Binxu
  • Bio
  • Papers
  • Talks
  • Experience
  • Teaching
  • Recent & Upcoming Talks
    • SfN 2025 Nanosymposium
    • IAIFI Summer Workshop Talk
    • Talk at VSS2025 Session: Theory - Artificial neural networks
    • Talk at VSS2025 Symposium Model-optimized stimuli: more than just pretty pictures
    • Spring into Science Retreat Talk
    • Special Seminar at Washington University Neuroscience Department
    • Yale Cognitive & Neural Computation Lab Talk
    • SfN 2024 Nanosymposium
    • NAISYS2024 Conference Talk
    • KITP Deep Learning Program
    • SfN 2023 Nanosymposium
    • PhD Thesis Defense
    • Kempner Institute Invited Lecture
  • Publications
    • Feature accentuation along the encoding axes of IT neurons uncovers hidden differences in model-brain alignment
    • An analytical theory of power law spectral bias in the learning dynamics of diffusion models
    • Archetypal SAE: Adaptive and Stable Dictionary Learning for Concept Extraction in Large Vision Models
    • The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications
    • Diverse capability and scaling of diffusion and auto-regressive models when learning abstract rules
    • Do diffusion models generalize on abstract rules for reasoning?
    • Neural Dynamics of Object Manifold Alignment in the Ventral Stream
    • The hidden linear structure in score-based models and its application
    • Understanding Learning Dynamics of Neural Representations via Feature Visualization at Scale
    • Charting the Landscape of Ventral Stream Neural Code on Generative Image Manifolds
    • Diffusion models generate images like painters: an analytical theory of outline first, details later
    • On the Level Sets and Invariance of Neural Tuning Landscapes
    • Tuning landscapes of the ventral stream
    • High-performance Evolutionary Algorithms for Online Neuron Control
    • Factorized convolution models for interpreting neuron-guided images synthesis
    • On the use of Cortical Magnification and Saccades as Biological Proxies for Data Augmentation
    • The Geometry of Deep Generative Image Models and its Applications
    • Visual prototypes in the ventral stream are attuned to complexity and gaze behavior
    • What constitutes understanding of ventral pathway function?
    • A mechanism for synaptic copy between neural circuits
    • Mutual information and information gating in synfire chains
  • Projects
  • Blog
    • ๐ŸŽ‰ Easily create your own simple yet highly customizable blog
    • ๐Ÿง  Sharpen your thinking with a second brain
    • ๐Ÿ“ˆ Communicate your results effectively with the best data visualizations
    • ๐Ÿ‘ฉ๐Ÿผโ€๐Ÿซ Teach academic courses
    • โœ… Manage your projects
  • Projects
    • PyTorch
    • scikit-learn
    • Learn Python
  • Experience
  • Teaching
    • Neuro140/240 - Biological and Artificial Intelligence
    • Neuro 120 - Introduction to Computational Neuroscience
    • Machine Learning from Scratch
    • BIOL 5648 - Coding and Statistical Thinking in the Neurosciences
  • Academic notes
    • Note on Variants of Diffusion Scheduler, DDPM DDIM PNDM
    • Note on Hippo- Recurrent Memory with Optimal Polynomial Projection
    • Note on S4-Efficiently Modeling Long Sequences with Structured State Spaces
    • Note on Equivalent Score Matching Objective
    • Note on EM algorithm and likelihood lower bound
    • Note on Diffusion Generative Models
    • Probabilistic Models of Neural Population
    • Some Famous Matrix Determinant and Inversion Identities
    • Note on Kernel PCA
    • Analytical Techniques for Finding Spectrum of Tridiagonal Toeplitz Matrix
    • PCA of High Dimensional Trajectory
    • Note on Kernel Ridge Regression
    • Note on Hopfield Network
    • Note on Modern Hopfield Network and Transformers
    • Note on Feedback Stablization
    • Note on Bifurcation Normal Form
    • Note on Invariance and Stable Manifold
    • Note on Lyapnov Stability Theory
    • Note on Nonlinear Dynamic System
    • Note on Classic CNNs
    • Note on Word2Vec
    • Note on Non-Parametric Regression
    • Note on Neural Tuning and Information
    • Note on Variational Inference (Updating)
    • Note on Bayesian Optimization
    • Note on Gaussian Process
    • Brief Note on Online Correlation Computation
    • Note on MinMax Game
    • Note on Laplacian Operator (Diffusion) in Geometry Processing
    • Note on Cortical Waves
    • Spectral Graph Theory and Segmentation
    • Computations on Hyperbolic Geometry
    • Note on Deep Reinforcement Learning
    • Note on Photometric Reasoning
    • Note on Generative Adversarial Network
    • Note on Computational Photography
    • Note on Hardware Based Computational Photography
