arXiv subjects

Saikat Chakraborty

Publications and source records attributed to Saikat Chakraborty.

At least 55 records · Page 3Linked to original sources

arXiv2023

Scalar field evolution at background and perturbation levels for a broad class of potentials

In this paper, we investigate a non-interacting scalar field cosmology with an arbitrary potential using the $f$-deviser method that relies on the differentiability properties of the potential. Using this alternative mathematical approach, we present a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary potentials. For illustration, we consider a monomial and double exponential potential. These two classes of potentials comprise the asymptotic behaviour of several classes of scalar field potentials, and, therefore, they provide the skeleton for the typical behaviour of arbitrary potentials. Moreover, we analyse the linear cosmological perturbations in the matterless case by considering three scalar perturbations: the evolution of the Bardeen potentials, the comoving curvature perturbation, the so-called Sasaki-Mukhanov variable, or the scalar field perturbation in uniform curvature gauge. Finally, an exhaustive dynamical system analysis for each scalar perturbation is presented, including the evolution of Bardeen potentials in the presence of matter.

gr-qc↗

arXiv2023

On the uniqueness of $Λ$CDM-like evolution for homogeneous and isotropic cosmology in General Relativity

We address the question of the uniqueness of spatially flat $Λ$CDM-like evolution for FLRW cosmologies in General Relativity, i.e. whether any model other than the spatially flat $Λ$CDM can give rise to the same type of scale factor evolution. Firstly, we elaborate on what we exactly imply by a $Λ$CDM-like evolution or kinematic/cosmographic degeneracy with the $Λ$CDM model, using the lessons from the statefinder diagnostic. Then, we consider two models with interaction in the dark sector: coupled fluid-fluid model and coupled quintessence model. We enforce the \emph{kinematic} degeneracy with the spatially flat $Λ$CDM model via the cosmographic condition $j=1$ ($j$ being the jerk parameter), which in turn fixes the function of the interaction term that is a priori unspecified. We argue that in General Relativity this cosmographic condition is consistent only with spatial flatness. Employing a dynamical system approach, we show that the spatially flat coupled fluid-fluid interacting models kinematically degenerate with $Λ$CDM must necessarily be based on a phantom fluid, whereas the set of physically viable spatially flat coupled quintessence models with power law or exponential potential kinematically degenerate to $Λ$CDM is of measure zero. Our analysis establishes that coupled fluid-fluid models with non-phantom fluids or coupled quintessence models with power law and exponential potential can never reproduce a cosmological evolution similar to that of the $Λ$CDM. The astrophysical consequences of our findings are qualitatively discussed in light of observational cosmological tensions.

gr-qc↗

arXiv2023

AVATAR: A Parallel Corpus for Java-Python Program Translation

Program translation refers to migrating source code from one programming language to another. It has tremendous practical value in software development, as porting software across languages is time-consuming and costly. Automating program translation is of paramount importance in software migration, and recently researchers explored unsupervised approaches due to the unavailability of parallel corpora. However, the availability of pre-trained language models for programming languages enables supervised fine-tuning with a small number of labeled examples. Therefore, we present AVATAR, a collection of 9,515 programming problems and their solutions written in two popular languages, Java and Python. AVATAR is collected from competitive programming sites, online platforms, and open-source repositories. Furthermore, AVATAR includes unit tests for 250 examples to facilitate functional correctness evaluation. We benchmark several pre-trained language models fine-tuned on AVATAR. Experiment results show that the models lack in generating functionally accurate code.

cs.SE↗

arXiv2023

Towards Generating Functionally Correct Code Edits from Natural Language Issue Descriptions

Large language models (LLMs), such as OpenAI's Codex, have demonstrated their potential to generate code from natural language descriptions across a wide range of programming tasks. Several benchmarks have recently emerged to evaluate the ability of LLMs to generate functionally correct code from natural language intent with respect to a set of hidden test cases. This has enabled the research community to identify significant and reproducible advancements in LLM capabilities. However, there is currently a lack of benchmark datasets for assessing the ability of LLMs to generate functionally correct code edits based on natural language descriptions of intended changes. This paper aims to address this gap by motivating the problem NL2Fix of translating natural language descriptions of code changes (namely bug fixes described in Issue reports in repositories) into correct code fixes. To this end, we introduce Defects4J-NL2Fix, a dataset of 283 Java programs from the popular Defects4J dataset augmented with high-level descriptions of bug fixes, and empirically evaluate the performance of several state-of-the-art LLMs for the this task. Results show that these LLMS together are capable of generating plausible fixes for 64.6% of the bugs, and the best LLM-based technique can achieve up to 21.20% top-1 and 35.68% top-5 accuracy on this benchmark.

