DepNeCTI: Dependency-based Nested Compound Type Identification for Sanskrit

Multi-component compounding is a prevalent phenomenon in Sanskrit, and understanding the implicit structure of a compound's components is crucial for deciphering its meaning. Earlier approaches in Sanskrit have focused on binary compounds and neglected the multi-component compound setting. This work introduces the novel task of nested compound type identification (NeCTI), which aims to identify nested spans of a multi-component compound and decode the implicit semantic relations between them. To the best of our knowledge, this is the first attempt in the field of lexical semantics to propose this task. We present 2 newly annotated datasets including an out-of-domain dataset for this task. We also benchmark these datasets by exploring the efficacy of the standard problem formulations such as nested named entity recognition, constituency parsing and seq2seq, etc. We present a novel framework named DepNeCTI: Dependency-based Nested Compound Type Identifier that surpasses the performance of the best baseline with an average absolute improvement of 13.1 points F1-score in terms of Labeled Span Score (LSS) and a 5-fold enhancement in inference efficiency. In line with the previous findings in the binary Sanskrit compound identification task, context provides benefits for the NeCTI task. The codebase and datasets are publicly available at: https://github.com/yaswanth-iitkgp/DepNeCTI

Modeling interdisciplinary interactions among Physics, Mathematics & Computer Science

Interdisciplinarity has over the recent years have gained tremendous importance and has become one of the key ways of doing cutting edge research. In this paper we attempt to model the citation flow across three different fields -- Physics (PHY), Mathematics (MA) and Computer Science (CS). For instance, is there a specific pattern in which these fields cite one another? We carry out experiments on a dataset comprising more than 1.2 million articles taken from these three fields. We quantify the citation interactions among these three fields through temporal bucket signatures. We present numerical models based on variants of the recently proposed relay-linking framework to explain the citation dynamics across the three disciplines. These models make a modest attempt to unfold the underlying principles of how citation links could have been formed across the three fields over time.

A Robust SINDy Approach by Combining Neural Networks and an Integral Form

The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and scarce data still pose a severe challenge to the success of the SINDy approach. In this work, we discuss a robust method to discover nonlinear governing equations from noisy and scarce data. To do this, we make use of neural networks to learn an implicit representation based on measurement data so that not only it produces the output in the vicinity of the measurements but also the time-evolution of output can be described by a dynamical system. Additionally, we learn such a dynamic system in the spirit of the SINDy framework. Leveraging the implicit representation using neural networks, we obtain the derivative information -- required for SINDy -- using an automatic differentiation tool. To enhance the robustness of our methodology, we further incorporate an integral condition on the output of the implicit networks. Furthermore, we extend our methodology to handle data collected from multiple initial conditions. We demonstrate the efficiency of the proposed methodology to discover governing equations under noisy and scarce data regimes by means of several examples and compare its performance with existing methods.

Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers a framework for global linearization for nonlinear systems, thereby allowing the usage of linear tools for design studies. In this work, we focus on the identification of global linearized embeddings for canonical nonlinear Hamiltonian systems through a symplectic transformation. While this task is often challenging, we leverage the power of deep learning to discover the desired embeddings. Furthermore, to overcome the shortcomings of Koopman operators for systems with continuous spectra, we apply the lifting principle and learn global cubicized embeddings. Additionally, a key emphasis is paid to enforce the bounded stability for the dynamics of the discovered embeddings. We demonstrate the capabilities of deep learning in acquiring compact symplectic coordinate transformation and the corresponding simple dynamical models, fostering data-driven learning of nonlinear canonical Hamiltonian systems, even those with continuous spectra.

Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference

Scientific machine learning for learning dynamical systems is a powerful tool that combines data-driven modeling models, physics-based modeling, and empirical knowledge. It plays an essential role in an engineering design cycle and digital twinning. In this work, we primarily focus on an operator inference methodology that builds dynamical models, preferably in low-dimension, with a prior hypothesis on the model structure, often determined by known physics or given by experts. Then, for inference, we aim to learn the operators of a model by setting up an appropriate optimization problem. One of the critical properties of dynamical systems is{stability. However, such a property is not guaranteed by the inferred models. In this work, we propose inference formulations to learn quadratic models, which are stable by design. Precisely, we discuss the parameterization of quadratic systems that are locally and globally stable. Moreover, for quadratic systems with no stable point yet bounded (e.g., Chaotic Lorenz model), we discuss an attractive trapping region philosophy and a parameterization of such systems. Using those parameterizations, we set up inference problems, which are then solved using a gradient-based optimization method. Furthermore, to avoid numerical derivatives and still learn continuous systems, we make use of an integration form of differential equations. We present several numerical examples, illustrating the preservation of stability and discussing its comparison with the existing state-of-the-art approach to infer operators. By means of numerical examples, we also demonstrate how proposed methods are employed to discover governing equations and energy-preserving models.

