From 0597afb51113c84970c284afa65d6d452d986c30 Mon Sep 17 00:00:00 2001 From: Trance-0 <60459821+Trance-0@users.noreply.github.com> Date: Fri, 14 Nov 2025 11:15:12 -0600 Subject: [PATCH] updates? --- .gitignore | 1 + content/CSE510/CSE510_L23.md | 3 + content/CSE510/_meta.js | 1 + content/CSE5313/CSE5313_L22.md | 247 +++++++++ content/CSE5313/_meta.js | 1 + content/CSE5519/CSE5519_A4.md | 13 + content/CSE5519/CSE5519_E5.md | 13 + content/Math4201/Math4201_L32.md | 14 + content/Math4201/_meta.js | 3 + next-env.d.ts | 2 +- next.config.mjs | 14 +- package.json | 2 +- public/sitemap.xml | 838 ++++++++++++++++--------------- tsconfig.json | 5 +- 14 files changed, 746 insertions(+), 411 deletions(-) create mode 100644 content/CSE510/CSE510_L23.md create mode 100644 content/CSE5313/CSE5313_L22.md create mode 100644 content/Math4201/Math4201_L32.md diff --git a/.gitignore b/.gitignore index ab7a57a..b2396ba 100644 --- a/.gitignore +++ b/.gitignore @@ -143,6 +143,7 @@ analyze/ # pagefind postbuild public/_pagefind/ +public/sitemap.xml # npm package lock file for different platforms package-lock.json \ No newline at end of file diff --git a/content/CSE510/CSE510_L23.md b/content/CSE510/CSE510_L23.md new file mode 100644 index 0000000..3fb7f63 --- /dev/null +++ b/content/CSE510/CSE510_L23.md @@ -0,0 +1,3 @@ +# CSE510 Deep Reinforcement Learning (Lecture 23) + +## Offline Reinforcement Learning \ No newline at end of file diff --git a/content/CSE510/_meta.js b/content/CSE510/_meta.js index 9680727..9b154d0 100644 --- a/content/CSE510/_meta.js +++ b/content/CSE510/_meta.js @@ -25,4 +25,5 @@ export default { CSE510_L20: "CSE510 Deep Reinforcement Learning (Lecture 20)", CSE510_L21: "CSE510 Deep Reinforcement Learning (Lecture 21)", CSE510_L22: "CSE510 Deep Reinforcement Learning (Lecture 22)", + CSE510_L23: "CSE510 Deep Reinforcement Learning (Lecture 23)", } \ No newline at end of file diff --git a/content/CSE5313/CSE5313_L22.md b/content/CSE5313/CSE5313_L22.md new file mode 100644 index 0000000..2bd8e98 --- /dev/null +++ b/content/CSE5313/CSE5313_L22.md @@ -0,0 +1,247 @@ +# CSE5313 Coding and information theory for data science (Lecture 21) + +## Approximate Gradient Coding + +### Exact gradient computation and approximate gradient computation + +In the previous formulation, the gradient $\sum_i v_i$ +is computed exactly. + +- Accurate +- Requires $d \geq s + 1$ (high replication factor). +- Need to know $s$ in advance! + +However: + +- Approximate gradient computation are very common! + - E.g., stochastic gradient descent. +- Machine learning is inherently inaccurate. + - Relies on biased data, unverified assumptions about model, etc. + +Idea: If we relax the exact computation requirement, can have $d < s + 1$? + +- No fixed $s$ anymore. + +Approximate computation: + +- Exact computation: $\nabla \triangleq v = \sum_i v_i = (1, \cdots, 1) v_1, \cdots, v_n^\top$. +⊤. +- Approximate computation: $\nabla \triangleq v = \sum_i v_i \approx u v_1, \cdots, v_n^\top$, + - Where $d_2(u, \mathbb{I})$ is "small" ($d_2(u, v) =\sqrt{ \sum_i (u_i - v_i)^2}$). + - Why? +- Lemma: Let $v_u = u (v_1, \cdots, v_n)^\top$. If $d_2(u, \mathbb{I}) \leq \epsilon$ then $d_2(v, v_u) \leq \epsilon \cdot \ell_{spec}(V)$. + - $V$ is the matrix whose rows are the $v_i$'s. + - $\ell_{spec}$ is the spectral norm (positive sqrt of maximum eigenvalue of $V^\top