cs.SE↗

arXiv2023

Dynamical systems analysis of tachyon dark energy model from a new perspective

In this work we present a new scheme to study the tachyon dark energy model using dynamical systems analysis by considering parametrization of the equation of state(EoS) of the dark energy. Both the canonical and phantom field dynamics are investigated. In our method we do not require any explicit form of the tachyon potential. Instead of the potential we start with an approximate form of the EoS of the tachyon field. This EoS is phenomenologically motivated and contains some dimensionless parameters. Using our method we can construct the dynamical system which gives rise to the time evolution of the universe. We have considered two different parametrizations of the EoS and studied the phase space dynamics in details. Our analysis shows Taylor series parametrization of the EoS has serious cosmological limitations. Our proposal is generic in nature and can be applied to other scalar field dark energy models.

gr-qc↗

arXiv2023

On ML-Based Program Translation: Perils and Promises

With the advent of new and advanced programming languages, it becomes imperative to migrate legacy software to new programming languages. Unsupervised Machine Learning-based Program Translation could play an essential role in such migration, even without a sufficiently sizeable reliable corpus of parallel source code. However, these translators are far from perfect due to their statistical nature. This work investigates unsupervised program translators and where and why they fail. With in-depth error analysis of such failures, we have identified that the cases where such translators fail follow a few particular patterns. With this insight, we develop a rule-based program mutation engine, which pre-processes the input code if the input follows specific patterns and post-process the output if the output follows certain patterns. We show that our code processing tool, in conjunction with the program translator, can form a hybrid program translator and significantly improve the state-of-the-art. In the future, we envision an end-to-end program translation tool where programming domain knowledge can be embedded into an ML-based translation pipeline using pre- and post-processing steps.

cs.PL↗

arXiv2023

Summarize and Generate to Back-translate: Unsupervised Translation of Programming Languages

Back-translation is widely known for its effectiveness in neural machine translation when there is little to no parallel data. In this approach, a source-to-target model is coupled with a target-to-source model trained in parallel. The target-to-source model generates noisy sources, while the source-to-target model is trained to reconstruct the targets and vice versa. Recent developments of multilingual pre-trained sequence-to-sequence models for programming languages have been very effective for a broad spectrum of downstream software engineering tasks. Hence, training them to build programming language translation systems via back-translation is compelling. However, these models cannot be further trained via back-translation since they learn to output sequences in the same language as the inputs during pre-training. As an alternative, we propose performing back-translation via code summarization and generation. In code summarization, a model learns to generate natural language (NL) summaries given code snippets. In code generation, the model learns to do the opposite. Therefore, target-to-source generation in back-translation can be viewed as a target-to-NL-to-source generation. We show that our proposed approach performs competitively with state-of-the-art methods. We have made the code publicly available.

cs.CL↗

arXiv2022

A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature

We present a comprehensive dynamical systems analysis of homogeneous and isotropic Friedmann-Laîmatre-Robertson-Walker cosmologies in the Hu-Sawicki $f(R)$ dark energy model for the parameter choice $\{n,C_1\}=\{1,1\}$. For a generic $f(R)$ theory, we outline the procedures of compactification of the phase space, which in general is 4-dimensional. We also outline how, given an $f(R)$ model, one can determine the coordinate of the phase space point that corresponds to the present day universe and the equation of a surface in the phase space that represents the $Λ$CDM evolution history. Next, we apply these procedures to the Hu-Sawicki model under consideration. We identify some novel features of the phase space of the model such as the existence of invariant submanifolds and 2-dimensional sheets of fixed points. We determine the physically viable region of the phase space, the fixed point corresponding to possible matter dominated epochs and discuss the possibility of a non-singular bounce, re-collapse and cyclic evolution. We also provide a numerical analysis comparing the $Λ$CDM evolution and the Hu-Sawicki evolution.

gr-qc↗

arXiv2022

Can $f(R)$ gravity isotropize a pre-bounce contracting universe?

