Softmax vs Sigmoid ✍️ Interact 👉 = Softmax =... Softmax is how deep networks turn raw scores into a probability distribution — the final layer of every classifier, and the core of every attention head in a transformer. To see what it does, picture five boba tea shops on the same block, all competing for your dollar. Five candidates: a, b, c, d, e — different chains, different brewing styles, different pearls. A boba reviewer hands you a 𝘤𝘩𝘦𝘸𝘪𝘯𝘦𝘴𝘴 𝘴𝘤𝘰𝘳𝘦 for each — higher means perfectly chewy "QQ" pearls with the right bite (ask a Taiwanese friend to find out what QQ means). Negative scores are real: mushy bobas, overcooked pearls, a batch left sitting too long. How do you turn five chewiness scores into an allocation that adds to a whole dollar? You could spend everything at the chewiest shop, but that ignores how good the runners-up are. Softmax is the smooth alternative. Read the diagram left to right. First, raise each score to e^{x} — this does two things: it turns negative chewiness into small positives, and it stretches the gaps between scores exponentially. Then sum all five into a single total Z. Finally, divide each e^{x} by Z to get a probability. The five probabilities add up to one, so you can read them as percentages of your dollar. The chewiest shop gets the biggest slice — but never the whole dollar. That's the point of softmax: it ranks confidently while still leaving room for the others. = Sigmoid = Sigmoid squashes any real number into a probability between 0 and 1 — the classic activation for binary classification, and still the gating function inside LSTMs and GRUs. Same boba block as the previous Softmax example, narrowed to just two contenders — a hot new shop `a` with chewiness score x, and your usual go-to `b` whose score is pinned at zero (the neutral baseline you've come to expect). Sigmoid is just softmax with two players, one of them pinned to zero. Read the diagram left to right. First, raise each score to e^{x} — for the usual shop `b` whose score is zero, this is just e^0 = 1 (the constant baseline). Then sum the two into a total Z. Finally, divide each e^{x} by Z to get a probability. The two probabilities add up to one — the new shop wins more of your dollar when its pearls get chewier, and your usual keeps the rest. That's the point of sigmoid: it turns a single chewiness score into a clean 0-to-1 chance you'll try the new place over your usual. --- AI Math, Algorithms, Architectures by hand ✍️ Subscribe to my 60K+ reader newsletter 👉show more

ReLU vs Leaky ReLU 👉 = ReLU = ReLU... is the default activation in modern deep learning — cheap to compute, and stable enough to train networks hundreds of layers deep. To see what it does, picture five boba tea shops on the same block — 𝚊, 𝚋, 𝚌, 𝚍, 𝚎 — each running their own books. Each value is a shop's monthly profit — receipts minus rent, ingredients, and wages. When profit is positive, the shop stays open and the owner pockets every dollar. When profit turns negative, the shop runs out of cash and shutters — the lights go off, the books are wiped to zero. ReLU is exactly that rule, applied one shop at a time. Read the diagram left to right. The first column is the raw value x — each shop's profit at month's end. The second column is the gate: 1 if the shop is open (x > 0), 0 if it has shuttered. The last column is the ReLU output: open shops pass their profit through untouched, while shuttered ones are zeroed out. Five rows means five parallel shops on the same block, each evaluated independently. That's why ReLU is called an element-wise activation: every neuron decides its own fate. = LeakyRelu = Plain ReLU wipes negative values to zero — clean, but a shop that shutters can never recover, since both its output and its gradient stay pinned at zero. This is the dying ReLU problem, and in deep networks it can quietly kill a meaningful fraction of the units. Leaky ReLU is the one-line fix: instead of shuttering, the shop files for Chapter 11 protection and keeps the lights on at reduced capacity. Its debt is restructured down to a fraction α (typically 0.1) — the rest is forgiven, and the shop is wounded, not killed. A small negative signal still flows through, so the gradient survives, and the shop can crawl back to life if a TikTok goes viral. Read the diagram left to right. The first column is the raw value x — each shop's profit at month's end. The second column is the leakage α — the fraction of the loss held over after restructuring (default 0.1, editable). The third column is the gate: 1 for shops still in the black, α for those operating under bankruptcy protection. The last column is the Leaky ReLU output: y = x · gate. Profitable shops pass through untouched; struggling ones shrink by a factor of α but still carry a sign. Five rows means five parallel shops, each evaluated independently. Like ReLU, this is an element-wise activation: every neuron's fate is decided on its own merits. #aibyhahdshow more

