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Softmax vs Sigmoid ✍️ Interact 👉 https://byhand.ai/Khlg9b

= 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 𝘤𝘩𝘦𝘪𝘨𝘩𝘦𝘴𝘵 𝘤𝘰𝘳𝘦 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 🚀.

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🤖 What is a perceptron, and how does it work?

Don’t worry, we have an easy-to-understand explanation for you!

Let’s dive in.👇🏽

1️⃣ History

The idea of a perceptron was first presented by Frank Rosenblatt in 1957. It was inspired on the neuron model by McCulloch and Pitt. The concept of the perceptron still forms the basis for modern artificial neural networks today.

2️⃣ Concept of a Single-Layer Perceptron

A perceptron consists of an artificial neuron with adjustable weights and a threshold. The neuron in the perceptron is called a Linear Threshold Unit (LTU) because it uses the step function as its output function and performs a linear separation of the input data.

3️⃣ Detailed view

The figure illustrates a perceptron with an input layer, an artificial neuron, and an output layer. The input layer contains the input value and x_0 as bias. In a neural network, a bias is required to shift the activation function either to the positive or negative side.

The perceptron has weights on its edges. It calculates the weighted sum of input values and weights. It is also known as aggregation. The result a finally serves as input into the activation function. The step function is used as the activation function. Here, all values of a > 0 map to 1, and values a < 0 map to -1.

4️⃣ Limitations

The single-layer Perceptron can only solve linearly separable problems and struggles with complex patterns. The XOR problem, a simple nonlinear classification problem, showed the limitations of the perceptron.

5️⃣ Advancements

The introduction of the multilayer perceptron (MLP) and the backpropagation algorithm led to the ability to solve nonlinear problems.

https://t.iss.one/DataScienceM 🧠