arXiv subjects

Karthikeyan Natesan Ramamurthy

Publications and source records attributed to Karthikeyan Natesan Ramamurthy.

At least 37 records · Page 2Linked to original sources

arXiv2024

Position: Topological Deep Learning is the New Frontier for Relational Learning

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

cs.LG↗

arXiv2024

Active Sequential Two-Sample Testing

A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. To address the problem, we devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries}. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is provided by a probabilistic classification model. The classification model is adaptively updated and used to predict where the (unlabelled) features have a high dependency on labels; labeling the ``high-dependency'' features leads to the increased power of the proposed testing framework. In theory, we provide the proof that our framework produces an \emph{anytime-valid} $p$-value. In addition, we characterize the proposed framework's gain in testing power by analyzing the mutual information between the feature and label variables in asymptotic and finite-sample scenarios. In practice, we introduce an instantiation of our framework and evaluate it using several experiments; the experiments on the synthetic, MNIST, and application-specific datasets demonstrate that the testing power of the instantiated active sequential test significantly increases while the Type I error is under control.

cs.LG↗

arXiv2024

Ranking Large Language Models without Ground Truth

Evaluation and ranking of large language models (LLMs) has become an important problem with the proliferation of these models and their impact. Evaluation methods either require human responses which are expensive to acquire or use pairs of LLMs to evaluate each other which can be unreliable. In this paper, we provide a novel perspective where, given a dataset of prompts (viz. questions, instructions, etc.) and a set of LLMs, we rank them without access to any ground truth or reference responses. Inspired by real life where both an expert and a knowledgeable person can identify a novice our main idea is to consider triplets of models, where each one of them evaluates the other two, correctly identifying the worst model in the triplet with high probability. We also analyze our idea and provide sufficient conditions for it to succeed. Applying this idea repeatedly, we propose two methods to rank LLMs. In experiments on different generative tasks (summarization, multiple-choice, and dialog), our methods reliably recover close to true rankings without reference data. This points to a viable low-resource mechanism for practical use.

cs.CL↗

arXiv2024

Trust Regions for Explanations via Black-Box Probabilistic Certification

Given the black box nature of machine learning models, a plethora of explainability methods have been developed to decipher the factors behind individual decisions. In this paper, we introduce a novel problem of black box (probabilistic) explanation certification. We ask the question: Given a black box model with only query access, an explanation for an example and a quality metric (viz. fidelity, stability), can we find the largest hypercube (i.e., $\ell_{\infty}$ ball) centered at the example such that when the explanation is applied to all examples within the hypercube, (with high probability) a quality criterion is met (viz. fidelity greater than some value)? Being able to efficiently find such a \emph{trust region} has multiple benefits: i) insight into model behavior in a \emph{region}, with a \emph{guarantee}; ii) ascertained \emph{stability} of the explanation; iii) \emph{explanation reuse}, which can save time, energy and money by not having to find explanations for every example; and iv) a possible \emph{meta-metric} to compare explanation methods. Our contributions include formalizing this problem, proposing solutions, providing theoretical guarantees for these solutions that are computable, and experimentally showing their efficacy on synthetic and real data.

cs.LG↗

arXiv2024

Reasoning about concepts with LLMs: Inconsistencies abound

The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical knowledge. However, we demonstrate that, when methodically questioned, large language models (LLMs) often display and demonstrate significant inconsistencies in their knowledge. Computationally, the basic aspects of the conceptualization of a given domain can be represented as Is-A hierarchies in a knowledge graph (KG) or ontology, together with a few properties or axioms that enable straightforward reasoning. We show that even simple ontologies can be used to reveal conceptual inconsistencies across several LLMs. We also propose strategies that domain experts can use to evaluate and improve the coverage of key domain concepts in LLMs of various sizes. In particular, we have been able to significantly enhance the performance of LLMs of various sizes with openly available weights using simple knowledge-graph (KG) based prompting strategies.

cs.CL↗

arXiv2024

Alignment Studio: Aligning Large Language Models to Particular Contextual Regulations

The alignment of large language models is usually done by model providers to add or control behaviors that are common or universally understood across use cases and contexts. In contrast, in this article, we present an approach and architecture that empowers application developers to tune a model to their particular values, social norms, laws and other regulations, and orchestrate between potentially conflicting requirements in context. We lay out three main components of such an Alignment Studio architecture: Framers, Instructors, and Auditors that work in concert to control the behavior of a language model. We illustrate this approach with a running example of aligning a company's internal-facing enterprise chatbot to its business conduct guidelines.