🎉 Five Weeks, Five Free GSAP Resources! Hey everyone!... We’re super excited to partner with Codrops and GSAP to celebrate the news that GSAP’s club plugins are now 100% free thanks to Webflow's support. To mark the occasion, we’ll be dropping one free GSAP resource every week for the next five weeks—each fully packaged as a Webflow clonable and a CodePen so you can plug it straight into your own projects. Each resource will feature at least one of those previously paid plugins, to hopefully spark some ideas and inspire your next interactive build. We’re kicking things off with a 'Glowing Interactive Dots Grid' powered by the InertiaPlugin. See how a simple dot matrix can come alive—glowing, springing, and rippling with realistic momentum under your cursor. Grab the CodePen or the Webflow cloneable, tweak the settings, and have a play with it! Sign up for our newsletter through the footer of our website to get all the free stuff in your inbox!show more

Self Attention vs Cross Attention by hand ✍️ Resize... the matrices yourself 👉 Two attention mechanisms, side by side. Both project X into queries; both compute attention via S = Kᵀ × Q and F = V × A. The only difference is the source of K and V. Self attention uses X for everything. Q, K, and V all come from projecting X. Each X token attends to every other X token. The score matrix S is square — 128 × 128. Cross attention uses X for queries and a second sequence E for keys and values. Each X token attends to every E token instead. The score matrix S is rectangular — 64 × 128. Notice what's shared and what's not: X is the same in both — same 36 × 128 input. Q and K share the 16 dimension — that's what makes the dot product Kᵀ × Q valid in either case. V dimensions are independent: self-attention uses 12, cross-attention uses 12. The choice doesn't depend on which mechanism you're using; it depends on what output dimension your downstream layer expects.show more

✈️React Advanced is packing its bags for a NEW... DESTINATION! But where?💥Drop your guess in the comments - and if you’re the first to get it right, you’ll score a FREE ticket to the conference! We’ll still be diving deep into⚛️React - and the venue? It’s an astonishing cinema!show more

[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)show more

Give this a try and let’s see how you... score. (But please read the full thread first) The Sit-to-Rise (SRT) test is a simple, clinically validated assessment that measures your ability to stand up from seated on the floor and then return to a seated position.show more

🏠Mining at home means the electricity bill is yours.... With a Digital Miner, it isn't. We handle the hardware and, the facilities, to keep it all running. You just get the daily BTC reward dropped into your wallet — nothing to pay, nothing to fix. How much of your mining "profit" disappears into your power bill right now?show more

“Bringing such scenes out into the open, through which... the authority responsible for them seeks to do two things: the first is to demean the veil and show it as a means of concealment, not as a religious duty, and the second is to change the well-known image of the Kingdom’s young men and women. #SaudiArabiashow more

⚽️ Cutback Small Sided Game 🗣️ This is a... practice from drill library. This small-sided game is played with 4v4 teams and 4 neutral players positioned at the 4 corners of the grid, known as the 'cutback' zones. The objective is to score 1 goal to win the game. After each goal, the losing team will switch with the neutral players, ensuring that both teams get equal opportunities in different roles. The neutral players are restricted to 1 touch, and the team in possession is encouraged to use them to create goal-scoring chances through quick cutbacks, crosses, or switching the play. The attacking team should aim to exploit the neutral zones to stretch the defense, pull defenders out of position, and open up space for a final delivery into the box. The defenders will need to be aware of their positioning and try to prevent passes into the neutral zones by maintaining close coverage on their opponents.show more