We address the important issue of isotropisation of a pre-bounce contracting phase in $f(R)$ gravity, which would be relevant to construct any viable nonsingular bouncing scenario in $f(R)$ gravity. The main motivation behind this work is to investigate whether the $f(R)$ gravity, by itself, can isotropise a contracting universe starting initially with small anisotropy without incorporating a super-stiff or non-ideal fluid, that is impossible in general relativity. Considering Bianchi I cosmology and employing a dynamical system analysis, we see that this is not possible for $R^n$ ($n>1$) and $R+αR^2$ ($α>0$) theory, but possible for $\frac{1}αe^{αR}$ ($α>0$) theory. On the other hand, if one does not specify an $f(R)$ theory a priori but demands a cosmology smoothly connecting an ekpyrotic contraction phase to a nonsingular bounce, the ekpyrotic phase \emph{may} not fulfil the condition for isotropisation and physically viability simultaneously.

gr-qc↗

arXiv2022

NatGen: Generative pre-training by "Naturalizing" source code

Pre-trained Generative Language models (e.g. PLBART, CodeT5, SPT-Code) for source code yielded strong results on several tasks in the past few years, including code generation and translation. These models have adopted varying pre-training objectives to learn statistics of code construction from very large-scale corpora in a self-supervised fashion; the success of pre-trained models largely hinges on these pre-training objectives. This paper proposes a new pre-training objective, "Naturalizing" of source code, exploiting code's bimodal, dual-channel (formal & natural channels) nature. Unlike natural language, code's bimodal, dual-channel nature allows us to generate semantically equivalent code at scale. We introduce six classes of semantic preserving transformations to introduce un-natural forms of code, and then force our model to produce more natural original programs written by developers. Learning to generate equivalent, but more natural code, at scale, over large corpora of open-source code, without explicit manual supervision, helps the model learn to both ingest & generate code. We fine-tune our model in three generative Software Engineering tasks: code generation, code translation, and code refinement with limited human-curated labeled data and achieve state-of-the-art performance rivaling CodeT5. We show that our pre-trained model is especially competitive at zero-shot and few-shot learning, and better at learning code properties (e.g., syntax, data flow).

cs.PL↗

arXiv2022

Towards Learning (Dis)-Similarity of Source Code from Program Contrasts

Understanding the functional (dis)-similarity of source code is significant for code modeling tasks such as software vulnerability and code clone detection. We present DISCO(DIS-similarity of COde), a novel self-supervised model focusing on identifying (dis)similar functionalities of source code. Different from existing works, our approach does not require a huge amount of randomly collected datasets. Rather, we design structure-guided code transformation algorithms to generate synthetic code clones and inject real-world security bugs, augmenting the collected datasets in a targeted way. We propose to pre-train the Transformer model with such automatically generated program contrasts to better identify similar code in the wild and differentiate vulnerable programs from benign ones. To better capture the structural features of source code, we propose a new cloze objective to encode the local tree-based context (e.g., parents or sibling nodes). We pre-train our model with a much smaller dataset, the size of which is only 5% of the state-of-the-art models' training datasets, to illustrate the effectiveness of our data augmentation and the pre-training approach. The evaluation shows that, even with much less data, DISCO can still outperform the state-of-the-art models in vulnerability and code clone detection tasks.

cs.PL↗

arXiv2022

A note on the dynamical system formulations in $f(R)$ gravity

A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting them in chronological order as they appeared in the history of the relevant scientific literature. In this way, we illuminate how the shortcoming(s) of an existing formulation encouraged the development of an alternative formulation. Whenever possible, a 2-dimensional phase portrait is given for a better visual representation of the dynamics of phase space. We also touch upon how cosmological perturbations can be analyzed using the phase space language.

gr-qc↗

arXiv2021

Time-averaging axion-like interacting scalar fields models

In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $ϕ_1$ and $ϕ_2$ interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein-Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior.

gr-qc↗

arXiv2021

Cosmological evolution with quadratic gravity and nonideal fluids

Some cosmological models based on the gravitational theory $f(R) = R+ζR^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different cosmic epochs. A dynamical system analysis reveals that these models contain fixed points which correspond to an inflationary, a radiation dominated and a late-time accelerating epoch, and a nonsingular bouncing solution, the latter being an asymptotic fixed point of the compactified phase space. The infinity of the compactified phase space is interpreted as a region in which the non-ideal behaviors of the previously mentioned cosmic fluids are suppressed. Physical constraints on the adopted dimensionless variables are derived by demanding the theory to be free from ghost and tachyonic instabilities, and a novel cosmological interpretation of such variables is proposed through a cosmographic analysis. The different effects of the equation of state parameters on the number of equilibrium solutions and on their stability nature are clarified. Some generic properties of these models, which are not sensitive to the particular fluid considered, are identified, while differences are critically examined by showing that the Redlich-Kwong scenario admits a second radiation-dominated epoch and a Big Rip Singularity.