V$). +- Idea: Distribute $S_1, \cdots, S_n$ as before, and + - as the master gets more and more responses, + - it can reconstruct $u v_1, \cdots, v_n^\top$, + - such that $d_2(u, \ell)$ gets smaller and smaller. + +> [!NOTE] +> $d \geq s + 1$ no longer holds. +> $s$ no longer a parameter of the system, but $s = n - \#responses$ at any given time. + +### Trivial Scheme + +Off the bat, the "do nothing" approach: + +- Send $S_i$ to worker $i$, i.e., $d = 1$. +- Worker $i$ replies with the $i$'th partial gradient $v_i$. +- The master averages up all the responses. + +How good is that? + +- For $u = \frac{n}{n-s} \cdot \mathbb{I}$, the factor $\frac{n}{n-s}$ corrects the $\frac{1}{n}$ in $v_i = \frac{1}{n} \cdot \nabla \text{ on } S_i$. +- Is this $\approx \sum_i v_i$? In other words, what is $d_2(\frac{n}{n-s} \cdot \mathbb{I}, \mathbb{I})$? + +Trivial scheme: $\frac{n}{n-s} \cdot \mathbb{I}$ approximation. + +Must do better than that! + +### Roadmap + +- Quick reminder from linear algebra. + - Eigenvectors and orthogonality. +- Quick reminder from graph theory. + - Adjacency matrix of a graph. +- Graph theoretic concept: expander graphs. + - "Well connected" graphs. + - Extensively studied. +- An approximate gradient coding scheme from expander graphs. + +### Linear algebra - Reminder + +- Let $A \in \mathbb{R}^{n \times n}$. +- If $A v = \lambda v$ then $\lambda$ is an eigenvalue and $v$ is an eigenvector. +- $v_1, \cdots, v_n \in \mathbb{R}^n$ are orthonormal: + - $\|v_i\|_2 = 1$ for all $i$. + - $v_i \cdot v_j^\top = 0$ for all $i \neq j$. +- Nice property: $\| \alpha_1 v_1 + \cdots + \alpha_n v_n \|_2^2 = \sqrt{\sum_i \alpha_i^2}$. +- $A$ is called symmetric if $A = A^\top$. +- Theorem: A **real and symmetric** matrix has an orthonormal basis of eigenvectors. + - That is, there exists an orthonormal basis $v_1, \cdots, v_n$ such that $A v_i = \lambda_i v_i$ for some $\lambda_i$'s. + +### Graph theory - Reminder + +- Undirected graph $G = V, E$. +- $V$ is a vertex set, usually $n = 1,2, \cdots, n$. +- $E \subseteq \binom{V}{2}$ is an edge set (i.e., $E$ is a collection of subsets of $V$ of size two). +- Each edge $e \in E$ is of the form $e = (a, b)$ for some distinct $a, b \in V$. +- Spectral graph theory: + - Analyze properties of graphs (combinatorial object) using matrices (algebraic object). + - Specifically, for a graph $G$ let $A_G \in \{0,1\}^{n \times n}$ be the adjacency matrix of $G$. + - $A_{i,j} = 1$ if and only if $\{i,j\} \in E$ (otherwise 0). + - $A$ is real and symmetric. + - Therefore, has an orthonormal basis of eigenvectors. + +#### Some nice properties of adjacency matrices + +- Let $G = (V, E)$ be $d$-regular, with adjacency matrix $A_G$ whose (real) eigenvalues $\lambda_1 \geq \cdots \geq \lambda_n$. +- Some theorems: + - $\lambda_1 = d$. + - $\lambda_n \geq -d$, equality if and only if $G$ is bipartite. + - $A_G \mathbb{I}^\top = \lambda_1 \mathbb{I}^\top = d \mathbb{I}^\top$ (easy to show!). + - Does that ring a bell? ;) + - If $\lambda_1 = \lambda_2$ then $G$ is not connected. + +#### Expander graphs - Intuition. + +- An important family of graphs. +- Multiple applications in: + - Algorithms, complexity theory, error correcting codes, etc. +- Intuition: A graph is called an expander if there are no "lonely small sets" of nodes. +- Every set of at most $n/2$ nodes is "well connected" to