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Belleville 2025 QB Bryce Underwood (LSU commit) fits it in triple coverage for a long TD to 2025 WR/CB Trey Graham D1 Regional Final: #3 Belleville (10-1) is tied with #2 Detroit Catholic Central (11-0) 7-7 1st quarter Belleville Football @TreyGraham06 Bryce Jay Underwood
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![#Patriots Voluntary OTA Notes [Non-Padded] (6/2): 𝗢𝗳𝗳𝗲𝗻𝘀𝗲 • QB Drake Maye connected with WR Kayshon Boutte for the play of the day — Maye perfectly placed the ball deep along the left side of the field and Boutte made a fingertip catch. • QB Drake Maye had no turnovers today and he had his best day of open OTAs by far — Maye completed 9 straight passes at one point. • Full QB Stats: Maye 14/16 Dobbs 11/13 Wooldridge 4/8, INT • WRs DeMario Douglas, Kayshon Boutte, Kyle Williams and Efton Chism spent the most time working with QB Drake Maye today. • WR Efton Chism III had 7 receptions on 7 targets and looked to always be open — the undrafted rookie took several snaps with QB Drake Maye and the top offensive unit. • RB Rhamondre Stevenson made an extremely impressive finger-tip grab for a 25-yard gain on a dot from QB Drake Maye. • OL Cole Strange and Wes Schweitzer were the two primary left guards today — that spot on the offensive line is truly a competition. • TE Jaheim Bell had a rough day — the former seventh-round pick had 2 bad drops. • It was a bit of a quiet day for rookie WR Kyle Williams who caught 1 of his 2 targets. • WR Stefon Diggs was limited today working with WR Ja’Lynn Polk off to the side at times — Diggs closely observed the offense towards the end of practice as they practiced plays. • Rookie TE CJ Dippre caught a nice pass thrown by QB Ben Wooldridge up the seam. • Veteran OT Morgan Moses once again stayed after practice to help and give advice to the young offensive lineman. • RG Mike Onwenu says he feels good getting back to an offense he is familiar with — Onwenu adds that he is rehabbing from a hand injury. • RB Rhamondre Stevenson says RBs coach Tony Dews flew to visit him in Las Vegas while Stevenson was dealing with his father’s passing. • Limited: WR Stefon Diggs WR Ja'Lynn Polk OL Mike Onwenu OL Jared Wilson OT Vederian Lowe TE Austin Hooper • Absent: WR Mack Hollins (Present But DNP) WR Kendrick Bourne (Unknown) RB Trayveon Williams (Unknown) OL Tyrese Robinson (Unknown) 𝗗𝗲𝗳𝗲𝗻𝘀𝗲 • DE Keion White was disruptive today — White sacked both QB Drake Maye and QB Josh Dobbs during team drills. • Rookie S Josh Minkins intercepted QB Ben Wooldridge during 11-on—11s • CB Christian Gonzalez, S Jaylinn Hawkins, and LB Monty Rice each had a pass break up. • DT Joshua Farmer batted another pass down during team drills — Farmer has been able to bat passes down consistently during OTAs. • CB Christian Gonzalez gave up a catch to WR Efton Chism — Chism got open after running an impressive dig route. • LB Jahlani Tavai went down during team period and was grabbing his left knee — the veteran had to be helped off the field after staying down for a couple minutes. • CBs Alex Austin and Marcellas Dial spent time in the slot — Austin has consistently taken reps in the slot since the start of OTAs. • The defensive line continues to disrupt the offense. • Limited: DL Jaquelin Roy DL Wilfried Pene • Absent: CB Carlton Davis (Unknown) CB Marcus Jones (Unknown) ED Anfernee Jennings (Unknown) 𝗦𝗽𝗲𝗰𝗶𝗮𝗹 𝗧𝗲𝗮𝗺𝘀 • Field Goals (33-50 Yards) Andy Borregales: 4/4 John Parker Romo: 2/4, missed wide right Borregales has yet to miss during open OTAs. #NEPats](https://image.24vids.com/tw-1929607371615359335/amplify_video_thumb/1929607290015121409/img/FMiKzNjfAtASdjVo.jpg)
![[Graph Convolutional Network] by hand ✍️ Graph Convolutional Networks (GCNs), introduced by Thomas Kipf and Max Welling in 2017, have emerged as a powerful tool in the analysis and interpretation of data structured as graphs. This exercise demonstrates how GCN works in a simple application: binary classification. -- Goal -- Predict if a node in a graph is X. -- Architecture -- 🟪 Graph Convolutional Network (GCN) 1. GCN1(4,3) 2. GCN2(3,3) 🟦 Fully Connected Network (FCN) 1. Linear1(3,5) 2. ReLU 3. Linear2(5,1) 4. Sigmoid Simplications: • Adjacent matrices are not normalized. • ReLU is applied to messages directly. -- Walkthrough -- [1] Given ↳ A graph with five nodes A, B, C, D, E [2] 🟩 Adjacency Matrix: Neighbors ↳ Add 1 for each edge to neighbors ↳ Repeat in both directions (e.g., A->C, C->A) ↳ Repeat for both GCN layers [3] 🟩 Adjacency Matrix: Self ↳ Add 1's for each self loop ↳ Equivalent to adding the identity matrix ↳ Repeat for both GCN layers [4] 🟪 GCN1: Messages ↳ Multiply the node embeddings 🟨 with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is one message per node [5] 🟪 GCN1: Pooling ↳ Multiply the messages with the adjacent matrix ↳ The purpose is the pool messages from each node's neighbors as well as from the node itself. ↳ The result is a new feature per node [6] 🟪 GCN1: Visualize ↳ For node 1, visualize how messages are pooled to obtain a new feature for better understanding ↳ [3,0,1] + [1,0,0] = [4,0,1] [7] 🟪 GCN2: Messages ↳ Multiply the node features with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is one message per node [8] 🟪 GCN2: Pooling ↳ Multiply the messages with the adjacent matrix ↳ The result is a new feature per node [9] 🟪 GCN2: Visualize ↳ For node 3, visualize how messages are pooled to obtain a new feature for better understanding ↳ [1,2,4] + [1,3,5] + [0,0,1] = [2,5,10] [10] 🟦 FCN: Linear 1 + ReLU ↳ Multiply node features with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is a new feature per node ↳ Unlike in GCN layers, no messages from other nodes are included. [11] 🟦 FCN: Linear 2 ↳ Multiply node features with weights and biases [12] 🟦 FCN: Sigmoid ↳ Apply the Sigmoid activation function ↳ The purpose is to obtain a probability value for each node ↳ One way to calculate Sigmoid by hand ✍️ is to use the approximation below: • >= 3 → 1 • 0 → 0.5 • <= -3 → 0 -- Outputs -- A: 0 (Very unlikely) B: 1 (Very likely) C: 1 (Very likely) D: 1 (Very likely) E: 0.5 (Neutral)](https://image.24vids.com/tw-1828407238408438145/ext_tw_video_thumb/1828407079696039936/pu/img/mjnHB1FbGJngAUIw.jpg)
![[LSTM] by Hand ✍️ LSTMs have been the most effective architecture to process long sequences of data, until our world was taken over by the Transformers. LSTMs belong to the broader family of recurrent neural network (RNNs) that process data sequentially in a recurrent manner. Transformers, on the other hand, abandon recurrence and use self-attention instead to process data concurrently in parallel. Recently, there is renewed interest in recurrence as people realized self-attention doesn’t scale to extremely long sequences, like hundreds of thousands of tokens. Mamba is a good example to bring back recurrence. All of a sudden, it is cool to study LSTMs. How do LSTMs work? [1] Given ↳ 🟨 Input sequence X1, X2, X3 (d = 3) ↳ 🟩 Hidden state h (d = 2) ↳ 🟦 Memory C (d = 2) ↳ Weight matrices Wf, Wc, Wi, Wo Process t = 1 [2] Initialize ↳ Randomly set the previous hidden state h0 to [1, 1] and memory cells C0 to [0.3, -0.5] [3] Linear Transform ↳ Multiply the four weight matrices with the concatenation of current input (X1) and the previous hidden state (h0). ↳ The results are feature values, each is a linear combination of the current input and hidden state. [4] Non-linear Transform ↳ Apply sigmoid σ to obtain gate values (between 0 and 1). • Forget gate (f1): [-4, -6] → [0, 0] • Input gate (i1): [6, 4] → [1, 1] • Output gate (o1): [4, -5] → [1, 0] ↳ Apply tanh to obtain candidate memory values (between -1 and 1) • Candidate memory (C’1): [1, -6] → [0.8, -1] [5] Update Memory ↳ Forget (C0 .* f1): Element-wise multiply the current memory with forget gate values. ↳ Input (C’1 .* o1): Element-wise multiply the “candidate” memory with input gate values. ↳ Update the memory to C1 by adding the two terms above: C0 .* f1 + C’1 .* o1 = C1 [6] Candiate Output ↳ Apply tanh to the new memory C1 to obtain candidate output o’1. [0.8, -1] → [0.7, -0.8] [7] Update Hidden State ↳ Output (o’1 .* o1 → h1): Element-wise multiply the candidate output with the output gate. ↳ The result is updated hidden state h1 ↳ Also, it is the first output. Process t = 2 [8] Initialize ↳ Copy previous hidden state h1 and memory C1 [9] Linear Transform ↳ Repeat [3] [10] Update Memory (C2) ↳ Repeat [4] and [5] [11] Update Hidden State (h2) ↳ Repeat [6] and [7] Process t = 3 [12] Initialize ↳ Copy previous hidden state h2 and memory C2 [13] Linear Transform ↳ Repeat [3] [14] Update Memory (C3) ↳ Repeat [4] and [5] [15] Update Hidden State (h3) ↳ Repeat [6] and [7]](https://image.24vids.com/tw-1806285518126317877/ext_tw_video_thumb/1806285245903482880/pu/img/9-DANs-lC9ghBLvA.jpg)