gr-qc↗

arXiv2021

Retrieval Augmented Code Generation and Summarization

Software developers write a lot of source code and documentation during software development. Intrinsically, developers often recall parts of source code or code summaries that they had written in the past while implementing software or documenting them. To mimic developers' code or summary generation behavior, we propose a retrieval augmented framework, REDCODER, that retrieves relevant code or summaries from a retrieval database and provides them as a supplement to code generation or summarization models. REDCODER has a couple of uniqueness. First, it extends the state-of-the-art dense retrieval technique to search for relevant code or summaries. Second, it can work with retrieval databases that include unimodal (only code or natural language description) or bimodal instances (code-description pairs). We conduct experiments and extensive analysis on two benchmark datasets of code generation and summarization in Java and Python, and the promising results endorse the effectiveness of our proposed retrieval augmented framework.

cs.SE↗

arXiv2021

On Multi-Modal Learning of Editing Source Code

In recent years, Neural Machine Translator (NMT) has shown promise in automatically editing source code. Typical NMT based code editor only considers the code that needs to be changed as input and suggests developers with a ranked list of patched code to choose from - where the correct one may not always be at the top of the list. While NMT based code editing systems generate a broad spectrum of plausible patches, the correct one depends on the developers' requirement and often on the context where the patch is applied. Thus, if developers provide some hints, using natural language, or providing patch context, NMT models can benefit from them. As a proof of concept, in this research, we leverage three modalities of information: edit location, edit code context, commit messages (as a proxy of developers' hint in natural language) to automatically generate edits with NMT models. To that end, we build MODIT, a multi-modal NMT based code editing engine. With in-depth investigation and analysis, we show that developers' hint as an input modality can narrow the search space for patches and outperform state-of-the-art models to generate correctly patched code in top-1 position.

cs.SE↗

arXiv2021

A model independent approach to the study of $f(R)$ cosmologies with expansion histories close to $Λ$CDM

We propose a new framework for studying the cosmology of $f(R)$ gravity which completely avoids using the reconstruction programme. This allows us to easily obtain a qualitative feel of how much the $Λ$CDM model differs from other $f(R)$ theories of gravity at the level of linear perturbation theory for theories that share the same background dynamics. This is achieved by using the standard model independent cosmographic parameters to develop a new dynamical system formulation of $f(R)$ gravity which is free from the limitation of having to first specify the functional form of $f(R)$. By considering a set of representative trajectories, which are indistinguishable from $Λ$CDM, we use purely qualitative arguments to determine the extent to which these models deviate from the standard model by including an analysis of the linear growth rate of density fluctuations and also whether or not they suffer from the Dolgov-Kawasaki instability. We find that if one demands that a late time $f(R)$ cosmology is observationally close to the $Λ$CDM model, there is a higher risk that it suffers from a Dolgov-Kawasaki instability. Conversely, the more one tries to construct a physically viable late time $f(R)$ cosmology, the more likely it is observationally different from the $Λ$CDM model.

gr-qc↗

arXiv2021

Unified Pre-training for Program Understanding and Generation

Code summarization and generation empower conversion between programming language (PL) and natural language (NL), while code translation avails the migration of legacy code from one PL to another. This paper introduces PLBART, a sequence-to-sequence model capable of performing a broad spectrum of program and language understanding and generation tasks. PLBART is pre-trained on an extensive collection of Java and Python functions and associated NL text via denoising autoencoding. Experiments on code summarization in the English language, code generation, and code translation in seven programming languages show that PLBART outperforms or rivals state-of-the-art models. Moreover, experiments on discriminative tasks, e.g., program repair, clone detection, and vulnerable code detection, demonstrate PLBART's effectiveness in program understanding. Furthermore, analysis reveals that PLBART learns program syntax, style (e.g., identifier naming convention), logical flow (e.g., if block inside an else block is equivalent to else if block) that are crucial to program semantics and thus excels even with limited annotations.

cs.CL↗