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Deep generative models learn continuous representations of complex data manifolds using a finite number of samples during training. For a pre-trained generative model, the common way to evaluate the quality of the manifold representation learned, is by computing global metrics like Fr\'echet Inception Distance using a large number of generated and real samples. However, generative model performance is not uniform across the learned manifold, e.g., for \textit{foundation models} like Stable Diffusion generation performance can vary significantly based on the conditioning or initial noise vector being denoised. In this paper we study the relationship between the \textit{local geometry of the learned manifold} and downstream generation. Based on the theory of continuous piecewise-linear (CPWL) generators, we use three geometric descriptors - scaling ($\psi$), rank ($\nu$), and complexity ($\delta$) - to characterize a pre-trained generative model manifold locally. We provide quantitative and qualitative evidence showing that for a given latent, the local descriptors are correlated with generation aesthetics, artifacts, uncertainty, and even memorization. Finally we demonstrate that training a \textit{reward model} on the local geometry can allow controlling the likelihood of a generated sample under the learned distribution., Comment: Pre-print. 11 pages main, 8 pages app., 28 figures

The rise of foundation models holds immense promise for advancing AI, but this progress may amplify existing risks and inequalities, leaving marginalized communities behind. In this position paper, we discuss that disparities towards marginalized communities - performance, representation, privacy, robustness, interpretability and safety - are not isolated concerns but rather interconnected elements of a cascading disparity phenomenon. We contrast foundation models with traditional models and highlight the potential for exacerbated disparity against marginalized communities. Moreover, we emphasize the unique threat of cascading impacts in foundation models, where interconnected disparities can trigger long-lasting negative consequences, specifically to the people on the margin. We define marginalized communities within the machine learning context and explore the multifaceted nature of disparities. We analyze the sources of these disparities, tracing them from data creation, training and deployment procedures to highlight the complex technical and socio-technical landscape. To mitigate the pressing crisis, we conclude with a set of calls to action to mitigate disparity at its source., Comment: 14 pages, 1 figure

Deep learning classifiers are prone to latching onto dominant confounders present in a dataset rather than on the causal markers associated with the target class, leading to poor generalization and biased predictions. Although explainability via counterfactual image generation has been successful at exposing the problem, bias mitigation strategies that permit accurate explainability in the presence of dominant and diverse artifacts remain unsolved. In this work, we propose the DeCoDEx framework and show how an external, pre-trained binary artifact detector can be leveraged during inference to guide a diffusion-based counterfactual image generator towards accurate explainability. Experiments on the CheXpert dataset, using both synthetic artifacts and real visual artifacts (support devices), show that the proposed method successfully synthesizes the counterfactual images that change the causal pathology markers associated with Pleural Effusion while preserving or ignoring the visual artifacts. Augmentation of ERM and Group-DRO classifiers with the DeCoDEx generated images substantially improves the results across underrepresented groups that are out of distribution for each class. The code is made publicly available at https://github.com/NimaFathi/DeCoDEx., Comment: Accepted to Medical Imaging with Deep Learning (MIDL) 2024

While neural networks are capable of achieving human-like performance in many tasks such as image classification, the impressive performance of each model is limited to its own dataset. Source-free domain adaptation (SFDA) was introduced to address knowledge transfer between different domains in the absence of source data, thus, increasing data privacy. Diversity in representation space can be vital to a model`s adaptability in varied and difficult domains. In unsupervised SFDA, the diversity is limited to learning a single hypothesis on the source or learning multiple hypotheses with a shared feature extractor. Motivated by the improved predictive performance of ensembles, we propose a novel unsupervised SFDA algorithm that promotes representational diversity through the use of separate feature extractors with Distinct Backbone Architectures (DBA). Although diversity in feature space is increased, the unconstrained mutual information (MI) maximization may potentially introduce amplification of weak hypotheses. Thus we introduce the Weak Hypothesis Penalization (WHP) regularizer as a mitigation strategy. Our work proposes Penalized Diversity (PD) where the synergy of DBA and WHP is applied to unsupervised source-free domain adaptation for covariate shift. In addition, PD is augmented with a weighted MI maximization objective for label distribution shift. Empirical results on natural, synthetic, and medical domains demonstrate the effectiveness of PD under different distributional shifts.

