Jipeng Sun

1. Neuromorphic Computing Surrogate Gradient Learning (SGL) Surrogate Gradient Learning (SGL) is a technique primarily used to train neural networks that contain non-differentiable activation functions. It is…
2. Optics Orthographic Images to Hologram While the layer-based method we just discussed slices a 3D scene by depth (the z-axis), the common orthographic method slices the 3D scene by angle…
3. Optimization Neural Proximal Operators This is the exact conceptual leap that birthed the Plug-and-Play (PnP) and Regularization by Denoising (RED) frameworks, revolutionizing how we solve…
4. Neuromorphic Computing Spike-Timing-Dependent Plasticity (STDP) Spike-Timing-Dependent Plasticity (STDP) is a biologically plausible learning rule that adjusts the strength of synaptic connections based on the…
5. Neuromorphic Computing Hebbian Learning At its core, Hebbian Learning is a neuroscientific theory introduced by Donald Hebb in 1949, famously summarized as: "Neurons that fire together, wire…
6. Neuromorphic Computing Leaky Integrate-and-Fire (LIF) Dynamics The Leaky Integrate-and-Fire (LIF) model is a foundational mathematical model in computational neuroscience. It is an elegant abstraction that captures…
7. Math Hilbert Transform The Hilbert Transform is a fundamental mathematical operation in signal processing. While the Fourier Transform tells you *what frequencies* are in a…
8. Math Graph Fourier Transform In a classical setting, if you have a signal sampled on a perfectly regular grid—like an audio wave over uniform time intervals or an image on a 2D…
9. Math Eigenvalue Decomposition For a square \(n \times n\) matrix \(A\), an eigenvector \(\mathbf{v}\) and its corresponding eigenvalue \(\lambda\) must satisfy the following equation:
10. Machine Learning Self Attention At its core, self-attention is a sequence-to-sequence operation. It takes a sequence of vectors and produces a new sequence of vectors of the same…
11. Optimization HQS (Half-Quadratic Splitting) It is designed to minimize an objective function that consists of two competing terms: a data fidelity term (how well the solution matches the…
12. Computer Graphics NeRF Neural Radiance Fields (NeRF) represent a breakthrough approach to synthesizing novel views of complex 3D scenes from a sparse set of 2D images.…
13. Computer Vision Camera Extrinsic Matrix Estimating the camera extrinsic matrix—which defines the rigid transformation from the world coordinate system to the camera's local 3D coordinate…
14. Computer Vision Bundle Adjustment Bundle adjustment is the cornerstone of 3D reconstruction, Structure from Motion (SfM), and visual SLAM. At its core, it is a large-scale, non-linear…