cs.CL↗

arXiv2024

ICML 2023 Topological Deep Learning Challenge : Design and Results

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.LG↗

arXiv2023

Topo-MLP : A Simplicial Network Without Message Passing

Due to their ability to model meaningful higher order relations among a set of entities, higher order network models have emerged recently as a powerful alternative for graph-based network models which are only capable of modeling binary relationships. Message passing paradigm is still dominantly used to learn representations even for higher order network models. While powerful, message passing can have disadvantages during inference, particularly when the higher order connectivity information is missing or corrupted. To overcome such limitations, we propose Topo-MLP, a purely MLP-based simplicial neural network algorithm to learn the representation of elements in a simplicial complex without explicitly relying on message passing. Our framework utilizes a novel Higher Order Neighborhood Contrastive (HONC) loss which implicitly incorporates the simplicial structure into representation learning. Our proposed model's simplicity makes it faster during inference. Moreover, we show that our model is robust when faced with missing or corrupted connectivity structure.

cs.LG↗

arXiv2023

The Impact of Positional Encoding on Length Generalization in Transformers

Length generalization, the ability to generalize from small training context sizes to larger ones, is a critical challenge in the development of Transformer-based language models. Positional encoding (PE) has been identified as a major factor influencing length generalization, but the exact impact of different PE schemes on extrapolation in downstream tasks remains unclear. In this paper, we conduct a systematic empirical study comparing the length generalization performance of decoder-only Transformers with five different position encoding approaches including Absolute Position Embedding (APE), T5's Relative PE, ALiBi, and Rotary, in addition to Transformers without positional encoding (NoPE). Our evaluation encompasses a battery of reasoning and mathematical tasks. Our findings reveal that the most commonly used positional encoding methods, such as ALiBi, Rotary, and APE, are not well suited for length generalization in downstream tasks. More importantly, NoPE outperforms other explicit positional encoding methods while requiring no additional computation. We theoretically demonstrate that NoPE can represent both absolute and relative PEs, but when trained with SGD, it mostly resembles T5's relative PE attention patterns. Finally, we find that scratchpad is not always helpful to solve length generalization and its format highly impacts the model's performance. Overall, our work suggests that explicit position embeddings are not essential for decoder-only Transformers to generalize well to longer sequences.

cs.CL↗

arXiv2023

Topological Deep Learning: Going Beyond Graph Data

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications.

cs.LG↗

arXiv2023

Function Composition in Trustworthy Machine Learning: Implementation Choices, Insights, and Questions

Ensuring trustworthiness in machine learning (ML) models is a multi-dimensional task. In addition to the traditional notion of predictive performance, other notions such as privacy, fairness, robustness to distribution shift, adversarial robustness, interpretability, explainability, and uncertainty quantification are important considerations to evaluate and improve (if deficient). However, these sub-disciplines or 'pillars' of trustworthiness have largely developed independently, which has limited us from understanding their interactions in real-world ML pipelines. In this paper, focusing specifically on compositions of functions arising from the different pillars, we aim to reduce this gap, develop new insights for trustworthy ML, and answer questions such as the following. Does the composition of multiple fairness interventions result in a fairer model compared to a single intervention? How do bias mitigation algorithms for fairness affect local post-hoc explanations? Does a defense algorithm for untargeted adversarial attacks continue to be effective when composed with a privacy transformation? Toward this end, we report initial empirical results and new insights from 9 different compositions of functions (or pipelines) on 7 real-world datasets along two trustworthy dimensions - fairness and explainability. We also report progress, and implementation choices, on an extensible composer tool to encourage the combination of functionalities from multiple pillars. To-date, the tool supports bias mitigation algorithms for fairness and post-hoc explainability methods. We hope this line of work encourages the thoughtful consideration of multiple pillars when attempting to formulate and resolve a trustworthiness problem.

cs.LG↗

arXiv2023

Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Models

We introduce equi-tuning, a novel fine-tuning method that transforms (potentially non-equivariant) pretrained models into group equivariant models while incurring minimum $L_2$ loss between the feature representations of the pretrained and the equivariant models. Large pretrained models can be equi-tuned for different groups to satisfy the needs of various downstream tasks. Equi-tuned models benefit from both group equivariance as an inductive bias and semantic priors from pretrained models. We provide applications of equi-tuning on three different tasks: image classification, compositional generalization in language, and fairness in natural language generation (NLG). We also provide a novel group-theoretic definition for fairness in NLG. The effectiveness of this definition is shown by testing it against a standard empirical method of fairness in NLG. We provide experimental results for equi-tuning using a variety of pretrained models: Alexnet, Resnet, VGG, and Densenet for image classification; RNNs, GRUs, and LSTMs for compositional generalization; and GPT2 for fairness in NLG. We test these models on benchmark datasets across all considered tasks to show the generality and effectiveness of the proposed method.

cs.LG↗

arXiv2022

A label-efficient two-sample test

Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are easily measured whereas sample labels are unknown and costly to obtain. Accordingly, we devise a three-stage framework in service of performing an effective two-sample test with only a small number of sample label queries: first, a classifier is trained with samples uniformly labeled to model the posterior probabilities of the labels; second, a novel query scheme dubbed \emph{bimodal query} is used to query labels of samples from both classes, and last, the classical Friedman-Rafsky (FR) two-sample test is performed on the queried samples. Theoretical analysis and extensive experiments performed on several datasets demonstrate that the proposed test controls the Type I error and has decreased Type II error relative to uniform querying and certainty-based querying. Source code for our algorithms and experimental results is available at \url{https://github.com/wayne0908/Label-Efficient-Two-Sample}.