Aesthetics of Sanskrit Poetry from the Perspective of Computational Linguistics: A Case Study Analysis on Siksastaka

Sanskrit poetry has played a significant role in shaping the literary and cultural landscape of the Indian subcontinent for centuries. However, not much attention has been devoted to uncovering the hidden beauty of Sanskrit poetry in computational linguistics. This article explores the intersection of Sanskrit poetry and computational linguistics by proposing a roadmap of an interpretable framework to analyze and classify the qualities and characteristics of fine Sanskrit poetry. We discuss the rich tradition of Sanskrit poetry and the significance of computational linguistics in automatically identifying the characteristics of fine poetry. The proposed framework involves a human-in-the-loop approach that combines deterministic aspects delegated to machines and deep semantics left to human experts. We provide a deep analysis of Siksastaka, a Sanskrit poem, from the perspective of 6 prominent kavyashastra schools, to illustrate the proposed framework. Additionally, we provide compound, dependency, anvaya (prose order linearised form), meter, rasa (mood), alankar (figure of speech), and riti (writing style) annotations for Siksastaka and a web application to illustrate the poem's analysis and annotations. Our key contributions include the proposed framework, the analysis of Siksastaka, the annotations and the web application for future research. Link for interactive analysis: https://sanskritshala.github.io/shikshastakam/

Data-Driven Identification of Quadratic Symplectic Representations of Nonlinear Hamiltonian Systems

We present a framework for learning Hamiltonian systems using data. This work is based on the lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a symplectic auto-encoder. The enforced Hamiltonian structure exhibits long-term stability of the system, while the cubic Hamiltonian function provides relatively low model complexity. For low-dimensional data, we determine a higher-order transformed coordinate system, whereas, for high-dimensional data, we find a lower-order coordinate system with the desired properties. We demonstrate the proposed methodology by means of both low-dimensional and high-dimensional nonlinear Hamiltonian systems.

$FPDM$: Domain-Specific Fast Pre-training Technique using Document-Level Metadata

Pre-training Transformers has shown promising results on open-domain and domain-specific downstream tasks. However, state-of-the-art Transformers require an unreasonably large amount of pre-training data and compute. In this paper, we propose $FPDM$ (Fast Pre-training Technique using Document Level Metadata), a novel, compute-efficient framework that utilizes Document metadata and Domain-Specific Taxonomy as supervision signals to pre-train transformer encoder on a domain-specific corpus. The main innovation is that during domain-specific pretraining, an open-domain encoder is continually pre-trained using sentence-level embeddings as inputs (to accommodate long documents), however, fine-tuning is done with token-level embeddings as inputs to this encoder. We show that $FPDM$ outperforms several transformer-based baselines in terms of character-level F1 scores and other automated metrics in the Customer Support, Scientific, and Legal Domains, and shows a negligible drop in performance on open-domain benchmarks. Importantly, the novel use of document-level supervision along with sentence-level embedding input for pre-training reduces pre-training compute by around $1,000$, $4,500$, and $500$ times compared to MLM and/or NSP in Customer Support, Scientific, and Legal Domains, respectively. Code and datasets are available at https://bit.ly/FPDMCode.

FinRED: A Dataset for Relation Extraction in Financial Domain

Relation extraction models trained on a source domain cannot be applied on a different target domain due to the mismatch between relation sets. In the current literature, there is no extensive open-source relation extraction dataset specific to the finance domain. In this paper, we release FinRED, a relation extraction dataset curated from financial news and earning call transcripts containing relations from the finance domain. FinRED has been created by mapping Wikidata triplets using distance supervision method. We manually annotate the test data to ensure proper evaluation. We also experiment with various state-of-the-art relation extraction models on this dataset to create the benchmark. We see a significant drop in their performance on FinRED compared to the general relation extraction datasets which tells that we need better models for financial relation extraction.

Financial Numeric Extreme Labelling: A Dataset and Benchmarking for XBRL Tagging

The U.S. Securities and Exchange Commission (SEC) mandates all public companies to file periodic financial statements that should contain numerals annotated with a particular label from a taxonomy. In this paper, we formulate the task of automating the assignment of a label to a particular numeral span in a sentence from an extremely large label set. Towards this task, we release a dataset, Financial Numeric Extreme Labelling (FNXL), annotated with 2,794 labels. We benchmark the performance of the FNXL dataset by formulating the task as (a) a sequence labelling problem and (b) a pipeline with span extraction followed by Extreme Classification. Although the two approaches perform comparably, the pipeline solution provides a slight edge for the least frequent labels.