    • Note on Epipolar Geometry and Optic Slow
    • Note on Semantic Vision Task
    • Note on Stereo Problem
    • Note on Image Prior-Markov Random Field Modelling
    • Note on Hessian Aware Zeroth Order Optimization Framework
    • Note on Advanced Computer Vision
    • Note on Image Prior-Spatial Relationship Modeling
    • Krylov Subspace, Conjugate Gradient and Lancosz Iteration
    • Comparison of Major Deep Learning Frameworks (Updating)
    • Note on Online Linear Regression Algorithm
    • LBFGS Algorithm
    • Note on Visual Imagery
    • Note on Local Feature Descriptors
    • Note on ShapeCollage and Patch Based Shape Interpretation
    • Note on Categorization and Concepts
    • Some Computation on Sphere
    • Note on CNN Interpretability
    • Note on Forms of Memory
    • Note on Optimization on Manifold
    • Note on Fragment Based Object Recognition
    • Note on Feature Visualization (Updating)
    • Note on Deep Unsupervised Learning
    • Note on Animal Perception
    • Note on Computer Vision
    • Note on Behavioral Study
    • Note on Network Commnunication
    • This Week's Learning about Brain 4 ็œ‹ๅพ—่ง่ฟ˜ๆ˜ฏ็œ‹ไธ่ง, ่ฟ™ๆ˜ฏไธ€ไธช้—ฎ้ข˜โ€”โ€”่ง†่ง‰ๆ„่ฏ†็š„็ฅž็ป็›ธๅ…ณ็‰ฉ (To see or not to see, that's a question)
    • Note on Algorithm for Non-Negative Matrix Factorization
    • Note on Computation by Synaptic Plasticity
    • Note on Selective Attention
    • Constrained CMA-ES Algorithm
    • Note on Belief Propagation Algorithm (Updating)
    • Distance-Matrix-Based
    • Image-Prior-Reading-Note
    • Note on Belief Propagation for Early Vision
    • Note on Generating Random Shapes
    • Note on VC Dimension
    • Note-on-Fitting-LNP
    • Note-on-Geodesic-and-Curvature
    • Note-on-Graph-Cut
    • Note-on-NEAT-CPPN
    • Note-on-Pareto-Front
    • Note-on-Smoothness-of-Function-on-Manifold
    • Note-on-SNR-for-Neuron
    • Note-on-StyleGAN
    • Note-on-Synaptic-Learning-Rules
    • Optimizer-Design-for-BigGAN
    • pandas_table_wrangling
  • Technical notes
    • Julia for Matlab and Python Users (Updating)
    • JavaScript + HTML Programming 101 (Updating)
    • MTurk 101
    • Scene Programming in MonkeyLogic2
    • Compiling C Extensions for PyTorch
    • Debugging StyleGAN2 in PyTorch
    • Publishing and Using Pretrained model through `Torch.hub`
    • GUI programming in Matlab
    • Hybrid Programming Matlab and Python
    • Importing Geometry from Google Map to Blender
    • Learning CMD / Shell Scripting in Windows
    • Show Animation in PDF Through Latex
    • Transporting Data Between Matlab, Python
    • Procedurally Generating Slides from Script
    • Handling and Printing Parameters in matlab
    • Note on Matlab and Python (matplotlib) Plotting system
    • Windows Working Environment Build Up (Updating)
    • Note on Pandas
    • Autograd Mechanism and Hessian Computation in PyTorch
    • Dynamic Visualization in Python
    • Computer Graphics Environment in Matlab
    • Multi-platform Matlab compiling
    • Working with Caffe
    • Using Google Cloud Service for Large Scale Image Labelling
    • How to Parse Anatomical/Physiological Terms in Latin/Greek
    • Linux Working Environment Build Up (Updating)
    • Understanding conda and python package management (Updating)
    • DeepLabCut Trouble Shooting
    • Common Statistical Problems in Neural Data Analysis (Updating)
    • Resources for Zebrafish Study
    • Note on Automatic 3D Instance Segmentation Pipeline
    • Automatic Behavioral Quantification Pipeline
    • How to translate matlab code into python (numpy)
    • Math Intensive Github Blog Construction
    • 3d-printing-tricks
    • Basic-Java-Concepts
    • Build-RL-Environment
    • Caffe-prototxt-format
    • Common-Recurrent-Modules
    • Compiling C Code for Python
    • Connecting Matlab and TF
    • Drawing-Meshes-in-Illustrator
    • Extracting WeChat Database
    • GUI-programming-python
    • Hacking Matlab Deep Learning
    • IO-Video-in-matlab-python
    • Music21_basics
    • NN_Training_Practicality
    • Note-on-Jax
    • Note_on_Optimizer_Development
    • pytest-usage
    • Python-Logging
    • Stanford-CoreNLP-Usage
    • Translating_TF_and_Torch
    • Vector-Figure-Editing-in-Illustrator

Note on Nonlinear Dynamic System

Apr 9, 2021 ยท 1 min read

Bifurcation Normal Form

Invariance and Stable Manifold

Lyapnov Stability Theory

Feedback Stablization

Last updated on Apr 9, 2021
Math Geometry Dynamic System Control Theory
Binxu Wang
Authors
Binxu Wang
Research Fellow
← Note on Lyapnov Stability Theory Apr 9, 2021
Note on Classic CNNs Jan 17, 2021 →

ยฉ 2025 Me. This work is licensed under CC BY NC ND 4.0

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