[Discrete Fourier Transform] by Hand ✍️ In signal processing,... the Discrete Fourier Transform (DFT) is no doubt the most important method. But the math involved is extremely complex, literally, involving a summation over a complex number term e^(-iwt). I developed this exercise to demonstrate that underneath such complexity, DFT is just a series of matrix multiplications you can calculate by hand. ✍️ Once you see that, it should not surprise you that a deep neural network, which is also a series of matrix multiplications, with activation functions in-between, can learn to perform DFT to process and analyze signals so effectively. How does DFT work? [1] Given ↳ Signals A, B, and C in the 🟧 frequency domain: ◦ A = cos(w) + 2cos(2w) ◦ B = cos(w) + cos(3w) + cos(4w) ◦ C = -cos(2w) + cos(3w) ◦ Each signal is a weighed sum of four cosine waves at frequencies 1w, 2w, 3w, and 4w. ◦ We will apply Inverse DFT to convert the signals to time domain representations, and then demonstrate DFT can convert back to their original frequency domain representations. ↳ Signal X in the 🟩 time domain. X is sampled at 10 time points 1t, 2t, …, 10t: ◦ X = [-2.5, -1.8, 3, -0.7, -1.0, -0.7, 3, -1.8, -2.5, 5] ◦ Suppose X is also a weighted sum of the same four cosine waves, but we don’t already know their weights. We will apply DFT to discover them. [2] 🟧 Frequency Matrix (F) ↳ Write the coefficients of A, B, C as a matrix F. Each signal is a row. Each frequency is a column. ↳ A → [1, 2, 0, 0] ↳ B → [1, 0, 1, 1] ↳ C → [0, 1-, 1, 0] [3] Cosine → Discrete ↳ Sample from the continuous cosine waves at discrete time points 1t, 2t, 3t, to 10t. [4] Cosine Matrix (W) ↳ Write the samples as a matrix, Each frequency is a row. Each time point is a column. [5] Inverse DFT: 🟧 Frequency → 🟩 Time ↳ Multiply the frequency matrix F and the cosine matrix W. ↳ The meaning of this multiplication is to linearly combine the four cosine waves (rows in W) into time-domain signals (rows in T) using the weights specified in F. ↳ The result is matrix T, which are signals A, B, C converted to the time domain. Each signal is a row. Each time point is a column. [6] Transpose ↳ Transpose T, converting each signal’s time domain representation from a row to a column. [7] DFT: 🟩 Time → 🟧 Frequency ↳ Multiply the cosine matrix W with the transpose of matrix T. ↳ The purpose of this multiplication is to take a dot-product between each time-domain signal (columns in the transpose of T) and each cosine wave (rows in W), which has the effect of projecting the signal onto a cosine wave to determine how much they are correlated. Zero means not correlated at all. ↳ The result is an intermediate version of the “recovered” frequency matrix where each column corresponds to a signal and each row corresponds to a frequency. ↳ Compared to the original frequency matrix F, this intermediate matrix has non-zero weights in the correct places, but scaled up by a factor of 5 (n/2, n=10). For example, signal A, originally [1,2,0,0], is recovered at [5,10,0,0]. [8] Scale ↳ Multiply each value by 2/n = 1/5 to scale down the intermediate matrix to match the magnitude of the original frequency matrix F. [9] Transpose ↳ Transpose the recovered frequency matrix back to the same orientation of the original frequency matrix F. ↳ Like magic 🪄, the result is identical to the original F, which means DFT successfully recovered the frequency components of signals A, B, C. [10] Apply DFT to X: 🟩 Time → 🟧 Frequency ↳ Now that we have some confidence in DFT’s ability to recover frequency components, we apply DFT to X’s time-domain representation by multiplying W with X. ↳ The result is the an intermediate matrix. [11] Scale ↳ Similarly, we scale down by a factor of 5 to obtain the recovered frequency components of X (a column). [12] Transpose ↳ Similarly, we transpose the recovered column to row to match the orientation of the frequency matrix. ↳ Using the coefficients [0,0,3,2], we can write the equation of X as 3cos(3w) + 2cos(4w). Notes: I hope this by hand exercise helps you understand the essence of DFT. But there is more technical details, such as: • Sine: The complete DFT math also includes sine waves that follow a similar calculation process. • Phase: Here, we assume all the cosine waves are aligned at the origin, namely, phase is 0. If a phase p is added, for example, cos(w+p), we will need to calculate the sine component and use their ratio to figure out what p is. • Magnitude: If phase is not zero, the magnitude will need to be calculated by combining both cosine and sine terms.show more

