# Drill 11 One perceptron learning update

Subject: Deep Learning

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/#tee/read/17/tee-c17-s11

Canonical: https://deep-learning-study-room.vercel.app/read/dl/tee/section/tee-c17-s11/

## Question

**Question.** Binary perceptron, w = [0,0], b = 0, x = [1,1], target 1, η = 0.5. Use output 1 if z>0 else 0. Perform one update.

## Answer — step by step

### Given

w = [0,0]; b = 0; x = [1,1]; target t = 1.

Learning rate η = 0.5.

Output 1 only when z > 0; otherwise output 0.

### To find

Perform one update and report new weights and bias.

### Formula — which one and why

**Perceptron learning rule.** Evaluate the stated threshold, compare the predicted class with its target, then correct weights and bias. The next sample uses the newly updated parameters.

t = target; o = thresholded output; η = learning rate; xᵢ = input i. Binary and bipolar output conventions must follow the question.



$$
z=\sum_iw_ix_i+b
$$





$$
w_i^{\mathrm{new}}=w_i+\eta(t-o)x_i
$$





$$
b^{\mathrm{new}}=b+\eta(t-o)
$$



**Yaad rakhne ka cue:** Prediction nikalo; target−prediction se correction nikalo.

### Solution — step by step

### Meaning and formula

A perceptron first computes a weighted sum z and then applies the exact threshold rule in the question. This question uses **strictly greater than zero**, so z = 0 produces output 0.



$$
z=w_1x_1+w_2x_2+b,\qquad o=\begin{cases}1&z>0\\0&z\le0\end{cases}
$$



The perceptron learning rule uses target minus output, written e below. This is a discrete perceptron rule, not the sigmoid backpropagation derivative.



$$
e=t-o,\qquad w_{j,\mathrm{new}}=w_j+\eta e x_j,\qquad b_{\mathrm{new}}=b+\eta e
$$



### Step 1: obtain the old output



$$
z=0\times1+0\times1+0=0,\qquad o=0
$$



### Step 2: compare it with the target



$$
e=1-0=1
$$



### Step 3: update each weight separately



$$
w_{1,\mathrm{new}}=0+0.5\times1\times1=0.5
$$





$$
w_{2,\mathrm{new}}=0+0.5\times1\times1=0.5
$$





$$
b_{\mathrm{new}}=0+0.5\times1=0.5
$$



### Step 4: interpret the updated prediction



$$
z_{\mathrm{new}}=0.5\times1+0.5\times1+0.5=1.5
$$



Since 1.5 > 0, the new output is 1. **Final parameters: w = [0.5, 0.5], b = 0.5.**