Humans have perfected the art of learning from multiple modalities through sensory organs. Despite their impressive predictive performance on a single modality, neural networks cannot reach human level accuracy with respect to multiple modalities. This is a particularly challenging task due to variations in the structure of respective modalities. Conditional Batch Normalization (CBN) is a popular method that was proposed to learn contextual features to aid deep learning tasks. This technique uses auxiliary data to improve representational power by learning affine transformations for convolutional neural networks. Despite the boost in performance observed by using CBN layers, our work reveals that the visual features learned by introducing auxiliary data via CBN deteriorates. We perform comprehensive experiments to evaluate the brittleness of CBN networks to various datasets, suggesting that learning from visual features alone could often be superior for generalization. We evaluate CBN models on natural images for bird classification and histology images for cancer type classification. We observe that the CBN network learns close to no visual features on the bird classification dataset and partial visual features on the histology dataset. Our extensive experiments reveal that CBN may encourage shortcut learning between the auxiliary data and labels., Comment: Accepted at ICBINB workshop @ NeurIPS 2022

Federated learning aims to train predictive models for data that is distributed across clients, under the orchestration of a server. However, participating clients typically each hold data from a different distribution, which can yield to catastrophic generalization on data from a different client, which represents a new domain. In this work, we argue that in order to generalize better across non-i.i.d. clients, it is imperative to only learn correlations that are stable and invariant across domains. We propose FL GAMES, a game-theoretic framework for federated learning that learns causal features that are invariant across clients. While training to achieve the Nash equilibrium, the traditional best response strategy suffers from high-frequency oscillations. We demonstrate that FL GAMES effectively resolves this challenge and exhibits smooth performance curves. Further, FL GAMES scales well in the number of clients, requires significantly fewer communication rounds, and is agnostic to device heterogeneity. Through empirical evaluation, we demonstrate that FL GAMES achieves high out-of-distribution performance on various benchmarks., Comment: Accepted as ORAL at NeurIPS Workshop on Federated Learning: Recent Advances and New Challenges. arXiv admin note: text overlap with arXiv:2205.11101

Few-shot learning has recently attracted wide interest in image classification, but almost all the current public benchmarks are focused on natural images. The few-shot paradigm is highly relevant in medical-imaging applications due to the scarcity of labeled data, as annotations are expensive and require specialized expertise. However, in medical imaging, few-shot learning research is sparse, limited to private data sets and is at its early stage. In particular, the few-shot setting is of high interest in histology due to the diversity and fine granularity of cancer related tissue classification tasks, and the variety of data-preparation techniques. This paper introduces a highly diversified public benchmark, gathered from various public datasets, for few-shot histology data classification. We build few-shot tasks and base-training data with various tissue types, different levels of domain shifts stemming from various cancer sites, and different class-granularity levels, thereby reflecting realistic scenarios. We evaluate the performances of state-of-the-art few-shot learning methods on our benchmark, and observe that simple fine-tuning and regularization methods achieve better results than the popular meta-learning and episodic-training paradigm. Furthermore, we introduce three scenarios based on the domain shifts between the source and target histology data: near-domain, middle-domain and out-domain. Our experiments display the potential of few-shot learning in histology classification, with state-of-art few shot learning methods approaching the supervised-learning baselines in the near-domain setting. In our out-domain setting, for 5-way 5-shot, the best performing method reaches 60% accuracy. We believe that our work could help in building realistic evaluations and fair comparisons of few-shot learning methods and will further encourage research in the few-shot paradigm., Comment: Code available at: https://github.com/mboudiaf/Few-shot-histology

In Federated Learning (FL), a number of clients or devices collaborate to train a model without sharing their data. Models are optimized locally at each client and further communicated to a central hub for aggregation. While FL is an appealing decentralized training paradigm, heterogeneity among data from different clients can cause the local optimization to drift away from the global objective. In order to estimate and therefore remove this drift, variance reduction techniques have been incorporated into FL optimization recently. However, these approaches inaccurately estimate the clients' drift and ultimately fail to remove it properly. In this work, we propose an adaptive algorithm that accurately estimates drift across clients. In comparison to previous works, our approach necessitates less storage and communication bandwidth, as well as lower compute costs. Additionally, our proposed methodology induces stability by constraining the norm of estimates for client drift, making it more practical for large scale FL. Experimental findings demonstrate that the proposed algorithm converges significantly faster and achieves higher accuracy than the baselines across various FL benchmarks., Comment: Published as a conference paper at ECCV 2022; Corrected some typos in the text and a baseline algorithm