![[Backpropagation] by Hand✍️ [1] Forward Pass ↳ Given a multi layer perceptron (3 levels), an input vector X, predictions Y^{Pred} = [0.5, 0.5, 0], and ground truth label Y^{Target} = [0, 1, 0]. [2] Backpropagation ↳ Insert cells to hold our calculations. [3] Layer 3 - Softmax (blue) ↳ Calculate ∂L / ∂z3 directly using the simple equation: Y^{Pred} - Y^{Target} = [0.5, -0.5, 0]. ↳ This simple equation is the benefit of using Softmax and Cross Entropy Loss together. [4] Layer 3 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W3 and ∂L / ∂b3 by multiplying ∂L / ∂z3 and [ a2 | 1 ]. [5] Layer 2 - Activations (green) ↳ Calculate ∂L / ∂a2 by multiplying ∂L / ∂z3 and W3. [6] Layer 2 - ReLU (blue) ↳ Calculate ∂L / ∂z2 by multiplying ∂L / ∂a2 with 1 for positive values and 0 otherwise. [7] Layer 2 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W2 and ∂L / ∂b2 by multiplying ∂L / ∂z2 and [ a1 | 1 ]. [8] Layer 1 - Activations (green) ↳ Calculate ∂L / ∂a1 by multiplying ∂L / ∂z2 and W2. [9] Layer 1 - ReLU (blue) ↳ Calculate ∂L / ∂z1 by multiplying ∂L / ∂a1 with 1 for positive values and 0 otherwise. [10] Layer 1 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W1 and ∂L / ∂b1 by multiplying ∂L / ∂z1 and [ x | 1 ]. [11] Gradient Descent ↳ Update weights and biases (typically a learning rate is applied here). 💡 Matrix Multiplication is All You Need: Just like in the forward pass, backpropagation is all about matrix multiplications. You can definitely do everything by hand as I demonstrated in this exercise, albeit slow and imperfect. This is why GPU's ability to multiply matrices efficiently plays such an important role in the deep learning evolution. This is why NVIDIA is now close to $1 trillion in valuation. 💡Exploding Gradients: We can already see the gradients are getting larger as we back-propagate up, even in this simple 3-layer network. This motivates using methods like skip connections to handle exploding (or diminishing) gradients as in the ResNet. I did the calculations entirely by hand. Please let me know if you spot any error or have any questions!](https://image.24vids.com/tw-1818652735535038715/ext_tw_video_thumb/1818652595235569664/pu/img/fBeCqhUByyXiDBbp.jpg)
![I'm starting on a new project #buildinpublic 🤠 ✅ ahrefs sub 📚 initial keyword research 🆕 .com domain name But this is different. Why? I'm starting with SEO & marketing, then fleshing out the product afterwards. It's been a busy morning already thanks to Ahrefs. From the learnings of grandmaster sensei — I will be using my other projects for backlinks & focus on SEO instead of adding as an afterthought. The plan: ------------------------- [hacks explained further down] 1. keyword research 2. more keyword research [HACK #1] 3. content plan 4. choose topics, subtopics & post outline using long-tail keywords found in 1. & 2. [HACK #2] 5. landing page, blog & initial marketing 6. barebone MVP 7. blog with content hubs [HACK #3] 8. initial backlinks [HACK #4] 9. marketing & launch 10. talk to users & iterate while SEO is slowly cooking in the background (hopefully by the time the product matures SEO is booming) ... 🔁 continue to fill in posts according to the content plan. then back to 1 & 2. more long-tail posts & create free tools to improve ranking + increase no. of backlinks. Hack #1 --------- Explore keywords for "result intent" SEO. Figure out guides & tutorials for keywords with DR long tail ones. Create structure for internal links, e.g.: /generic-topic-keyword (links to all posts) ➡️/more-specific-subtopic-keyword (links to child posts) ➡️➡️/very-specific-post-1 ➡️➡️/very-specific-post-2 etc. Hack #3 --------- Create hubs for generic keywords with links to subtopics and long-tail posts. The hubs themselves should be somewhat informative but mostly an overview. => My crazy idea: before I have the content, add external links to authoritative sources for each specific post. I'll slowly write my own content to replace those and move the links inside the post. Hack #4 --------- Use my other projects to write posts on the new product and link to it to get a decent domain ranking fast. Launch on PH with a beta, mostly for the good backlink. Add repos with md files to Github, Gitlab, Bitbucket etc. for some easy backlinks. 🤠 Crazy enough to work, right?* *to note: I've validated the idea and am somewhat sure people will pay for it. But, I'd still like to shorten each step to minimize my risk & ship fast. Thinking: 1 week research, 1 week dev, 1 week marketing, 1 week content. What could go wrong? :D](https://image.24vids.com/tw-1696475630504648989/ext_tw_video_thumb/1696473936395948032/pu/img/FhI4fGVM6r1xzoIv.jpg)