cs.LG↗

arXiv2022

Your fairness may vary: Pretrained language model fairness in toxic text classification

The popularity of pretrained language models in natural language processing systems calls for a careful evaluation of such models in down-stream tasks, which have a higher potential for societal impact. The evaluation of such systems usually focuses on accuracy measures. Our findings in this paper call for attention to be paid to fairness measures as well. Through the analysis of more than a dozen pretrained language models of varying sizes on two toxic text classification tasks (English), we demonstrate that focusing on accuracy measures alone can lead to models with wide variation in fairness characteristics. Specifically, we observe that fairness can vary even more than accuracy with increasing training data size and different random initializations. At the same time, we find that little of the fairness variation is explained by model size, despite claims in the literature. To improve model fairness without retraining, we show that two post-processing methods developed for structured, tabular data can be successfully applied to a range of pretrained language models. Warning: This paper contains samples of offensive text.

cs.CL↗

arXiv2022

Augmenting Molecular Deep Generative Models with Topological Data Analysis Representations

Deep generative models have emerged as a powerful tool for learning useful molecular representations and designing novel molecules with desired properties, with applications in drug discovery and material design. However, most existing deep generative models are restricted due to lack of spatial information. Here we propose augmentation of deep generative models with topological data analysis (TDA) representations, known as persistence images, for robust encoding of 3D molecular geometry. We show that the TDA augmentation of a character-based Variational Auto-Encoder (VAE) outperforms state-of-the-art generative neural nets in accurately modeling the structural composition of the QM9 benchmark. Generated molecules are valid, novel, and diverse, while exhibiting distinct electronic property distribution, namely higher sample population with small HOMO-LUMO gap. These results demonstrate that TDA features indeed provide crucial geometric signal for learning abstract structures, which is non-trivial for existing generative models operating on string, graph, or 3D point sets to capture.

physics.chem-ph↗

arXiv2022

Analogies and Feature Attributions for Model Agnostic Explanation of Similarity Learners

Post-hoc explanations for black box models have been studied extensively in classification and regression settings. However, explanations for models that output similarity between two inputs have received comparatively lesser attention. In this paper, we provide model agnostic local explanations for similarity learners applicable to tabular and text data. We first propose a method that provides feature attributions to explain the similarity between a pair of inputs as determined by a black box similarity learner. We then propose analogies as a new form of explanation in machine learning. Here the goal is to identify diverse analogous pairs of examples that share the same level of similarity as the input pair and provide insight into (latent) factors underlying the model's prediction. The selection of analogies can optionally leverage feature attributions, thus connecting the two forms of explanation while still maintaining complementarity. We prove that our analogy objective function is submodular, making the search for good-quality analogies efficient. We apply the proposed approaches to explain similarities between sentences as predicted by a state-of-the-art sentence encoder, and between patients in a healthcare utilization application. Efficacy is measured through quantitative evaluations, a careful user study, and examples of explanations.

cs.LG↗

arXiv2021

Ground-Truth, Whose Truth? -- Examining the Challenges with Annotating Toxic Text Datasets

The use of machine learning (ML)-based language models (LMs) to monitor content online is on the rise. For toxic text identification, task-specific fine-tuning of these models are performed using datasets labeled by annotators who provide ground-truth labels in an effort to distinguish between offensive and normal content. These projects have led to the development, improvement, and expansion of large datasets over time, and have contributed immensely to research on natural language. Despite the achievements, existing evidence suggests that ML models built on these datasets do not always result in desirable outcomes. Therefore, using a design science research (DSR) approach, this study examines selected toxic text datasets with the goal of shedding light on some of the inherent issues and contributing to discussions on navigating these challenges for existing and future projects. To achieve the goal of the study, we re-annotate samples from three toxic text datasets and find that a multi-label approach to annotating toxic text samples can help to improve dataset quality. While this approach may not improve the traditional metric of inter-annotator agreement, it may better capture dependence on context and diversity in annotators. We discuss the implications of these results for both theory and practice.

cs.CL↗

arXiv2021

Data-Centric AI Requires Rethinking Data Notion

The transition towards data-centric AI requires revisiting data notions from mathematical and implementational standpoints to obtain unified data-centric machine learning packages. Towards this end, this work proposes unifying principles offered by categorical and cochain notions of data, and discusses the importance of these principles in data-centric AI transition. In the categorical notion, data is viewed as a mathematical structure that we act upon via morphisms to preserve this structure. As for cochain notion, data can be viewed as a function defined in a discrete domain of interest and acted upon via operators. While these notions are almost orthogonal, they provide a unifying definition to view data, ultimately impacting the way machine learning packages are developed, implemented, and utilized by practitioners.

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