Diversity in data is critical for the successful training of deep learning models. Leveraged by a recurrent generative adversarial network, we propose the CT-SGAN model that generates large-scale 3D synthetic CT-scan volumes ($\geq 224\times224\times224$) when trained on a small dataset of chest CT-scans. CT-SGAN offers an attractive solution to two major challenges facing machine learning in medical imaging: a small number of given i.i.d. training data, and the restrictions around the sharing of patient data preventing to rapidly obtain larger and more diverse datasets. We evaluate the fidelity of the generated images qualitatively and quantitatively using various metrics including Fr\'echet Inception Distance and Inception Score. We further show that CT-SGAN can significantly improve lung nodule detection accuracy by pre-training a classifier on a vast amount of synthetic data., Comment: In Proceedings of MICCAI Deep Generative Models workshop, October 2021

We propose a hypothesis disparity regularized mutual information maximization~(HDMI) approach to tackle unsupervised hypothesis transfer -- as an effort towards unifying hypothesis transfer learning (HTL) and unsupervised domain adaptation (UDA) -- where the knowledge from a source domain is transferred solely through hypotheses and adapted to the target domain in an unsupervised manner. In contrast to the prevalent HTL and UDA approaches that typically use a single hypothesis, HDMI employs multiple hypotheses to leverage the underlying distributions of the source and target hypotheses. To better utilize the crucial relationship among different hypotheses -- as opposed to unconstrained optimization of each hypothesis independently -- while adapting to the unlabeled target domain through mutual information maximization, HDMI incorporates a hypothesis disparity regularization that coordinates the target hypotheses jointly learn better target representations while preserving more transferable source knowledge with better-calibrated prediction uncertainty. HDMI achieves state-of-the-art adaptation performance on benchmark datasets for UDA in the context of HTL, without the need to access the source data during the adaptation., Comment: Accepted to AAAI 2021

Synthetic medical image generation has a huge potential for improving healthcare through many applications, from data augmentation for training machine learning systems to preserving patient privacy. Conditional Adversarial Generative Networks (cGANs) use a conditioning factor to generate images and have shown great success in recent years. Intuitively, the information in an image can be divided into two parts: 1) content which is presented through the conditioning vector and 2) style which is the undiscovered information missing from the conditioning vector. Current practices in using cGANs for medical image generation, only use a single variable for image generation (i.e., content) and therefore, do not provide much flexibility nor control over the generated image. In this work we propose a methodology to learn from the image itself, disentangled representations of style and content, and use this information to impose control over the generation process. In this framework, style is learned in a fully unsupervised manner, while content is learned through both supervised learning (using the conditioning vector) and unsupervised learning (with the inference mechanism). We undergo two novel regularization steps to ensure content-style disentanglement. First, we minimize the shared information between content and style by introducing a novel application of the gradient reverse layer (GRL); second, we introduce a self-supervised regularization method to further separate information in the content and style variables. We show that in general, two latent variable models achieve better performance and give more control over the generated image. We also show that our proposed model (DRAI) achieves the best disentanglement score and has the best overall performance., Comment: Published in Medical Image Analysis

We present an approach for unsupervised domain adaptation---with a strong focus on practical considerations of within-domain class imbalance and between-domain class distribution shift---from a class-conditioned domain alignment perspective. Current methods for class-conditioned domain alignment aim to explicitly minimize a loss function based on pseudo-label estimations of the target domain. However, these methods suffer from pseudo-label bias in the form of error accumulation. We propose a method that removes the need for explicit optimization of model parameters from pseudo-labels directly. Instead, we present a sampling-based implicit alignment approach, where the sample selection procedure is implicitly guided by the pseudo-labels. Theoretical analysis reveals the existence of a domain-discriminator shortcut in misaligned classes, which is addressed by the proposed implicit alignment approach to facilitate domain-adversarial learning. Empirical results and ablation studies confirm the effectiveness of the proposed approach, especially in the presence of within-domain class imbalance and between-domain class distribution shift., Comment: Accepted at ICML2020. For code, see https://github.com/xiangdal/implicit_alignment

