, improving upon methods such as SpQR by up to two times in terms of perplexity.

Modern deep learning models are over-parameterized, where different optima can result in widely varying generalization performance. The Sharpness-Aware Minimization (SAM) technique modifies the fundamental loss function that steers gradient descent methods toward flatter minima, which are believed to exhibit enhanced generalization prowess. Our study delves into a specific variant of SAM known as micro-batch SAM (mSAM). This variation involves aggregating updates derived from adversarial perturbations across multiple shards (micro-batches) of a mini-batch during training. We extend a recently developed and well-studied general framework for flatness analysis to theoretically show that SAM achieves flatter minima than SGD, and mSAM achieves even flatter minima than SAM. We provide a thorough empirical evaluation of various image classification and natural language processing tasks to substantiate this theoretical advancement. We also show that contrary to previous work, mSAM can be implemented in a flexible and parallelizable manner without significantly increasing computational costs. Our implementation of mSAM yields superior generalization performance across a wide range of tasks compared to SAM, further supporting our theoretical framework., Comment: arXiv admin note: substantial text overlap with arXiv:2212.04343

Modern deep learning models are over-parameterized, where the optimization setup strongly affects the generalization performance. A key element of reliable optimization for these systems is the modification of the loss function. Sharpness-Aware Minimization (SAM) modifies the underlying loss function to guide descent methods towards flatter minima, which arguably have better generalization abilities. In this paper, we focus on a variant of SAM known as mSAM, which, during training, averages the updates generated by adversarial perturbations across several disjoint shards of a mini-batch. Recent work suggests that mSAM can outperform SAM in terms of test accuracy. However, a comprehensive empirical study of mSAM is missing from the literature -- previous results have mostly been limited to specific architectures and datasets. To that end, this paper presents a thorough empirical evaluation of mSAM on various tasks and datasets. We provide a flexible implementation of mSAM and compare the generalization performance of mSAM to the performance of SAM and vanilla training on different image classification and natural language processing tasks. We also conduct careful experiments to understand the computational cost of training with mSAM, its sensitivity to hyperparameters and its correlation with the flatness of the loss landscape. Our analysis reveals that mSAM yields superior generalization performance and flatter minima, compared to SAM, across a wide range of tasks without significantly increasing computational costs.

Many tasks that rely on representations of nodes in graphs would benefit if those representations were faithful to distances between nodes in the graph. Geometric techniques to extract such representations have poor scaling over large graph size, and recent advances in Graph Neural Network (GNN) algorithms have limited ability to reflect graph distance information beyond the first degree neighborhood. To enable this highly desired capability, we propose a technique to learn Isometric Graph Neural Networks (IGNN), which requires changing the input representation space and loss function to enable any GNN algorithm to generate representations that reflect distances between nodes. We experiment with the isometric technique on several GNN architectures for modeling multiple prediction tasks on multiple datasets. In addition to an improvement in AUC-ROC as high as $43\%$ in these experiments, we observe a consistent and substantial improvement as high as 400% in Kendall's Tau (KT), a measure that directly reflects distance information, demonstrating that the learned embeddings do account for graph distances.

A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time $(t-1)$ as the shape parameters of those at time $t$, which are linked to observed or latent counts under the Poisson likelihood. The significant challenge of inferring the gamma shape parameters is fully addressed, using unique data augmentation and marginalization techniques for the negative binomial distribution. The same nonparametric Bayesian model also applies to the factorization of a dynamic binary matrix, via a Bernoulli-Poisson link that connects a binary observation to a latent count, with closed-form conditional posteriors for the latent counts and efficient computation for sparse observations. We apply the model to text and music analysis, with state-of-the-art results., Comment: Appeared in Artificial Intelligence and Statistics (AISTATS), May 2015. The ArXiv version fixes a typo in (8), the equation right above Section 3.2 in Page 4 of http://www.jmlr.org/proceedings/papers/v38/acharya15.pdf

Unsupervised models can provide supplementary soft constraints to help classify new target data under the assumption that similar objects in the target set are more likely to share the same class label. Such models can also help detect possible differences between training and target distributions, which is useful in applications where concept drift may take place. This paper describes a Bayesian framework that takes as input class labels from existing classifiers (designed based on labeled data from the source domain), as well as cluster labels from a cluster ensemble operating solely on the target data to be classified, and yields a consensus labeling of the target data. This framework is particularly useful when the statistics of the target data drift or change from those of the training data. We also show that the proposed framework is privacy-aware and allows performing distributed learning when data/models have sharing restrictions. Experiments show that our framework can yield superior results to those provided by applying classifier ensembles only.

Unsupervised models can provide supplementary soft constraints to help classify new, "target" data since similar instances in the target set are more likely to share the same class label. Such models can also help detect possible differences between training and target distributions, which is useful in applications where concept drift may take place, as in transfer learning settings. This paper describes a general optimization framework that takes as input class membership estimates from existing classifiers learnt on previously encountered "source" data, as well as a similarity matrix from a cluster ensemble operating solely on the target data to be classified, and yields a consensus labeling of the target data. This framework admits a wide range of loss functions and classification/clustering methods. It exploits properties of Bregman divergences in conjunction with Legendre duality to yield a principled and scalable approach. A variety of experiments show that the proposed framework can yield results substantially superior to those provided by popular transductive learning techniques or by naively applying classifiers learnt on the original task to the target data.