the remaining nodes in the graph. +- A bit more formally: + - An infinite family of graphs $G_n$ $n=1$ $\infty$ (where $G_n$ has $n$ nodes) is called an **expander family**, if the "minimal connectedness" of small sets in $G_n$ does not go to zero with $n$. + +#### Expander graphs - Definitions. + +- All graphs in this lecture are $d$-regular, i.e., all nodes have the same degree $d$. +- For sets of nodes $S, T \subseteq V$, let $E(S, T)$ be the set of edges between $S$ and $T$. I.e., $E(S, T) = \{(i,j) \in E | i \in S \text{ and } j \in T\}$. +- For a set of nodes $S$ let: + - $S^c = n \setminus S$ be its complement. + - Let $\partial S = E(S, S^c)$ be the boundary of $S$. + - I.e., the set of edges between $S$ and its complement $S^c$. +- The expansion parameter $h_G$ of $G$ is: + - I.e., how many edges leave $S$, relative to its size. + - How "well connected" $S$ is to the remaining nodes. + +> [!NOTE] +> $h_G = \min_{S \subseteq V, |S| \leq n/2} \frac{\partial S}{|S|}$. + +- An infinite family of $d$-regular graphs $(G_n)_{n=1}^\infty$ (where $G_n$ has $n$ nodes) is called an **expander family** if $h(G_n) \geq \epsilon$ for all $n$. + - Same $d$ and same $\epsilon$ for all $n$. +- Expander families with large $\epsilon$ are hard to build explicitly. +- Example: (Lubotsky, Philips and Sarnak '88) + - $V = \mathbb{Z}_p$ (prime). + - Connect $x$ to $x + 1, x - 1, x^{-1}$. + - $d = 3$, very small $\epsilon$. +- However, **random** graphs are expanders with high probability. + +#### Expander graphs - Eigenvalues + +- There is a strong connection between the expansion parameter of a graph and the eigenvalues $\lambda_1 \geq \cdots \geq \lambda_n$ of its adjacency matrix. +- Some theorems (no proof): + - $\frac{d-\lambda_2}{2} \leq h_G \leq \sqrt{2d (d - \lambda_2)}$. + - $d - \lambda_2$ is called the **spectral gap** of $G$. + - If the spectral gap is large, $G$ is a good expander. + - How large can it be? + - Let $\lambda = \max \{|\lambda_2|, |\lambda_n|\}$. Then $\lambda \geq 2 d - 1 - o_n(1)$. (Alon-Boppana Theorem). + - Graphs which achieve the Alon-Boppana bound (i.e., $\lambda \leq 2 d - 1$) are called **Ramanujan graphs**. + - The "best" expanders. + - Some construction are known. + - Efficient construction of Ramanujan graphs for all parameters is very recent (2016). + +#### Approximate GC from Expander Graphs + +Back to approximate gradient coding. + +- Let $d$ be any replication parameter. +- Let $G$ be an expander graph (i.e., taken from an infinite expander family $(G_n)_{n=1}^\infty$) + - With eigenvalues $\lambda_1 \geq \cdots \geq \lambda_n$, and respective eigenvectors $w_1, \cdots, w_n$ + - Assume $\|w_1\|_2 =\| w_2\|_2 = \cdots = \|w_n\|_2 = 1$, and $w_i w_j^\top = 0$ for all $i \neq j$. +- Let the gradient coding matrix $B=\frac{1}{d} A_G$. + - The eigenvalues of $B$ are $\mu_1 = 1\geq \mu_2 \geq \cdots \geq \mu_n$. where $\mu_i = \frac{\lambda_i}{d}$. + - Let $\mu = \max \{|\mu_2|, |\mu_n|\}$. + - $d$ nonzero entries in each row $\Rightarrow$ Replication factor $d$. +- Claim: For any number of stragglers $s$, we can get close to $\mathbb{I}$. + - Much better than the trivial scheme. + - Proximity is a function of $d$ and $\lambda$. +- For every $s$ and any set $\mathcal{K}$ of $n - s$ responses, we build an "decoding vector". + - A function of $s$ and of the identities of the responding workers. + - Will be used to linearly combine the $n - s$ responses to get the approximate gradient. +- Let $w_{\mathcal{K}} \in \mathbb{R}^n$ such that $(w_{\mathcal{K}})_i = \begin{cases} -1 & \text{if } i \notin \mathcal{K} \\ \frac{s}{n-s} & \text{if } i \in \mathcal{K} \end{cases}$. + +Lemma 1: $w_{\mathcal{K}}$ is spanned by $w_2, \cdots, w_n$, the $n - 1$ last eigenvectors of $A_G$. + +