The latent variables learned by VAEs have seen considerable interest as an unsupervised way of extracting features, which can then be used for downstream tasks. There is a growing interest in the question of whether features learned on one environment will generalize across different environments. We demonstrate here that VAE latent variables often focus on some factors of variation at the expense of others - in this case we refer to the features as ``imbalanced''. Feature imbalance leads to poor generalization when the latent variables are used in an environment where the presence of features changes. Similarly, latent variables trained with imbalanced features induce the VAE to generate less diverse (i.e. biased towards dominant features) samples. To address this, we propose a regularization scheme for VAEs, which we show substantially addresses the feature imbalance problem. We also introduce a simple metric to measure the balance of features in generated images.

Despite the powerful feature extraction capability of Convolutional Neural Networks, there are still some challenges in saliency detection. In this paper, we focus on two aspects of challenges: i) Since salient objects appear in various sizes, using single-scale convolution would not capture the right size. Moreover, using multi-scale convolutions without considering their importance may confuse the model. ii) Employing multi-level features helps the model use both local and global context. However, treating all features equally results in information redundancy. Therefore, there needs to be a mechanism to intelligently select which features in different levels are useful. To address the first challenge, we propose a Multi-scale Attention Guided Module. This module not only extracts multi-scale features effectively but also gives more attention to more discriminative feature maps corresponding to the scale of the salient object. To address the second challenge, we propose an Attention-based Multi-level Integrator Module to give the model the ability to assign different weights to multi-level feature maps. Furthermore, our Sharpening Loss function guides our network to output saliency maps with higher certainty and less blurry salient objects, and it has far better performance than the Cross-entropy loss. For the first time, we adopt four different backbones to show the generalization of our method. Experiments on five challenging datasets prove that our method achieves the state-of-the-art performance. Our approach is fast as well and can run at a real-time speed., Comment: Accepted by Engineering Applications of Artificial Intelligence. 22 pages, 8 figures

Learning in non-stationary environments is one of the biggest challenges in machine learning. Non-stationarity can be caused by either task drift, i.e., the drift in the conditional distribution of labels given the input data, or the domain drift, i.e., the drift in the marginal distribution of the input data. This paper aims to tackle this challenge in the context of continuous domain adaptation, where the model is required to learn new tasks adapted to new domains in a non-stationary environment while maintaining previously learned knowledge. To deal with both drifts, we propose variational domain-agnostic feature replay, an approach that is composed of three components: an inference module that filters the input data into domain-agnostic representations, a generative module that facilitates knowledge transfer, and a solver module that applies the filtered and transferable knowledge to solve the queries. We address the two fundamental scenarios in continuous domain adaptation, demonstrating the effectiveness of our proposed approach for practical usage.

In this paper, we propose a general framework in continual learning for generative models: Feature-oriented Continual Learning (FoCL). Unlike previous works that aim to solve the catastrophic forgetting problem by introducing regularization in the parameter space or image space, FoCL imposes regularization in the feature space. We show in our experiments that FoCL has faster adaptation to distributional changes in sequentially arriving tasks, and achieves the state-of-the-art performance for generative models in task incremental learning. We discuss choices of combined regularization spaces towards different use case scenarios for boosted performance, e.g., tasks that have high variability in the background. Finally, we introduce a forgetfulness measure that fairly evaluates the degree to which a model suffers from forgetting. Interestingly, the analysis of our proposed forgetfulness score also implies that FoCL tends to have a mitigated forgetting for future tasks.

Beneficial from Fully Convolutional Neural Networks (FCNs), saliency detection methods have achieved promising results. However, it is still challenging to learn effective features for detecting salient objects in complicated scenarios, in which i) non-salient regions may have "salient-like" appearance; ii) the salient objects may have different-looking regions. To handle these complex scenarios, we propose a Feature Guide Network which exploits the nature of low-level and high-level features to i) make foreground and background regions more distinct and suppress the non-salient regions which have "salient-like" appearance; ii) assign foreground label to different-looking salient regions. Furthermore, we utilize a Multi-scale Feature Extraction Module (MFEM) for each level of abstraction to obtain multi-scale contextual information. Finally, we design a loss function which outperforms the widely-used Cross-entropy loss. By adopting four different pre-trained models as the backbone, we prove that our method is very general with respect to the choice of the backbone model. Experiments on five challenging datasets demonstrate that our method achieves the state-of-the-art performance in terms of different evaluation metrics. Additionally, our approach contains fewer parameters than the existing ones, does not need any post-processing, and runs fast at a real-time speed of 28 FPS when processing a 480 x 480 image., Comment: 25 pages, 10 figures, 5 tables, Accepted by Elsevier, Pattern Recognition