This paper introduces a privacy-aware Bayesian approach that combines ensembles of classifiers and clusterers to perform semi-supervised and transductive learning. We consider scenarios where instances and their classification/clustering results are distributed across different data sites and have sharing restrictions. As a special case, the privacy aware computation of the model when instances of the target data are distributed across different data sites, is also discussed. Experimental results show that the proposed approach can provide good classification accuracies while adhering to the data/model sharing constraints.

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for erroneous data., Comment: 16th IEEE International Conference on Advanced Computing and Communication, 2008

The paper presents an exponential pheromone deposition approach to improve the performance of classical Ant System algorithm which employs uniform deposition rule. A simplified analysis using differential equations is carried out to study the stability of basic ant system dynamics with both exponential and constant deposition rules. A roadmap of connected cities, where the shortest path between two specified cities are to be found out, is taken as a platform to compare Max-Min Ant System model (an improved and popular model of Ant System algorithm) with exponential and constant deposition rules. Extensive simulations are performed to find the best parameter settings for non-uniform deposition approach and experiments with these parameter settings revealed that the above approach outstripped the traditional one by a large extent in terms of both solution quality and convergence time., Comment: 16th IEEE International Conference on Advanced Computing and Communication, 2008

This article presents a unique design for a parser using the Ant Colony Optimization algorithm. The paper implements the intuitive thought process of human mind through the activities of artificial ants. The scheme presented here uses a bottom-up approach and the parsing program can directly use ambiguous or redundant grammars. We allocate a node corresponding to each production rule present in the given grammar. Each node is connected to all other nodes (representing other production rules), thereby establishing a completely connected graph susceptible to the movement of artificial ants. Each ant tries to modify this sentential form by the production rule present in the node and upgrades its position until the sentential form reduces to the start symbol S. Successful ants deposit pheromone on the links that they have traversed through. Eventually, the optimum path is discovered by the links carrying maximum amount of pheromone concentration. The design is simple, versatile, robust and effective and obviates the calculation of the above mentioned sets and precedence relation tables. Further advantages of our scheme lie in i) ascertaining whether a given string belongs to the language represented by the grammar, and ii) finding out the shortest possible path from the given string to the start symbol S in case multiple routes exist., Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 2008

The paper presents an exponential pheromone deposition rule to modify the basic ant system algorithm which employs constant deposition rule. A stability analysis using differential equation is carried out to find out the values of parameters that make the ant system dynamics stable for both kinds of deposition rule. A roadmap of connected cities is chosen as the problem environment where the shortest route between two given cities is required to be discovered. Simulations performed with both forms of deposition approach using Elitist Ant System model reveal that the exponential deposition approach outperforms the classical one by a large extent. Exhaustive experiments are also carried out to find out the optimum setting of different controlling parameters for exponential deposition approach and an empirical relationship between the major controlling parameters of the algorithm and some features of problem environment., Comment: 2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA. Paper ID: 250

Particle swarm optimization (PSO) is extensively used for real parameter optimization in diverse fields of study. This paper describes an application of PSO to the problem of designing a fractional-order proportional-integral-derivative (FOPID) controller whose parameters comprise proportionality constant, integral constant, derivative constant, integral order (lambda) and derivative order (delta). The presence of five optimizable parameters makes the task of designing a FOPID controller more challenging than conventional PID controller design. Our design method focuses on minimizing the Integral Time Absolute Error (ITAE) criterion. The digital realization of the deigned system utilizes the Tustin operator-based continued fraction expansion scheme. We carry out a simulation that illustrates the effectiveness of the proposed approach especially for realizing fractional-order plants. This paper also attempts to study the behavior of fractional PID controller vis-a-vis that of its integer order counterpart and demonstrates the superiority of the former to the latter., Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 2008

Ant Colony Optimization (ACO) is a metaheuristic for solving difficult discrete optimization problems. This paper presents a deterministic model based on differential equation to analyze the dynamics of basic Ant System algorithm. Traditionally, the deposition of pheromone on different parts of the tour of a particular ant is always kept unvarying. Thus the pheromone concentration remains uniform throughout the entire path of an ant. This article introduces an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of basic Ant System algorithm. The idea here is to introduce an additional attracting force to guide the ants towards destination more easily by constructing an artificial potential field identified by increasing pheromone concentration towards the goal. Apart from carrying out analysis of Ant System dynamics with both traditional and the newly proposed deposition rules, the paper presents an exhaustive set of experiments performed to find out suitable parameter ranges for best performance of Ant System with the proposed deposition approach. Simulations reveal that the proposed deposition rule outperforms the traditional one by a large extent both in terms of solution quality and algorithm convergence. Thus, the contributions of the article can be presented as follows: i) it introduces differential equation and explores a novel method of analyzing the dynamics of ant system algorithms, ii) it initiates an exponentially increasing pheromone deposition approach by artificial ants to improve the performance of algorithm in terms of solution quality and convergence time, iii) exhaustive experimentation performed facilitates the discovery of an algebraic relationship between the parameter set of the algorithm and feature of the problem environment., Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 2008

System identification refers to estimation of process parameters and is a necessity in control theory. Physical systems usually have varying parameters. For such processes, accurate identification is particularly important. Online identification schemes are also needed for designing adaptive controllers. Real processes are usually of fractional order as opposed to the ideal integral order models. In this paper, we propose a simple and elegant scheme of estimating the parameters for such a fractional order process. A population of process models is generated and updated by particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. Results show that the proposed scheme offers a high degree of accuracy even when the observations are corrupted to a significant degree. Additional schemes to improve the accuracy still further are also proposed and analyzed., Comment: 2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA. Paper Identification Number 239