+Proof + +$w_2, \cdots, w_n$ are independent, and all orthogonal to $w_1 = \mathbb{I}$. + +$\Rightarrow$ The span of $w_2, \cdots, w_n$ is exactly all vectors whose sum of entries is zero. + +Sum of entries of $w_{\mathcal{K}}$ is zero $\Rightarrow$ $w_{\mathcal{K}}$ is in their span. + +Corollary: $w_{\mathcal{K}} = \alpha_2 w_2 + \cdots + \alpha_n w_n$ for some $\alpha_i$'s in $\mathbb{R}$. +
+ +Lemma 2: From direct computation, the norm of $w_{\mathcal{K}} = \alpha_2 w_2 + \cdots + \alpha_n w_n$ is $\frac{ns}{n-s}$. + +Corollary: $w_{\mathcal{K}}^2 = \sum_{i=2}^n \alpha_i^2 = \frac{ns}{n-s}$ (from Lemma 2 + orthonormality of $w_2, \cdots, w_n$). + +The scheme: + +- If the set of responses is $\mathcal{K}$, the decoding vector is $w_{\mathcal{K}} + \ell_2$. +- Notice that $\operatorname{supp}(w_{\mathcal{K}} + \ell_2) = \mathcal{K}$. +- The responses the master receives are the rows of $B v_1, \cdots, v_n^\top$ indexed by $\mathcal{K}$. +- $\Rightarrow$ The master can compute $w_{\mathcal{K}} + \ell_2 B v_1, \cdots, v_n^\top$. + +Left to show: How close is $w_{\mathcal{K}} + \ell_2 B$ to $\ell_2$? + +
+Proof + +Recall that: + +1. $w_{\mathcal{K}} = \alpha_2 w_2 + \cdots + \alpha_n w_n$. +2. $w_i$'s are eigenvectors of $A_G$ (with eigenvalues $\lambda_i$) and of $B = \frac{1}{d} A_G$ (with eigenvalues $\mu_i = \frac{\lambda_i}{d}$). + +$d_2 (w_{\mathcal{K}} + \mathbb{I} B, \mathbb{I}) = d_2 (\mathbb{I} + \alpha_2 w_2 + \cdots + \alpha_n w_n B, \mathbb{I})$ (from 1.) + +$d_2 (w_{\mathcal{K}} + \mathbb{I} B, \mathbb{I}) = d_2 (\mathbb{I} + \alpha_2 \mu_2 w_2 + \cdots + \alpha_n \mu_n w_n, \mathbb{I})$ (eigenvalues of $B$, and $\mu_1 = 1$) + +$d_2 (w_{\mathcal{K}} + \mathbb{I} B, \mathbb{I}) = d_2 (\mathbb{I} + \alpha_2 \mu_2 w_2 + \cdots + \alpha_n \mu_n w_n , \mathbb{I})$ (by def.). + +$d_2 (w_{\mathcal{K}} + \mathbb{I} B, \mathbb{I}) = \|\sum_{i=2}^n \alpha_i \mu_i w_i\|_2$ + +$d_2 (w_{\mathcal{K}} + \mathbb{I} B, \mathbb{I}) = \|\sum_{i=2}^n \alpha_i \mu_i w_i\|_2$ (w_i's are orthonormal). + +$d_2 (w_{\mathcal{K}} + \mathbb{I} B, \mathbb{I}) = \sqrt{\sum_{i=2}^n \alpha_i^2 \mu_i^2}$ (w_i's are orthonormal). + +
+ +#### Improvement factor + +Corollary: If $B = \frac{1}{d} A_G$ for a (d-regular) Ramanujan graph $G$, + +- $\Rightarrow$ improvement factor $\approx \frac{2}{d}$. +- Some explicit constructions of Ramanujan graphs (Lubotsky, Philips and Sarnak '88) + - with 2 $\frac{2}{d}$ $\approx$ 0.5! + +### Recap + +- Expander graph: A $d$-regular graph with no lonely small subsets of nodes. + - Every subset with $\leq n/2$ has a large ratio $\partial S / S$ (not $\rightarrow 0$ with $n$). + - Many constructions exist, random graph is expander w.h.p. + - The expansion factor is determined by the spectral gap $d - \lambda_2$, + - Where $\lambda = \max \{\lambda_2, \lambda_n\}$, and $\lambda_1 = d \geq \lambda_2 \geq \cdots \geq \lambda_n$ are the eigenvalues of $A_G$. + - "Best" expander = Ramanujan graph = has $\lambda \leq 2 d - 