Synthesizing images from a given text description involves engaging two types of information: the content, which includes information explicitly described in the text (e.g., color, composition, etc.), and the style, which is usually not well described in the text (e.g., location, quantity, size, etc.). However, in previous works, it is typically treated as a process of generating images only from the content, i.e., without considering learning meaningful style representations. In this paper, we aim to learn two variables that are disentangled in the latent space, representing content and style respectively. We achieve this by augmenting current text-to-image synthesis frameworks with a dual adversarial inference mechanism. Through extensive experiments, we show that our model learns, in an unsupervised manner, style representations corresponding to certain meaningful information present in the image that are not well described in the text. The new framework also improves the quality of synthesized images when evaluated on Oxford-102, CUB and COCO datasets., Comment: Accepted to ICCV 2019

The scarcity of richly annotated medical images is limiting supervised deep learning based solutions to medical image analysis tasks, such as localizing discriminatory radiomic disease signatures. Therefore, it is desirable to leverage unsupervised and weakly supervised models. Most recent weakly supervised localization methods apply attention maps or region proposals in a multiple instance learning formulation. While attention maps can be noisy, leading to erroneously highlighted regions, it is not simple to decide on an optimal window/bag size for multiple instance learning approaches. In this paper, we propose a learned spatial masking mechanism to filter out irrelevant background signals from attention maps. The proposed method minimizes mutual information between a masked variational representation and the input while maximizing the information between the masked representation and class labels. This results in more accurate localization of discriminatory regions. We tested the proposed model on the ChestX-ray8 dataset to localize pneumonia from chest X-ray images without using any pixel-level or bounding-box annotations., Comment: Accepted to MICCAI 2019

Current deep learning based text classification methods are limited by their ability to achieve fast learning and generalization when the data is scarce. We address this problem by integrating a meta-learning procedure that uses the knowledge learned across many tasks as an inductive bias towards better natural language understanding. Based on the Model-Agnostic Meta-Learning framework (MAML), we introduce the Attentive Task-Agnostic Meta-Learning (ATAML) algorithm for text classification. The essential difference between MAML and ATAML is in the separation of task-agnostic representation learning and task-specific attentive adaptation. The proposed ATAML is designed to encourage task-agnostic representation learning by way of task-agnostic parameterization and facilitate task-specific adaptation via attention mechanisms. We provide evidence to show that the attention mechanism in ATAML has a synergistic effect on learning performance. In comparisons with models trained from random initialization, pretrained models and meta trained MAML, our proposed ATAML method generalizes better on single-label and multi-label classification tasks in miniRCV1 and miniReuters-21578 datasets., Comment: 13 pages, 4 figures, submitted to NIPS

In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its corresponding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and inference. Second, we analyze the family of inverse autoregressive flows (inverse AF) and show that with further improvement, inverse AF could be used as universal approximation to any complicated posterior. Our analysis results in a unified approach to parameterizing a VAE, without the need to restrict ourselves to use factorial Gaussians in the latent real space., Comment: 2 figures, 5 pages, submitted to ICML Principled Approaches to Deep Learning workshop

We introduce a deep learning image segmentation framework that is extremely robust to missing imaging modalities. Instead of attempting to impute or synthesize missing data, the proposed approach learns, for each modality, an embedding of the input image into a single latent vector space for which arithmetic operations (such as taking the mean) are well defined. Points in that space, which are averaged over modalities available at inference time, can then be further processed to yield the desired segmentation. As such, any combinatorial subset of available modalities can be provided as input, without having to learn a combinatorial number of imputation models. Evaluated on two neurological MRI datasets (brain tumors and MS lesions), the approach yields state-of-the-art segmentation results when provided with all modalities; moreover, its performance degrades remarkably gracefully when modalities are removed, significantly more so than alternative mean-filling or other synthesis approaches., Comment: Accepted as an oral presentation at MICCAI 2016