This seems like it would be on an episode... of “I Shouldn’t Be Alive,” you and your friend go to the mall to get a nice outfit for an outing later. The department you need to go to is on the second floor, so you and your friend decide it would be quicker to go on the escalator. All of a sudden as you are approaching the middle of the escalator, you hear the escalator come to a screeching halt. You and your friend are now stranded in the middle of the escalator. Every second counts, it’s been two hours now since you’ve had food or water since you e been stuck on the escalator and time is ticking, do you risk an escape plan?show more

If order to hit a big league fastball your... brain needs to decide to pull the trigger roughly 25 feet from the ball reaching the plate…. In order to do that, your eyes must be oriented at a spot 25 feet to your left for a righty or 25 feet to your right if you are a lefty…. This begs the question what is the point of hitting off of a tee?…The body will never work the same vs a live ball…. Look how different Mike Trout looks when hitting off of a tee vs hitting a live ball…Watch his left arm and left shoulder do completely different things. The right forearm supinates vs an overhand pitch but it pronates vs the tee…. It’s a function of where the biceps inserts onto the radius. There isn’t a hitter on earth that will use the same swing mechanics off of a tee as they will vs an overhand pitch.show more

FINAL from Dunlap: 1B Isaac Babbs (2027) and LF... Brett Alkire (2027) each connect on two-run singles to highlight a seven run inning for the Eagles. Dunlap wins the Regional Final in five innings by a score of 10-0.show more

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Ethos Score is now part of every Legion project... page. You can now see the reputation score of the project and its founders before you get into a sale. A better way to evaluate deals — built with Ethosshow more

This guy built a visual scanner that reads 468... points on his face and 42 points on his hands from a regular webcam and turns them into a cloud of thousands of particles right between his palms. Inside, MediaPipe and TouchDesigner are linked: the first captures hands and face from the webcam with high accuracy, the second turns those coordinates into a live plane and feeds it into a POP system that instantly generates a swarm of particles in the shape of a head. No studio, no render farmer, no VR headset. Just a laptop, a webcam, and 1 TouchDesigner session. And traditional VJ studios keep teams of 5 people on a setup with lighting, custom hardware, and commercial plugins, while his expenses are only a TouchDesigner subscription and a regular USB camera. One laptop runs MediaPipe and TouchDesigner simultaneously, holds the camera stream at 60 FPS without drops, and in parallel processes 468 face points + 21 points on each hand. The camera captures frame after frame, MediaPipe in real time sends TouchDesigner the finger coordinates and face geometry, and the POP operator inside the engine translates those numbers into thousands of particle points with colors from bright pink to gold. This setup immediately defines the role of the tool and the limits of its autonomy. It knows where the fingertips are at every moment of the frame. It knows how to read the face geometry at any angle to the camera. It knows how to draw a swarm of particles between them with the right color and contour. → MediaPipe pulls 468 points from the face and 21 points from each hand, 60 times per second → TouchDesigner receives those coordinates, builds a virtual rectangle between the fingertips, and feeds it into the POP system → POP generates thousands of particle points in the shape of a head, coloring them in a gradient from bright pink to gold → The HUD layer adds green corners and a blue neon frame, styling the image like an AR interface → All layers assemble into 1 real-time frame that projects back onto the video in the camera window → The final image is recorded to a file or broadcast to a projector for a live installation And only when the guy spreads his hands wider does the plane between the palms stretch; brings them together, it narrows. Otherwise the system runs on its own. And when he moves from his home room to a concert hall, the same laptop with the same webcam launches the same TouchDesigner session in just 5 minutes, without reconfiguration, without a new team, and without a single line of new code. In his work setup there is no studio of his own and no team for assembly. On the desk sits a laptop with a webcam, on top run MediaPipe and TouchDesigner with POP operators, and the same setup through a USB camera moves to any concert without a new configuration. Out of everything I have seen this year, this is the cleanest Creative Coding setup on 1 laptop: 0 render farms, 0 studio lighting, and between them 3 libraries, thousands of particle points, and 1 webcam.show more