1$. +- "Do nothing" approach: approximation $\frac{ns}{n-s}$. +- Approximate gradient coding: + - Send $d$ subsets $S_{j1}, \cdots, S_{jd}$ to each node $i$, which returns a linear combination according to a coefficient matrix $B$. + - Let $B = \frac{1}{d} A_G$, for $G$ a Ramanujan graph: approximation $\frac{\lambda}{d} \frac{ns}{n-s}$. + - Up to 50% closer than "do nothing", at the price of higher computation load + +>[!NOTE] +> Faster = more computation load. diff --git a/content/CSE5313/_meta.js b/content/CSE5313/_meta.js index f0aa3e9..bc21a24 100644 --- a/content/CSE5313/_meta.js +++ b/content/CSE5313/_meta.js @@ -25,4 +25,5 @@ export default { CSE5313_L19: "CSE5313 Coding and information theory for data science (Lecture 19)", CSE5313_L20: "CSE5313 Coding and information theory for data science (Lecture 20)", CSE5313_L21: "CSE5313 Coding and information theory for data science (Lecture 21)", + CSE5313_L22: "CSE5313 Coding and information theory for data science (Lecture 22)", } \ No newline at end of file diff --git a/content/CSE5519/CSE5519_A4.md b/content/CSE5519/CSE5519_A4.md index 53ba0d9..9aca733 100644 --- a/content/CSE5519/CSE5519_A4.md +++ b/content/CSE5519/CSE5519_A4.md @@ -1,2 +1,15 @@ # CSE5519 Advances in Computer Vision (Topic A: 2025: Semantic Segmentation) +## Dual Semantic Guidance for Open Vocabulary Sematic segmentation + +[link to the paper](https://openaccess.thecvf.com/content/CVPR2025/papers/Wang_Dual_Semantic_Guidance_for_Open_Vocabulary_Semantic_Segmentation_CVPR_2025_paper.pdf) + +## Novelty in Dual Semantic Guidance + +Use dual semantic guidance for semantic segmentation. For each mask, deploy clip like object detection to align the mask with text description. + +> [!TIP] +> +> This paper proposed a generalizable semantic segmentation model with a CLIP-like image-text encoder to refine the mask prediction. +> +> However, I wonder how this model generalized to segment different faces of geometry and create a clear boundary between different objects and the background. In most cases, CLIP may not need complete image information to predict the object and can make a decision based on partial objects. If we have some novel objects containing features of two that might be out of CLIP's codebook, will the CLIP-alignment still work? \ No newline at end of file diff --git a/content/CSE5519/CSE5519_E5.md b/content/CSE5519/CSE5519_E5.md index 767d429..0524359 100644 --- a/content/CSE5519/CSE5519_E5.md +++ b/content/CSE5519/CSE5519_E5.md @@ -1,2 +1,15 @@ # CSE5519 Advances in Computer Vision (Topic E: 2025: Deep Learning for Geometric Computer Vision) +## VGGT: Visual Geometry Grounded Transformer + +[link to paper](https://arxiv.org/pdf/2503.11651) + +### Novelty in VGGT + +Use alternating attention to encode the image. + +> [!TIP] +> +>  VGGT uses a feed-forward neural network that directly infers all key 3D attributes of a scene using alternating attention and is robust to some non-rigid deformations. +> +> I wonder how this model adapts to different light settings for the same image, how the non-Lambertian reflectance is captured, and how this framework can be extended to recover the true color of the objects and evaluate the surface properties of the objects. \ No newline at end of file diff --git a/content/Math4201/Math4201_L32.md b/content/Math4201/Math4201_L32.md new file mode 100644 