Segmentation of focal (localized) brain pathologies such as brain tumors and brain lesions caused by multiple sclerosis and ischemic strokes are necessary for medical diagnosis, surgical planning and disease development as well as other applications such as tractography. Over the years, attempts have been made to automate this process for both clinical and research reasons. In this regard, machine learning methods have long been a focus of attention. Over the past two years, the medical imaging field has seen a rise in the use of a particular branch of machine learning commonly known as deep learning. In the non-medical computer vision world, deep learning based methods have obtained state-of-the-art results on many datasets. Recent studies in computer aided diagnostics have shown deep learning methods (and especially convolutional neural networks - CNN) to yield promising results. In this chapter, we provide a survey of CNN methods applied to medical imaging with a focus on brain pathology segmentation. In particular, we discuss their characteristic peculiarities and their specific configuration and adjustments that are best suited to segment medical images. We also underline the intrinsic differences deep learning methods have with other machine learning methods., Comment: Published in Machine Learning for Health Informatics

Purpose: In this paper, we investigate a framework for interactive brain tumor segmentation which, at its core, treats the problem of interactive brain tumor segmentation as a machine learning problem. Methods: This method has an advantage over typical machine learning methods for this task where generalization is made across brains. The problem with these methods is that they need to deal with intensity bias correction and other MRI-specific noise. In this paper, we avoid these issues by approaching the problem as one of within brain generalization. Specifically, we propose a semi-automatic method that segments a brain tumor by training and generalizing within that brain only, based on some minimum user interaction. Conclusion: We investigate how adding spatial feature coordinates (i.e. $i$, $j$, $k$) to the intensity features can significantly improve the performance of different classification methods such as SVM, kNN and random forests. This would only be possible within an interactive framework. We also investigate the use of a more appropriate kernel and the adaptation of hyper-parameters specifically for each brain. Results: As a result of these experiments, we obtain an interactive method whose results reported on the MICCAI-BRATS 2013 dataset are the second most accurate compared to published methods, while using significantly less memory and processing power than most state-of-the-art methods.

In this paper, we present a fully automatic brain tumor segmentation method based on Deep Neural Networks (DNNs). The proposed networks are tailored to glioblastomas (both low and high grade) pictured in MR images. By their very nature, these tumors can appear anywhere in the brain and have almost any kind of shape, size, and contrast. These reasons motivate our exploration of a machine learning solution that exploits a flexible, high capacity DNN while being extremely efficient. Here, we give a description of different model choices that we've found to be necessary for obtaining competitive performance. We explore in particular different architectures based on Convolutional Neural Networks (CNN), i.e. DNNs specifically adapted to image data. We present a novel CNN architecture which differs from those traditionally used in computer vision. Our CNN exploits both local features as well as more global contextual features simultaneously. Also, different from most traditional uses of CNNs, our networks use a final layer that is a convolutional implementation of a fully connected layer which allows a 40 fold speed up. We also describe a 2-phase training procedure that allows us to tackle difficulties related to the imbalance of tumor labels. Finally, we explore a cascade architecture in which the output of a basic CNN is treated as an additional source of information for a subsequent CNN. Results reported on the 2013 BRATS test dataset reveal that our architecture improves over the currently published state-of-the-art while being over 30 times faster.

Future services demand high data rate and quality. Thus, it is necessary to define new and robust algorithms to equalize channels and reduce noise in communications. Nowadays, new equalization algorithms are being developed to optimize the channel bandwidth and reduce noise, namely, Blind Channel Equalization. Conventional equalizations minimizing mean-square error generally require a training sequence accompanying the data sequence. In this study, the result of Least Mean Square (LMS) algorithm applied on two given communication channels is analyzed. Considering the fact that blind equalizers do not require pilot signals to recover the transmitted data, implementation of four types of Constant Modulus Algorithm (CMA) for blind equalization of the channels are shown. Finally, a comparison of the simulation results of LMS and CMA for the test channels is provided.

This paper deals with the implementation of Least Mean Square (LMS) algorithm in Decision Feedback Equalizer (DFE) for removal of Inter Symbol Interference (ISI) at the receiver. The channel disrupts the transmitted signal by spreading it in time. Although, the LMS algorithm is robust and reliable, it is slow in convergence. In order to increase the speed of convergence, modifications have been made in the algorithm where the weights get updated depending on the severity of disturbance.