Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

State Function, Exact and Inexact Differentials01:27

State Function, Exact and Inexact Differentials

24
A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
24
Approximate Integration01:24

Approximate Integration

78
In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
78
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

410
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
410
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.0K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
1.0K
Modeling with Differential Equations01:25

Modeling with Differential Equations

133
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
133
Linear Differential Equations01:27

Linear Differential Equations

126
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
126

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Lung-Protective Ventilation Strategies for Relief from Ventilator-Associated Lung Injury in Patients Undergoing Craniotomy: A Bicenter Randomized, Parallel, and Controlled Trial.

Oxidative medicine and cellular longevity·2017
Same author

Electrochemical Oxidation of EDTA in Nuclear Wastewater Using Platinum Supported on Activated Carbon Fibers.

International journal of environmental research and public health·2017
Same author

Novel biomimetic enzyme for sensitive detection of superoxide anions.

Talanta·2017
Same author

The Expression of Formyl Peptide Receptor 1 is Correlated with Tumor Invasion of Human Colorectal Cancer.

Scientific reports·2017
Same author

An excited state underlies gene regulation of a transcriptional riboswitch.

Nature chemical biology·2017
Same author

(-)-Epigallocatechin-3-gallate attenuates myocardial injury induced by ischemia/reperfusion in diabetic rats and in H9c2 cells under hyperglycemic conditions.

International journal of molecular medicine·2017
Same journal

Relation DETR+: Exploring Explicit Position Relation Prior for Dense Prediction.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

CAFE: Cross-View Adaptive Fusion and Cluster Center Enhancement for Robust Multi-View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

DIVER: Reinforced Diffusion Breaks Imitation Bottlenecks in End-to-End Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Ethics-Aware Safe Reinforcement Learning for Rare-Event Risk Control in Interactive Urban Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Learning Shape Anchors for Holistic Indoor Scene Understanding.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

Related Experiment Video

Updated: Mar 6, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

6.9K

Understanding Data Influence With Differential Approximation.

Haoru Tan, Sitong Wu, Xiuzhe Wu

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |March 4, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces Diff-In, a novel method for approximating data influence in artificial intelligence model training. Diff-In offers accurate, scalable, and computationally efficient data analysis, improving model performance and data utilization.

    More Related Videos

    Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
    04:35

    Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

    Published on: July 3, 2020

    3.8K
    A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
    08:12

    A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

    Published on: March 1, 2022

    3.0K

    Related Experiment Videos

    Last Updated: Mar 6, 2026

    Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
    08:13

    Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

    Published on: May 10, 2019

    6.9K
    Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
    04:35

    Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

    Published on: July 3, 2020

    3.8K
    A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
    08:12

    A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

    Published on: March 1, 2022

    3.0K

    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Data Science

    Background:

    • Accurate quantitative analysis of data is crucial for efficient and high-quality artificial intelligence model training.
    • Existing data analysis tools often lack accuracy and make simplifying assumptions, such as model convexity, hindering effective implementation.
    • Limitations in current methods necessitate the development of more robust and accurate data influence approximation techniques.

    Purpose of the Study:

    • To introduce a new formulation, Diff-In, for approximating sample influence in machine learning models.
    • To develop a method that accurately estimates data influence without requiring model convexity assumptions.
    • To provide a computationally efficient and scalable solution for data-centric tasks in artificial intelligence.

    Main Methods:

    • Formulated sample-wise influence as the cumulative sum of differences across successive training iterations.
    • Employed second-order approximations to accurately estimate difference terms, bypassing the need for model convexity.
    • Achieved computational complexity comparable to first-order methods by efficiently approximating Hessian-gradient products using finite differences.

    Main Results:

    • Theoretical analysis demonstrated significantly lower approximation error for Diff-In compared to existing influence estimators.
    • Empirical evaluations confirmed superior performance across multiple benchmark datasets in data cleaning, deletion, and coreset selection.
    • Experiments on large-scale vision-language pre-training showed Diff-In scales to millions of data points and outperforms baseline methods.

    Conclusions:

    • Diff-In provides a theoretically sound and empirically validated approach for accurate sample influence approximation.
    • The method offers a scalable and computationally efficient alternative to existing techniques for data-centric AI tasks.
    • Diff-In enhances data utilization and model performance, particularly in large-scale machine learning applications.