index 0000000..4055b42 --- /dev/null +++ b/content/Math4201/Math4201_L32.md @@ -0,0 +1,14 @@ +# Math4201 Topology I (Lecture 30) + +## Compact and connected spaces + +### Locally compact + +#### Theorem of Homeomorphism over locally compact Hausdorff spaces + +$X$ is a locally compact Hausdorff space if and only if there exists topological space $Y$ satisfying the following properties: + +1. $X$ is a subspace of $Y$. +2. $Y-X$ has one point (usually denoted by $\infty$). +3. $Y$ is compact and Hausdorff. + diff --git a/content/Math4201/_meta.js b/content/Math4201/_meta.js index 63e4077..5bcaabe 100644 --- a/content/Math4201/_meta.js +++ b/content/Math4201/_meta.js @@ -34,4 +34,7 @@ export default { Math4201_L28: "Topology I (Lecture 28)", Math4201_L29: "Topology I (Lecture 29)", Math4201_L30: "Topology I (Lecture 30)", + Math4201_L31: "Topology I (Lecture 31)", + Math4201_L32: "Topology I (Lecture 32)", + } diff --git a/next-env.d.ts b/next-env.d.ts index 830fb59..9edff1c 100644 --- a/next-env.d.ts +++ b/next-env.d.ts @@ -1,6 +1,6 @@ /// /// -/// +import "./.next/types/routes.d.ts"; // NOTE: This file should not be edited // see https://nextjs.org/docs/app/api-reference/config/typescript for more information. diff --git a/next.config.mjs b/next.config.mjs index f3ce42a..1ea75f9 100644 --- a/next.config.mjs +++ b/next.config.mjs @@ -21,9 +21,17 @@ const bundleAnalyzer = withBundleAnalyzer({ export default bundleAnalyzer(withNextra({ output: 'standalone', - eslint: { - ignoreDuringBuilds: true, - }, + + // static export start + // output: 'export', + // images: { + // unoptimized: true // mandatory, otherwise won't export + // }, + // static export end + + // eslint: { + // ignoreDuringBuilds: true, + // }, // compiler: { // // enable console log in production // removeConsole: false, diff --git a/package.json b/package.json index bd64197..5e3812b 100644 --- a/package.json +++ b/package.json @@ -4,7 +4,7 @@ "build": "cross-env VERCEL_FORCE_NO_BUILD_CACHE=1 NODE_OPTIONS='--max-old-space-size=16384' next build", "build:test": "cross-env ANALYZE=true NODE_OPTIONS='--inspect --max-old-space-size=4096' next build", "build:analyze": "cross-env ANALYZE=true NODE_OPTIONS='--max-old-space-size=16384' next build", - "postbuild": "next-sitemap && pagefind --site .next/server/app --output-path public/_pagefind && cp -r ./public/_pagefind ./out", + "postbuild": "next-sitemap && pagefind --site .next/server/app --output-path out/_pagefind && cp -r ./out/_pagefind ./out", "start": "next start" }, "dependencies": { diff --git a/public/sitemap.xml b/public/sitemap.xml index 804cac3..e47cb5d 100644 --- a/public/sitemap.xml +++ b/public/sitemap.xml @@ -1,407 +1,437 @@ -https://notenextra.trance-0.com2025-10-16T19:39:59.300Zweekly0.5 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+https://notenextra.trance-0.com/Swap/Music1260_M22025-11-14T02:59:47.090Zdaily0.5 \ No newline at end of file diff --git a/tsconfig.json b/tsconfig.json index 1fda10e..3f22d98 100644 --- a/tsconfig.json +++ b/tsconfig.json @@ -16,7 +16,7 @@ "moduleResolution": "bundler", "resolveJsonModule": true, "isolatedModules": true, - "jsx": "preserve", + "jsx": "react-jsx", "plugins": [ { "name": "next" @@ -28,7 +28,8 @@ "**/*.ts", "**/*.tsx", "next-env.d.ts", - ".next/types/**/*.ts" + ".next/types/**/*.ts", + ".next/dev/types/**/*.ts" ], "exclude": [ "node_modules"