Generating Elementary Integrable Expressions

• URL: http://arxiv.org/abs/2306.15572v1
• Date: Tue, 27 Jun 2023 15:48:40 GMT
• Title: Generating Elementary Integrable Expressions
• Authors: Rashid Barket, Matthew England and J\"urgen Gerhard
• Abstract summary: We describe how to use the Risch Algorithm for symbolic integration to create a dataset of elementary integrable expressions. We show that data generated this way alleviates some of the flaws found in earlier methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: There has been an increasing number of applications of machine learning to the field of Computer Algebra in recent years, including to the prominent sub-field of Symbolic Integration. However, machine learning models require an abundance of data for them to be successful and there exist few benchmarks on the scale required. While methods to generate new data already exist, they are flawed in several ways which may lead to bias in machine learning models trained upon them. In this paper, we describe how to use the Risch Algorithm for symbolic integration to create a dataset of elementary integrable expressions. Further, we show that data generated this way alleviates some of the flaws found in earlier methods.

Related papers

• Attribute-to-Delete: Machine Unlearning via Datamodel Matching [65.13151619119782]
  Machine unlearning -- efficiently removing a small "forget set" training data on a pre-divertrained machine learning model -- has recently attracted interest. Recent research shows that machine unlearning techniques do not hold up in such a challenging setting.
  arXiv  Detail & Related papers  (2024-10-30T17:20:10Z)
• Data Shapley in One Training Run [88.59484417202454]
  Data Shapley provides a principled framework for attributing data's contribution within machine learning contexts. Existing approaches require re-training models on different data subsets, which is computationally intensive. This paper introduces In-Run Data Shapley, which addresses these limitations by offering scalable data attribution for a target model of interest.
  arXiv  Detail & Related papers  (2024-06-16T17:09:24Z)
• Compositional Generative Modeling: A Single Model is Not All You Need [29.050431676226115]
  We argue that we should instead construct large generative systems by composing smaller generative models together. We show how such a compositional generative approach enables us to learn distributions in a more data-efficient manner.
  arXiv  Detail & Related papers  (2024-02-02T02:40:51Z)
• Surprisal Driven $k$-NN for Robust and Interpretable Nonparametric Learning [1.4293924404819704]
  We shed new light on the traditional nearest neighbors algorithm from the perspective of information theory. We propose a robust and interpretable framework for tasks such as classification, regression, density estimation, and anomaly detection using a single model. Our work showcases the architecture's versatility by achieving state-of-the-art results in classification and anomaly detection.
  arXiv  Detail & Related papers  (2023-11-17T00:35:38Z)
• On Inductive Biases for Machine Learning in Data Constrained Settings [0.0]
  This thesis explores a different answer to the problem of learning expressive models in data constrained settings. Instead of relying on big datasets to learn neural networks, we will replace some modules by known functions reflecting the structure of the data. Our approach falls under the hood of "inductive biases", which can be defined as hypothesis on the data at hand restricting the space of models to explore.
  arXiv  Detail & Related papers  (2023-02-21T14:22:01Z)
• Generalization Properties of Retrieval-based Models [50.35325326050263]
  Retrieval-based machine learning methods have enjoyed success on a wide range of problems. Despite growing literature showcasing the promise of these models, the theoretical underpinning for such models remains underexplored. We present a formal treatment of retrieval-based models to characterize their generalization ability.
  arXiv  Detail & Related papers  (2022-10-06T00:33:01Z)
• Advancing Reacting Flow Simulations with Data-Driven Models [50.9598607067535]
  Key to effective use of machine learning tools in multi-physics problems is to couple them to physical and computer models. The present chapter reviews some of the open opportunities for the application of data-driven reduced-order modeling of combustion systems.
  arXiv  Detail & Related papers  (2022-09-05T16:48:34Z)
• A Survey of Learning on Small Data: Generalization, Optimization, and Challenge [101.27154181792567]
  Learning on small data that approximates the generalization ability of big data is one of the ultimate purposes of AI. This survey follows the active sampling theory under a PAC framework to analyze the generalization error and label complexity of learning on small data. Multiple data applications that may benefit from efficient small data representation are surveyed.
  arXiv  Detail & Related papers  (2022-07-29T02:34:19Z)
• Growing Representation Learning [2.7231362265267127]
  We develop an attention based Gaussian Mixture, called GMAT, that learns interpretable representations of data with or without labels. We show that our method is capable learning new representations of data without labels or assumptions about the distributions of labels.
  arXiv  Detail & Related papers  (2021-10-17T15:55:13Z)
• ALT-MAS: A Data-Efficient Framework for Active Testing of Machine Learning Algorithms [58.684954492439424]
  We propose a novel framework to efficiently test a machine learning model using only a small amount of labeled test data. The idea is to estimate the metrics of interest for a model-under-test using Bayesian neural network (BNN)
  arXiv  Detail & Related papers  (2021-04-11T12:14:04Z)
• Learning ODE Models with Qualitative Structure Using Gaussian Processes [0.6882042556551611]
  In many contexts explicit data collection is expensive and learning algorithms must be data-efficient to be feasible. We propose an approach to learning a vector field of differential equations using sparse Gaussian Processes. We show that this combination improves extrapolation performance and long-term behaviour significantly, while also reducing the computational cost.
  arXiv  Detail & Related papers  (2020-11-10T19:34:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.