Jacobian Regularization

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Overview

Jacobian regularization studies how to constrain or supervise a model’s derivatives—how predictions, actions, or latent states respond to small input changes. Common approaches penalize Jacobian norms or spectra, apply layer-wise or direction-aligned penalties, estimate derivatives with stochastic Jacobian-vector products, or use PDE-based tangent supervision. These methods are used to reduce sensitivity under perturbations and covariate shift, stabilize control policies and long rollouts, and improve inverse problems and learned dynamical models. A key tension is that uniform smoothing can erase useful task-relevant directions or hinder downstream learning, so work increasingly targets specific directions and evaluates both predictive performance and sensitivity.

Latest papers

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18 papers1 paper in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. On the spectral properties of generative denoiser Jacobians

    Sep 28, 2026Alexandros Graikos, Nebojsa Jojic, Dimitris SamarasJacobian RegularizationDiffusion Models

    Stony Brook University · Microsoft Research

  2. Derivative-Informed Training of Neural Operators On-the-Fly via Sketched Tangent Consistency

    Sep 26, 2026Xinhan Yang, Lu Lu, Shancong MouNeural OperatorsPhysics-Informed Neural Operators

    Department of Industrial and Systems Engineering, University of Minnesota Minneapolis, MN 55455 · Department of Statistics and Data Science, Yale University New Haven, CT 06511, USA

  3. Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems

    Aug 30, 2026Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer +1PDE Surrogate ModelingJacobian Regularization

    Department of Civil and Environmental Engineering, Penn State University, University Park, PA 16802, USA · School of Electrical Engineering and Computer Science, Penn State University, University Park, PA 16802, USA

  4. Eigenanalysis framework for autoregressive neural emulators of multi-scale chaotic dynamics

    Aug 17, 2026Conrad Ainslie, Pedram Hassanzadeh, Michael W. Mahoney +1Neural Network StabilityNeural Surrogate Modeling

    Department of Applied Mathematics, University of California, Santa Cruz, Santa Cruz, 95064, CA · Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637 · Committee on Computational and Applied Mathematics, University of Chicago, Chicago, IL 60637 +3

  5. DREG: A Layer-Wise Jacobian Regularization as a General-Purpose Penalty

    Jun 22, 2026Rowan MartnishnNeural Network GeneralizationJacobian Regularization

  6. Layer-wise Derivative Controlled Networks Achieve Competitive Accuracy and Gradient Stability Across Data Regimes

    Jun 6, 2026Rowan MartnishnNeural Network GeneralizationPolynomial Neural Networks

  7. ChainzRule: Sample-Efficient, Robust Deep Learning Across Tabular, NLP, and Vision Tasks

    May 23, 2026Rowan MartnishnPolynomial Neural NetworksNeural Network Robustness

    Sentivity AI

  8. Dreaming Smoothly and Sample Efficiently with Gradient Penalized Latent Dynamics

    May 21, 2026Romil V. Sonigra, P. R. KumarLatent Dynamics ModelingJacobian Regularization

    Texas A&M University · Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843

  9. The Matching Principle: A Geometric Theory of Loss Functions for Nuisance-Robust Representation Learning

    May 21, 2026Vishal RajputDistribution Shift RobustnessJacobian Regularization

    KU Leuven

  10. Controlling Transient Amplification Improves Long-horizon Rollouts

    May 9, 2026Adeel Pervez, Francesco LocatelloJacobian RegularizationSpatiotemporal Forecasting

    Institute of Science and Technology Austria Klosterneuburg, Austria

  11. The Propagation Field: A Geometric Substrate Theory of Deep Learning

    May 8, 2026Xingrui GuNeural Network GeneralizationNeural Representation Geometry

    1EECS, University of California, Berkeley, Berkeley, CA.

  12. Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift

    May 6, 2026Jonathan R. LandersDistribution Shift RobustnessDistribution Shift

    Independent Researcher · New York, NY, USA

  13. Local Neighborhood Instability in Parametric Projections: Quantitative and Visual Analysis

    Apr 23, 2026Frederik L. Dennig, Daniel A. KeimDistribution Shift RobustnessJacobian Regularization

    University of Konstanz, Germany

  14. On the Role of Strain and Vorticity in Numerical Integration Error for Flow Matching

    Apr 22, 2026Chenxi Tao, Seung-Kyum ChoiFlow MatchingJacobian Regularization

    Georgia Institute of Technology

  15. Singularity Avoidance in Inverse Kinematics: A Unified Treatment of Classical and Learning-based Methods

    Apr 15, 2026Vishnu Rudrasamudram, Hariharasudan MalaichameeInverse KinematicsJacobian Regularization

  16. Robustness of Agentic AI Systems via Adversarially-Aligned Jacobian Regularization

    Mar 4, 2026Furkan Mumcu, Yasin YilmazAdversarial RobustnessAdversarial Robustness of Language Models

    University of South Florida

  17. On Geometry Regularization in Autoencoder Reduced-Order Models with Latent Neural ODE Dynamics

    Mar 3, 2026Mikhail OsipovReduced-Order ModelingAutoencoders

    Independent Researcher, Italy

  18. Learning Smooth Time-Varying Linear Policies with an Action Jacobian Penalty

    Feb 20, 2026Zhaoming Xie, Kevin Karol, Jessica HodginsRL ControlRobot Imitation Learning

    Robotics AI Institute, Cambridge, Massachusetts, USA