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15. Computer Vision COLMAP COLMAP is an end-to-end pipeline for Structure-from-Motion (SfM) and Multi-View Stereo (MVS). It takes a collection of 2D images and mathematically…
16. Computer Graphics 3D Gaussian Splatting 3D Gaussian Splatting (3DGS) is a breakthrough technique in computer graphics and computer vision for novel view synthesis. It emerged as a faster,…
17. Computer Vision Camera Intrinsic Matrix Intrinsics K, focal length, principal point, and pixel skew.
18. Machine Learning AutoDiff Automatic differentiation (AutoDiff) is the algorithmic foundation that makes modern machine learning frameworks like PyTorch and JAX possible. While…
19. Machine Learning Backpropagation Backpropagation (short for "backward propagation of errors") is the mathematical engine that allows neural networks to learn. At its core, it is an…
20. Machine Learning Improved Mean Flow (iMF) Improved mean flow (iMF) — faster sampling and training for flow-based generative models.
21. Machine Learning Diffusion Transformer (DiT) To understand the math behind the Diffusion Transformer (DiT), we have to separate it into two distinct parts: the mathematical framework (the…
22. Machine Learning Vision Transformer (ViT) The Vision Transformer (ViT) represents a massive paradigm shift in computer vision. Introduced by Google in 2020 ("An Image is Worth 16x16 Words"), it…
23. Machine Learning Classifier-Free Guidance (CFG) Classifier-Free Guidance (CFG) is arguably the most critical technique for achieving high-fidelity, strongly aligned generations in modern diffusion…
24. Machine Learning Mean Flow Notes on mean-flow generative modeling and its connection to flow matching.
25. Computer Vision RAFT(Recurrent All-Pairs Field Transforms) RAFT (Recurrent All-Pairs Field Transforms) represents a major paradigm shift from traditional optical flow methods like Lucas-Kanade.
26. Computer Vision Lucas-Kanade Method Example To see exactly how the Lucas-Kanade (LK) method solves for optical flow, we need to walk through the least-squares approximation.
27. Computer Vision Optical Flow Optical flow is the pattern of apparent motion of objects, surfaces, and edges in a visual scene, caused by the relative motion between an observer (an…
28. Optimization Proximal Algorithms Proximal algorithms are a class of optimization methods designed to handle objective functions that are non-smooth, constrained, or split into multiple…
29. Optimization Analytical Proximal Operators As a quick refresher, the proximal operator of a scaled convex function \(\lambda f(x)\) evaluated at a point \(v\) is defined as:
30. Optimization ADMM (Alternating Direction Method of Multipliers) The Alternating Direction Method of Multipliers (ADMM) is a powerful algorithm that solves convex optimization problems by breaking them into smaller,…
31. Optimization Lagrangian Method The standard Lagrangian is a mathematical trick to turn a *constrained* problem into an *unconstrained* one. It does this by taking the hard rules…
32. Machine Learning DDPMs, DDIMs, and Score-Based Methods The connection between DDPMs, DDIMs, and Score-Based Generative Models is one of the most elegant unifying theories in modern machine learning…
33. Machine Learning DDIM (Denoising Diffusion Implicit Models) The fundamental difference between DDPM (Denoising Diffusion Probabilistic Models) and DDIM (Denoising Diffusion Implicit Models) lies entirely in the…
34. Machine Learning Diffusion Model Diffusion models, specifically Denoising Diffusion Probabilistic Models (DDPMs), are generative models that learn to create data by reversing a gradual…
35. Machine Learning VAE vs. Diffusion from ELBO Perspective It is fascinating that two entirely different generative paradigms—Variational Autoencoders (VAEs) and Diffusion Models—are mathematically rooted in…
36. Machine Learning KL Divergence At its core, Kullback-Leibler (KL) Divergence is a statistical measure of how much one probability distribution differs from a second, reference…
37. Machine Learning ELBO (Evidence Lower Bound) In Bayesian inference and generative modeling, the Evidence Lower Bound (ELBO) is a crucial quantity used to approximate the marginal likelihood (the…
38. Machine Learning Diffusion from Stochastic Differential Equations (SDEs) Perspective From a mathematical perspective, diffusion models are fundamentally about defining a trajectory between a complex, intractable data distribution and a…
39. Computational Imaging PnP with Diffusion Plug-and-play priors with diffusion models for computational imaging inverse problems.
40. Optics Stokes Vectors While tools like the Jones calculus are great for describing perfectly polarized light using the electric field's complex amplitude, they fail when…
41. Computational Imaging Generative Methods for Deconv At its core, deconvolution is fundamentally ill-posed. Information is lost when an image is blurred, meaning multiple different sharp images could…
42. Machine Learning Flow Matching Flow matching is a highly effective mathematical framework for generative modeling. It serves as an alternative to Diffusion Models and provides a more…
43. Optics Angular Spectrum Method The ASM is the standard algorithm for simulating how light travels through space because it turns a massively complex 3D physics problem into a simple…
44. Optics Diffraction Grating Formula You have identified a famous paradox: the Fourier transform is a global integral (requiring information from \(-\infty\) to \(\infty\)), so how can a…

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