Full Fine-tuning vs. Freezing Layers. Interact 👉 and ==... Full Fine-tuning == A real network has many — three layers in this example, billions of parameters in a production model. What does fine-tuning look like when you update all of them? That’s full fine-tuning: continue training every weight in the pretrained network on your new task. Every layer’s W gets its own ΔW. Nothing is frozen — every parameter is in play. Think of an MLP as a chain of prerequisites leading to an advanced course. Layer 1 might be Linear Algebra, layer 2 Probability, layer 3 Advanced Machine Learning — each one building on what came before. Fine-tuning is what happens during graduate study: the foundations are already there from undergrad, so you’re not re-learning. Full fine-tuning is reviewing every prerequisite to see what new topics have appeared and what discoveries the field has made since the last time you sat through them. Effective — but exhausting. This diagram shows the same three-layer MLP twice, side by side. On the left, the pretrained network runs on input X: three weight matrices W₁, W₂, W₃, each followed by a ReLU activation. Full fine-tuning gives the model the most freedom to specialize. Every parameter can move — and every parameter that can move must be stored. But not every prerequisite needs revisiting. The further you go back in the chain, the less the material has changed since pretraining — the linear-algebra basics under your computer-vision course are largely the same as they ever were. The next page does exactly that: freeze the prerequisites that haven’t moved, and only refresh the advanced one closest to your specialization. == Freezing Layers == Full fine-tuning reviewed every prerequisite — Linear Algebra, Probability, Advanced ML — to refresh each subject with the latest topics. Effective, but exhausting. Then you realize something. The prerequisites haven’t actually changed that much. Linear Algebra is still Linear Algebra; the matrix decompositions you learned still hold. Probability is still Probability; the distributions and Bayes’ rule haven’t moved. Almost all the new material — the new ideas, the recent discoveries — lives in the advanced layer at the top. That’s freezing layers: keep the prerequisite layers fixed at their pretrained state, and only update the advanced one. In the diagram below, W1​ and W2​ — the foundational prerequisites — stay frozen. Only W3​ — the layer closest to your task-specific output — gets a ΔW.show more

Training glutes still doesn’t get the love it should... from men. Aesthetically, sure, your focus will be more on the V taper frame, or strong arms. But as the largest and strongest muscle in the body, the glutes have the potential to really boost your transformation to a top 1% physique. It’s the same concept as investing money into the market or a cash flowing real estate deal. You put in the capital… And then the asset pays you for your ownership. When you have strong glutes, you now have the biggest muscle in the human body paying you metabolic “dividends” around the clock. Burning more calories just by existing. As a result, you get leaner while having MORE wiggle room diet wise. Which makes your hormones improve, and all of the sudden you have this flywheel of positive change. It’s a compounding effect. Not to mention, it helps keeps your back and hips healthy and flexible. You retain more of your ability to move well as you get older. Strong glutes = absolutely one of your biggest ASSets (da dum, tssssk 😂) And the whole point of owning assets is that they work on your behalf, instead of you staying on the treadmill of the same effort over and over and over again just to get average results. If you want to get a top 1% physique without the suffering and sacrifice promoted all throughout the fitness industry, apply to partner with me 1-1 at the link in my bio.show more

This man received his check for dinner and notice... two things.. the restaurant had charged him five dollars each for two fortune cookies in addition to the total bill for the meal. The second thing was, they left him a note saying that they “knew your broke ass wouldn’t tip” with a smiley face on it. What are your thoughts on this?show more